Modeling normal behavior in dynamic, nonlinear time series data is challenging for effective anomaly detection. Traditional methods, such as nearest neighbor and clustering approaches, often depend on rigid assumptions, such as a predefined number of reliable neighbors or clusters, which frequently break down in complex temporal scenarios. To address these limitations, we introduce the Granular-ball One-Class Network (GBOC), a novel approach based on a data-adaptive representation called Granular-ball Vector Data Description (GVDD). GVDD partitions the latent space into compact, high-density regions represented by granular-balls, which are generated through a density-guided hierarchical splitting process and refined by removing noisy structures. Each granular-ball serves as a prototype for local normal behavior, naturally positioning itself between individual instances and clusters while preserving the local topological structure of the sample set. During training, GBOC improves the compactness of representations by aligning samples with their nearest granular-ball centers. During inference, anomaly scores are computed based on the distance to the nearest granular-ball. By focusing on dense, high-quality regions and significantly reducing the number of prototypes, GBOC delivers both robustness and efficiency in anomaly detection. Extensive experiments validate the effectiveness and superiority of the proposed method, highlighting its ability to handle the challenges of time series anomaly detection.

Concept-cognitive learning (CCL) simulates the human brain by incrementally adjusting the concept space to adapt to the dynamic environment. Traditional CCL methods use fuzzy granular concepts to handle continuous data, but the uncertainty caused by information granularity to form fuzzy cognitive operators may lead to low cognitive accuracy. Consequently, we propose a granular-ball fuzzy concept incremental learning (GBFCIL) method to obtain the optimal initial fuzzy concept space by granular-ball computing (GBC) while utilizing purity filtering mechanism to enhance GBC's responsiveness on dynamic data. Specifically, we introduce the definition of granular-ball fuzzy concept via the granular-ball knowledge representation method. And then, we build a static-dynamic balanced framework for constructing granular-ball fuzzy concept space: (1) an optimal initial granular-ball fuzzy concept space is established by GBC to achieve static perception of data; (2) the updating process of dynamic data involves internal generation among new samples and external fusion between the previous granular-ball fuzzy concept space and the newly learned concepts after filtering. Subsequently, a novel GBFCIL-based classification model is developed, along with the analysis of the optimal radius. Finally, experiments verify the advancement of GBFCIL in classification performance and robustness.

Neural network models in natural language processing have demonstrated remarkable proficiency, but they are still vulnerable to adversarial attacks, where minute and indistinguishable alterations can profoundly disturb their performance. Existing methods struggle to define synonyms accurately and rely on greedy traversal or gradient computation, making them difficult to deploy. Inspired by these, this paper proposes a novel text adversarial attack method, which constructs rich candidate adversarial examples by non-trivially combining theGranular-Ball computing andDifferentialEvolution, termed GBDE. Through iterative optimization guided by a meticulously crafted loss function, GBDE iteratively optimizes to generate effective and high-quality adversarial examples. Specifically, GBDE realizes a multi-granularity granular-ball clustering method following the data features, to establish robust synonym sets. It then performs synonym substitutions on target samples to create candidate adversarial samples and further diversifies these samples through a customized differential evolution process. Additionally, the loss function incorporates a reward and punishment mechanism to steer the optimization of attacks. Empirical results showcase GBDE's superiority when contrasted with cutting-edge models. Notably, GBDE produces high-quality adversarial texts with a larger success rate. Besides, ablation studies confirm the contributions of granular-ball clustering and differential evolution in text attacks, and the rationality of the loss function design.

In many real-world scenarios, data unreliability and information-processing uncertainty seriously affect the credibility and reliability of artificial intelligence models. Probing a valuable cognitive learning paradigm is crucial for supporting and implementing the proposed artificial intelligence hypothesis. Concept-cognitive learning (CCL), as an emerging cognitive learning technology, investigates the knowledge-learning process using limited data through the lens of concepts. However, the existing CCL research has one prevalent disadvantage: instability and complex cognition. Thus, this work focuses on constructing an effective and interpretable cognitive learning paradigm for acquiring knowledge. Inspired by a multi-granularity knowledge representation, this paper proposes an adaptive and robust fuzzy knowledge representation paradigm, namely granular-ball concept-cognitive learning(GB-CCL). Unlike existing CCL systems, GB-CCL is a non-parameter cognitive learning system that achieves more accurate, faster adaptive capabilities for concept learning. The concept acquired through cognitive learning is structured conceptual knowledge, which is naturally interpretable and robust. Finally, extensive experiments verify that GB-CCL is an effective cognitive learning method with significantly better performance than state-of-the-art models in classification and robust learning.

Most existing outlier detection methods rely on a single and fine-grained data representation, making them vulnerable to noise and inefficient in capturing local anomalies. Granular-ball computing (GBC), as an emerging multi-granularity representation and computation framework, provides an effective means to address these issues. Meanwhile, shadow set theory offers a flexible mechanism using three-way decision to handle uncertainty and boundary fuzziness in data. The integration of GBC with shadow set theory combines the strengths of both frameworks, offering promising potential for outlier detection tasks. In this study, we propose a novel outlier detection based on shadowed granular-balls. Firstly, we propose an unsupervised granular-ball generation method with the principle of justifiable granularity. Then, we further present an outlier detection method, named three-way outlier detection based on shadowed granular-ball (3W-SGBD). 3W-SGBD introduces an unsupervised granular-ball generation strategy guided by local density clustering, and adaptively splits granular-balls through a dual-entropy-driven mechanism to better capture local anomalies. In addition, by partitioning each granular-ball into positive, negative, and boundary regions via shadow mapping, 3W-SGBD refines boundary areas to enhance detection accuracy. Finally, extensive comparative experiments are conducted with several state-of-the-art baseline methods on 16 public benchmark datasets. The results show that the effectiveness, efficiency, and robustness of the method proposed in this paper. The code is publicly available athttps://github.com/2257352568/3W-SGBD.

Outlier detection is an effective technique for identifying abnormal samples in complex data. Random walks effectively detect outliers by analyzing graph transition patterns. However, existing methods only consider local transitions and fail to capture complex structural patterns in complex data. Granular-ball computing based outlier detection methods have better robustness and efficiency. Nevertheless, these methods use a coarse-granularity representation of granular-balls and ignore the large number of sample information within the granular-balls. To address the above issues, this paper develops a bi-level granular-ball based second-order biased random walk outlier detection method. First, a bi-level granular-ball knowledge representation method is proposed to address the information distortion inherent in granular-ball computing-based methods. Then, a granular-ball anomaly membership evaluation metric is introduced, which leverages second-order biased random walk, to endow granular-balls with coarse-granularity anomaly degrees. Subsequently, a bi-level granular-ball anomaly classifier is designed to map coarse-granularity granular-ball anomaly degrees to fine-granularity sample-level anomaly degrees. Finally, a distilled outlier factor is defined, which selects optimal attribute sequences through granular-ball construction on attributes, for outlier detection. At the same time, a corresponding outlier detection algorithm is proposed. Experiments on datasets are conducted to compare the proposed algorithm with six other algorithms. The experimental results show that the algorithm has better performance and a certain degree of robustness.

Although spectral clustering is capable of identifying clusters of arbitrary shapes, its high time and space complexity poses limitations in large-scale data clustering applications. To tackle this problem, researchers have proposed using anchor points to construct the similarity matrix, thereby reducing time and space complexity. However, current methods for generating anchor points do not fit the data well and are limited in approach. To improve upon existing anchor points generation methods, we proposes a pseudo-label-based anchor points generation approach and develops a fast spectral clustering algorithm for large-scale data, named FSC-PLGB. The algorithm first randomly selects r points as an initial granular-ball, applies K-Means on these points to obtain pseudo-labels, calculates the pseudo-purity of the granular-ball based on these pseudo labels, and then performs granular-ball division based on these pseudo-purity to generate anchor points. A similarity matrix is constructed between all sample points and anchor points, and finally, spectral clustering is applied to obtain the clustering results. The experimental results demonstrate that our proposed algorithm exhibits exceptional efficiency and significant superiority on large-scale datasets. The source code is available at https://github.com/DongdongCheng/FSC-PLGB.

Unsupervised feature selection aims to enhance the quality of unlabeled data, thereby improving the performance of subsequent unsupervised learning models. However, most of the existing unsupervised feature selection methods rely on single-granularity modeling, which reduces the expressive capability of data to some extent. In addition, the existing studies are generally based on a forward greedy feature selection strategy, which tends to fall into a local optimum. To address these issues, this paper proposes a novel unsupervised feature selection method for handling hybrid data, called unsupervised feature selection method using fuzzy graph momentum random walk in bi-level granular-ball knowledge space. Specifically, a Bi-level Granular-ball Knowledge Space (BGKS) is first constructed by combining fine granularity and coarse granularity representations through a hybrid Gaussian kernel function. Then, a multi-granularity fuzzy graph is built on the BGKS using upper and lower fuzzy approximation operators. Based on this graph, a Momentum Random Walk (MRW) mechanism is introduced to design the Fuzzy Graph Momentum Random Walk (FGMRW) model. Finally, an iterative unsupervised feature selection algorithm is developed. Extensive experiments on 20 public datasets demonstrate that, compared with existing algorithms, the proposed method is able to maintain or even improve clustering performance while selecting fewer features, thus achieving superior overall performance. The source code of this work is publicly available athttps://github.com/HongtaoGao-code/FGMRW-UFS.

Sketch-less facial image retrieval (SLFIR) framework efficiently retrieves target images with minimal strokes through human-computer interaction, thus overcoming the traditional model's reliance on high-quality sketch images. However, the variability in sketching styles and the randomness of stroke placement during the drawing process pose challenges in matching target images. To address this issue, we propose a feature-driven foundation model for sketch-less facial image retrieval (FDSRM), which is designed to be independent of the sketch style and comprises two core components: the feature observer and the adaptive fusion adapter (AFA). First, to address the diversity of sketch styles, we design the feature observer module (FOM). It employs multiple experts focused on extracting key features and semantic information common to various sketch styles and the target image. This helps the model to precisely identify crucial features for effective matching in stylistically diverse sketches. Second, to address the randomness of stroke placement, we introduce prior knowledge of sketching and, in conjunction with the AFA component, dynamically learn and adjust the fusion strategy of sketches and text based on the current state of sketch strokes. This enables more accurate and targeted feature fusion throughout the sketching process. Furthermore, we train a facial image-text alignment pretraining (FAIP) model on a large-scale facial dataset and use it as the backbone of FDSRM, which significantly improved the model's robustness to unknown facial features. Extensive experiments demonstrate that our method exhibits significant advantages in terms of accuracy in early retrieval and system generalization capabilities. Even without additional auxiliary information, it outperforms state-of-the-art methods in both qualitative and quantitative measures in multistyle application scenarios.

State space model (SSM) is a mathematical model used to describe and analyze the behavior of dynamic systems. This model has witnessed numerous applications in several fields, including control theory, signal processing, economics, and machine learning. In the field of deep learning, SSMs are used to process sequence data, such as time series analysis, natural language processing (NLP), and video understanding. By mapping sequence data to state space, long-term dependencies in the data can be better captured. In particular, modern SSMs have shown strong representational capabilities in NLP, especially in long sequence modeling, while maintaining linear time complexity. In particular, based on the latest SSMs, Mamba merges time-varying parameters into SSMs toward efficient training and inference. Given its impressive efficiency and strong long-range dependency modeling capability, Mamba is expected to become a new AI architecture that may be capable of surpassing Transformer. Recently, a number of works attempt to study the potential of Mamba in various fields, such as general vision, multimodal learning, medical image analysis, and remote sensing image analysis, by extending Mamba from natural language domain to visual domain. To fully understand Mamba in the visual domain, we conduct a comprehensive survey and present a taxonomy study. This survey focuses on Mamba's application to a variety of visual tasks and data types, and discusses its predecessors, recent advances, and far-reaching impact on a wide range of domains.

Partial multilabel feature selection (PMLFS) is a prevalent subject that aims to enhance the performance of multilabel learning (MLL) in the context of noisy labels. In PMLFS, a crucial aspect is handling the false positive labels hidden in the candidate label set, as the imprecise annotations could mislead the feature selection process. However, many existing approaches for partial label disambiguation rely on topology information and tend to be error-prone. Besides, feature selection frameworks are often built upon a linear regression model, leading to a reliance on the classifier and a deficiency in exploring local structures. Focusing on the issues above, this article proposes a novel two-stage PMLFS method, resorting to the ideology of granular computing. In the first stage, a label disambiguation method is developed using label-specific information. Specifically, a specific granular ball computing model is designed to characterize the distribution of datapoints labeled differently, and therefore, using the affinity relationships among samples and balls, the label-specific information concealed in the data distribution can be captured for label disambiguation. In the second stage, a filter-based feature selection method that explores the local structure of samples is presented. This method relies on a devised fuzzy decision neighborhood rough set (FDNRS) to capture more detailed membership information by maximizing the neighborhood consistency of samples' related labels. Simultaneously, the feature selection method minimizes the uncertainty derived from unrelated labels. Extensive experiments on 12 datasets in terms of four evaluation metrics demonstrated the effectiveness of the proposed approach.

Open intent classification is critical for the development of dialogue systems, aiming to accurately classify known intents into their corresponding classes while identifying unknown intents. Prior boundary-based methods assumed known intents fit within compact spherical regions, focusing on coarse-grained representation and precise spherical decision boundaries. However, these assumptions are often violated in practical scenarios, making it difficult to distinguish known intent classes from unknowns using a single spherical boundary. To tackle these issues, we propose a Multi-granularity Open intent classification method via adaptive Granular-Ball decision boundary (MOGB). Our MOGB method consists of two modules: representation learning and decision boundary acquiring. To effectively represent the intent distribution, we design a hierarchical representation learning method. This involves iteratively alternating between adaptive granular-ball clustering and nearest sub-centroid classification to capture fine-grained semantic structures within known intent classes. Furthermore, multi-granularity decision boundaries are constructed for open intent classification by employing granular-balls with varying centroids and radii. Extensive experiments conducted on three public datasets demonstrate the effectiveness of our proposed method.

Graph Neural Networks (GNNs) have demonstrated significant achievements in processing graph data, yet scalability remains a substantial challenge. To address this, numerous graph coarsening methods have been developed. However, most existing coarsening methods are training-dependent, leading to lower efficiency, and they all require a predefined coarsening rate, lacking an adaptive approach. In this paper, we employ granular-ball computing to effectively compress graph data. We construct a coarsened graph network by iteratively splitting the graph into granular-balls based on a purity threshold and using these granular-balls as super vertices. This granulation process significantly reduces the size of the original graph, thereby greatly enhancing the training efficiency and scalability of GNNs. Additionally, our algorithm can adaptively perform splitting without requiring a predefined coarsening rate. Experimental results demonstrate that our method achieves accuracy comparable to training on the original graph. Noise injection experiments further indicate that our method exhibits robust performance. Moreover, our approach can reduce the graph size by up to 20 times without compromising test accuracy, substantially enhancing the scalability of GNNs.

Existing optimization algorithms are designed based on the finest granularity, i.e., a point. This design limits global search capability and reduces efficiency in global exploration. To solve this problem, we propose a multi-granularity optimization algorithm (MGO), a novel evolutionary algorithm that uses granular-balls instead of points for optimization. MGO distributes a large number of granular-balls across the solution space to explore both critical regions, where optimal solutions are likely located, and non-critical regions for a broader search. Small, fine-granularity granular-balls focus on critical regions, while larger, coarse-granularity ones cover less critical areas. Additionally, there is competition and cooperation among different granular-balls to better utilize computational resources. This multi-granularity representation enhances global search efficiency and accelerates convergence. MGO outperforms many popular state-of-the-art algorithms in the CEC2013 single-objective optimization benchmarks and shows clear advantages in the social network influence maximization (IM) problem. With strong approximation capability, fast convergence speed, and simple design, MGO presents a competitive alternative to most existing optimization algorithms.

The Influence Maximization (IM) problem in social networks has been extensively studied, with greedy algorithms providing accurate and reliable solutions. However, their high computational cost renders them impractical for large-scale networks. Conversely, structure-based heuristic methods reduce computational complexity but often yield suboptimal solutions. To address these challenges, this paper proposes a novel cooperative and competitive multi-granularity fireworks algorithm (CCFWA). Unlike traditional point-based optimization algorithms, CCFWA employs spherical fireworks of varying granularity to enhance the search process. By distributing fireworks of different scales throughout the solution space, the algorithm effectively distinguishes between critical and less significant regions. Fine-granularity fireworks conduct detailed searches in key areas, while coarse-granularity fireworks enable rapid exploration of less important regions. This multi-granularity representation balances global exploration and local exploitation, improving both accuracy and efficiency in solving the IM problem. Experiments on four real-world social networks demonstrate that CCFWA consistently outperforms six state-of-the-art algorithms in terms of computational efficiency and solution quality.

With the swift advancement of information technology, vast amounts of high-dimensional data have accumulated across various domains. Clustering such data presents a significant challenge, as existing methods often suffer from slow execution speeds and reduced clustering accuracy. To tackle these issues, we introduce the granular-ball approach, which aims to decrease the number of sample points and enhance processing speed, while also improving clustering accuracy through feature selection. Granular-ball computing, a coarse-grained data representation technique, has demonstrated its advantages in enhancing classification and clustering models in recent studies. However, current granular-ball division techniques are inadequate for high-dimensional data. To confront the complexities arising from clustering high-dimensional data and improve upon existing granular-ball methods, this paper proposes a novel granular-ball division approach that leverages pseudo-labels and feature selection. This new method enables the identification of anchor points through an improved granular-ball division process, leading to the development of a fast spectral clustering algorithm for high-dimensional data, termed PLGB-FSC. Specifically, we initially employ weighted K-Means for feature to generate pseudo-labels. Subsequently, we conduct a primary stage of feature selection by utilizing the mutual information between pseudo-labels and features, thereby eliminating the interference caused by irrelevant features. We further refine the feature selection by combining standard deviation and pearson correlation coefficients to choose mutually independent features. Using these pseudo-labels, we then perform granular-ball division to obtain anchor points. Lastly, we construct a similarity matrix between all sample points and the anchor points, and leveraging spectral clustering for definitive clustering outcomes. Experimental evaluations reveal that PLGB-FSC surpasses state-of-the-art algorithms such as W-KMeans, WGB, GB-USC, RC-PCA-SC, GLUFC, FGOC, SFESA, SPCAFS, and LLSRFS, and it achieves higher accuracy and faster execution speed. The source code is available at https://github.com/DongdongCheng/PLGB-FSC.

Data sampling enhances classifier efficiency and robustness through data compression and quality improvement. Recently, the sampling method based on granular-ball (GB) has shown promising performance in generality and noisy clas-sification tasks. However, some limitations remain, including the absence of borderline sampling strategies and issues with class boundary blurring or shrinking due to overlap between GBs. In this paper, an approximate borderline sampling method using GBs is proposed for classification tasks. First, a restricted diffusion-based GB generation (RD-GBG) method is proposed, which prevents GB overlaps by constrained expansion, preserving precise geometric representation of GBs via redefined ones. Second, based on the concept of heterogeneous nearest neighbor, a GB-based approximate borderline sampling (GBABS) method is proposed, which is the first general sampling method capable of both borderline sampling and improving the quality of class noise datasets. Additionally, since RD-GBG incorporates noise detection and GBABS focuses on borderline samples, GBABS performs outstandingly on class noise datasets without the need for an opti-mal purity threshold. Experimental results demonstrate that the proposed methods outperform the GB-based sampling method and several representative sampling methods. Our source code is publicly available at https://github.com/CheryITse/GBABS.

360-degree videos (abbreviated as 360 videos) have gained widespread popularity due to their immersive experience. The massive amount of video data resulting from ultra-high resolution of 360 videos makes the coding process extremely complex and seriously limits their widespread applications. In this paper, we propose a new fast-Coding Unit (CU) partition algorithm for 360 videos based on Versatile Video Coding (VVC). The major novelty is that we establish databases and develop models based on stretching and split mode (SM) distribution for 360 videos on VVC. Specifically, first, we establish stretching-based CU partition databases for 360 videos. Second, we propose a new stretching-based multi-scale convolution kernel network structure and a corresponding synthetical loss function, which further considers both Rate-Distortion cost and imbalance issue. We then develop a unique multi-threshold selection scheme to select candidate SMs. Experimental results demonstrate that the proposed algorithm improves encoding speed by 69.63%, with only a 2.28% increase in Bjøntegaard Delta Bit Rate (BDBR), outperforming the state-of-the-art methods.

High time complexity is one of the biggest challenges faced by k-Nearest Neighbors (kNN). Although current classical and quantum kNN algorithms have made some improvements, they still have a speed bottleneck when facing large amounts of data. To address this issue, we propose an innovative algorithm called Granular-Ball based Quantum kNN(GB-QkNN). This approach achieves higher efficiency by first employing granular-balls, which reduces the data size needed to processed. The search process is then accelerated by adopting a Hierarchical Navigable Small World (HNSW) method. Moreover, we optimize the time-consuming steps, such as distance calculation, of the HNSW via quantization, further reducing the time complexity of the construct and search process. By combining the use of granular-balls and quantization of the HNSW method, our approach manages to take advantage of these treatments and significantly reduces the time complexity of the kNN-like algorithms, as revealed by a comprehensive complexity analysis.

Most existing multi-kernel clustering algorithms, such as multi-kernel K-means, often struggle with computational efficiency and robustness when faced with complex data distributions. These challenges stem from their dependence on point-to-point relationships for optimization, which can lead to difficulty in accurately capturing data sets' inherent structure and diversity. Additionally, the intricate interplay between multiple kernels in such algorithms can further exacerbate these issues, effectively impacting their ability to cluster data points in high-dimensional spaces. In this paper, we leverage granular-ball computing to improve the multi-kernel clustering framework. The core of granular-ball computing is to adaptively fit data distribution by balls from coarse to acceptable levels. Each ball can enclose data points based on a density consistency measurement. Such ball-based data description thus improves the computational efficiency and the robustness to unknown noises. Specifically, based on granular-ball representations, we introduce the granular-ball kernel (GBK) and its corresponding granular-ball multi-kernel K-means framework (GB-MKKM) for efficient clustering. Using granular-ball relationships in multiple kernel spaces, the proposed GB-MKKM framework shows its superiority in efficiency and clustering performance in the empirical evaluation of various clustering tasks.

The objective of graph coarsening is to generate smaller, more manageable graphs while preserving key information of the original graph. Previous work were mainly based on the perspective of spectrum-preserving, using some predefined coarsening rules to make the eigenvalues of the Laplacian matrix of the original graph and the coarsened graph match as much as possible. However, they largely overlooked the fact that the original graph is composed of subregions at different levels of granularity, where highly connected and similar nodes should be more inclined to be aggregated together as nodes in the coarsened graph. By combining the multi-granularity characteristics of the graph structure, we can generate coarsened graph at the optimal granularity. To this end, inspired by the application of granular-ball computing in multi-granularity, we propose a new multi-granularity, efficient, and adaptive coarsening method via granular-ball (GBGC), which significantly improves the coarsening results and efficiency. Specifically, GBGC introduces an adaptive granular-ball graph refinement mechanism, which adaptively splits the original graph from coarse to fine into granular-balls of different sizes and optimal granularity, and constructs the coarsened graph using these granular-balls as supernodes. In addition, compared with other state-of-the-art graph coarsening methods, the processing speed of this method can be increased by tens to hundreds of times and has lower time complexity. The accuracy of GBGC is almost always higher than that of the original graph due to the good robustness and generalization of the granular-ball computing, so it has the potential to become a standard graph data preprocessing method.

In the current scenario, a vast amount of unlabeled high-dimensional data exhibits intrinsic relationships, making it suitable for information extraction through graph-based clustering methods. However, these datasets often lack edge structure information and contain numerous irrelevant features. To address these challenges, we propose a comprehensive solution that involves: (1) applying a feature weighting approach to manage features, (2) constructing edges based on weighted granular-balls, and (3) integrating graph convolutional networks (GCNs) with edge generation to develop an autoencoder network. Our method significantly enhances the extraction of relevant information from high-dimensional, unlabeled data, improving the overall performance and reliability of the clustering process. Extensive experimental results demonstrate that our model, AW-GBGAE, excels in clustering tasks and exhibits strong competitiveness compared to baseline models. The code is publicly available at https://github.com/xjnine/AWGBGAE.

Sketch-Less Facial Image Retrieval (SLFIR) framework facilitates the retrieval of target images with minimal strokes through a human-computer interactive approach, thereby circumventing the need for high-quality sketches required by traditional frameworks. The primary approach utilizes a contrastive learning framework that minimizes the distance between sketch images and their target images in the embedding space, while maximizing the distance from non-target images, thus efficiently learning representations of sketches and images. However, during the initial stages of sketching, the sparse strokes that capture only partial facial features can inadvertently match non-target facial images, blurring the distinctions between positive and negative samples and impairing early retrieval performance. To overcome this challenge, we introduce a multimodal retrieval model based on diversified feedback reinforcement learning, which not only enhances the semantic integrity of sketches but also optimally ranks the sketches corresponding to positive samples using diversified feedback. Specifically, (1) we developed a Facial Language-Image Pre-training (FLIP) model and, leveraging this model, constructed an on-the-fly multimodal retrieval model that excels in recognizing sparse and exaggerated sketches by extracting and integrating multiscale features from both sketches and textual descriptions. (2) Furthermore, we implemented a novel reward mechanism that adjusts the rewards for target images, accommodating reasonable fluctuations in sketch rankings on actual images. This mechanism effectively differentiates similar images during retrieval, ensuring a more consistent and progressively improving ranking list. Extensive experiments validate that our proposed method significantly enhances early retrieval accuracy and generalization capability.

Granular-ball computing (GBC) proposed by Xia adaptively generates a different neighborhood for each object, resulting in greater generality and flexibility. Moreover, GBC greatly improves the efficiency by replacing point input with granular-ball. However, the current GB-based classifiers rigidly assign a specific class label to each data instance and lacks of the necessary strategies to address uncertain instances. These far-fetched certain classification approachs toward uncertain instances may suffer considerable risks. In this article, we introduce three-way decision (3WD) into GBC to construct a novel three-way decision with fuzzy granular-ball rough sets (3WD-FGBRS) from the perspective of uncertainty. This helps to construct reasonable multigranularity spaces for handling complex decision problems with uncertainty. First, 3WD-FGBRS is constructed in a data-driven method based on fuzziness, which avoids the subjective definition of certain risk parameters when calculating the threshold pairs. Based on 3WD-FGBRS, we further propose a sequential three-way decision with fuzzy granular-ball rough sets (S3WD-FGBRS) and analyze the fuzziness loss of multilevel decision result in S3WD-FGBRS. Then, the optimal granular-ball space selection mechanism of S3WD-FGBRS is introduced by combining fuzziness and granular-ball space distance. Finally, extensive comparative experiments are conducted with 3 state-of-the-art GB-based classifiers and 3 classical machine learning classifiers on 12 public benchmark datasets. The results show that our models almost outperform other comparison methods in terms of effectiveness, efficiency and robustness.

As an innovative methodology in data processing and knowledge representation, granular-ball computing (GBC) adaptively generates distinct neighborhoods for individual objects, thereby improving both generality and flexibility. By replacing point inputs with granular-balls (GBs), GBC achieves substantial efficiency gains. However, traditional GB-based classifiers may produce unreliable classifications under uncertain conditions. To address this limitation, we propose a novel approach that integrates three-way decision (3WD) theory with GBC, enabling robust handling of uncertain classification problems. This study first introduces a sequential three-way decision with fuzzy granular-ball rough sets (S3WD-FGBRS). We systematically analyze the changing rules of the multilevel decision cost in S3WD-FGBRS and its three regions. Building upon the principle of justifiable granularity, we develop a cost-sensitive three-way granular-ball generation method (CS3W-GBG) based on S3WD-FGBRS that incorporates a granularity optimization mechanism. To validate our approach, we conduct comprehensive experiments using three state-of-the-art GB classifiers and two benchmark classifiers on 12 publicly available datasets. Experimental results demonstrate that CS3W-GBG exhibits strong resilience in processing uncertain data through its 3WD strategy. Furthermore, our method achieves competitive performance compared to existing approaches in terms of classification accuracy and robustness.

Graph neural networks (GNNs) encounter challenges in establishing deep structures and managing a large number of parameters effectively to learn node features comprehensively. Consequently, in vision tasks, GNNs often struggle to achieve high classification accuracy compared to convolutional neural networks. Nonetheless, GNNs retain crucial advantages and potential, particularly in lightweight network scale and efficient, reliable decision-making. Thus, improving GNN performance in vision tasks remains a significant research endeavor, with numerous important works exploring the application of GNN models in such contexts, where the graph representation of images poses a key challenge. Existing methods often fall short in adaptively generating blocks of different sizes and their corresponding edges to form graph representations according to graph semantics. To address this issue, we propose a novel method to convert images into graphical forms using granular-ball computing. Our approach does not rely on manual annotation or other learning methods, yet it can dynamically generate block nodes of varying sizes and corresponding edges. Compared to other state-of-the-art methods, our approach better captures semantic information within the graph. Despite having fewer parameters, our method significantly enhances accuracy. Overall, our work holds substantial implications for improving the performance of graph neural networks in vision tasks.

Classical clustering algorithms such as k-means face limitations in handling clusters with heterogeneous shapes, densities, and sizes, while exhibiting sensitivity to initial centroid selection. To overcome these challenges, this article proposes a novel clustering framework based on regenerated granular ball (RGGB) with the principle of justifiable granularity. Unlike existing granular-ball (GB) techniques that overemphasize purity criteria at the expense of uncontrolled ball sizes, RGGB dynamically adjusts granularity levels through iterative regeneration, achieving an optimal balance between detailed data representation and computational efficiency. This adaptability enhances stability in capturing data similarities while mitigating sensitivity to initialization. To validate the method, we integrate RGGB with a novel k-nearest neighbor (KNN) classifier using regenerated GBs to evaluate classification performance and demonstrate practical applications. Experiments on diverse public and realistic datasets demonstrate that the RGGB-based KNN algorithm consistently outperforms existing techniques, including traditional KNN and other methods, making a promising advancement in clustering and classification tasks.

Granular-ball support vector machine (GBSVM) is a significant attempt to construct a classifier using the coarse-to-fine granularity of a granular ball as input, rather than a single data point. It is the first classifier whose input contains no points. However, the existing model has some errors, and its dual model has not been derived. As a result, the current algorithm cannot be implemented or applied. To address these problems, we fix the errors of the original model of the existing GBSVM and derive its dual model. Furthermore, a particle swarm optimization (PSO) algorithm is designed to solve the dual problem. The sequential minimal optimization (SMO) algorithm is also carefully designed to solve the dual problem. The latter is faster and more stable. The experimental results on the UCI benchmark datasets demonstrate that GBSVM is more robust and efficient. All codes have been released in the open source library available at: http://www.cquptshuyinxia.com/GBSVM.html or https://github.com/syxiaa/GBSVM.

Traditional clustering algorithms often focus on the most fine-grained information and achieve clustering by calculating the distance between each pair of data points or implementing other calculations based on points. This way is not inconsistent with the cognitive mechanism of "global precedence" in the human brain, resulting in those methods' bad performance in efficiency, generalization ability, and robustness. To address this problem, we propose a new clustering algorithm called granular-ball clustering via granular-ball computing. First, clustering algorithm based on granular-ball (GBCT) generates a smaller number of granular-balls to represent the original data and forms clusters according to the relationship between granular-balls, instead of the traditional point relationship. At the same time, its coarse-grained characteristics are not susceptible to noise, and the algorithm is efficient and robust; besides, as granular-balls can fit various complex data, GBCT performs much better in nonspherical datasets than other traditional clustering methods. The completely new coarse granularity representation method of GBCT and cluster formation mode can also be used to improve other traditional methods. All codes can be available at https://github.com/wylbdthxbw/GBC.

Pawlak rough set (PRS) and neighborhood rough set (NRS) are the two most common rough set theoretical models. Although the PRS can use equivalence classes to represent knowledge, it is unable to process continuous data. On the other hand, NRSs, which can process continuous data, rather lose the ability of using equivalence classes to represent knowledge. To remedy this deficit, this article presents a granular-ball rough set (GBRS) based on the granular-ball computing combining the robustness and the adaptability of the granular-ball computing. The GBRS can simultaneously represent both the PRS and the NRS, enabling it not only to be able to deal with continuous data and to use equivalence classes for knowledge representation as well. In addition, we propose an implementation algorithm of the GBRS by introducing the positive region of GBRS into the PRS framework. The experimental results on benchmark datasets demonstrate that the learning accuracy of the GBRS has been significantly improved compared with the PRS and the traditional NRS. The GBRS also outperforms nine popular or the state-of-the-art feature selection methods. We have open-sourced all the source codes of this article at https://www.cquptshuyinxia.com/GBRS.html, https://github.com/syxiaa/GBRS.

The granular-ball (GB)-based classifier introduced by Xia exhibits adaptability in creating coarse-grained information granules for input, thereby enhancing its generality and flexibility. Nevertheless, the current GB-based classifiers rigidly assign a specific class label to each data instance and lack the necessary strategies to address uncertain instances. These far-fetched certain classification approaches toward uncertain instances may suffer considerable risks. To solve this problem, we construct a robust three-way classifier with shadowed GBs (3WC-SGBs) for uncertain data. First, combined with information entropy, we propose an enhanced GB generation method with the principle of justifiable granularity. Subsequently, based on minimum uncertainty, a shadowed mapping is utilized to partition a GB into core region (COR), important region (IMP), and unessential region (UNE). Based on the constructed shadowed GBs, we establish a three-way classifier to categorize data instances into certain classes and uncertain case. Finally, extensive comparative experiments are conducted with two three-way classifiers, three state-of-the-art GB-based classifiers, and three classical machine learning classifiers on 12 public benchmark datasets. The results show that our model demonstrates robustness in managing uncertain data and effectively mitigates classification risks. Furthermore, our model almost outperforms the other comparison methods in both effectiveness and efficiency.

Unveiling, modeling, and comprehending the causal mechanisms underpinning natural phenomena stand as fundamental endeavors across myriad scientific disciplines. Meanwhile, new knowledge emerges when discovering causal relationships from data. Existing causal learning algorithms predominantly focus on the isolated effects of variables, overlook the intricate interplay of multiple variables and their collective behavioral patterns. Furthermore, the ubiquity of high-dimensional data exacts a substantial temporal cost for causal algorithms. In this paper, we develop a novel method called MgCSL (Multi-granularity Causal Structure Learning), which first leverages sparse auto-encoder to explore coarse-graining strategies and causal abstractions from micro-variables to macro-ones. MgCSL then takes multi-granularity variables as inputs to train multilayer perceptrons and to delve the causality between variables. To enhance the efficacy on high-dimensional data, MgCSL introduces a simplified acyclicity constraint to adeptly search the directed acyclic graph among variables. Experimental results show that MgCSL outperforms competitive baselines, and finds out explainable causal connections on fMRI datasets.

The previous advancements in pathology image understanding primarily involved developing models tailored to specific tasks. Recent studies has demonstrated that the large vision-language model can enhance the performance of various downstream tasks in medical image understanding. In this study, we developed a domain-specific large language-vision assistant (PA-LLaVA) for pathology image understanding. Specifically, (1) we first construct a human pathology image-text dataset by cleaning the public medical image-text data for domain-specific alignment; (2) Using the proposed image-text data, we first train a pathology language-image pretraining (PLIP) model as the specialized visual encoder for pathology image, and then we developed scale-invariant connector to avoid the information loss caused by image scaling; (3) We adopt two-stage learning to train PA-LLaVA, first stage for domain alignment, and second stage for end to end visual question & answering (VQA) task. In experiments, we evaluate our PA-LLaVA on both supervised and zero-shot VQA datasets, our model achieved the best overall performance among multimodal models of similar scale. The ablation experiments also confirmed the effectiveness of our design. We posit that our PA-LLaVA model and the datasets presented in this work can promote research in field of computational pathology. All codes are available at: https://github.com/ddw2AIGROUP2CQUPT/PA-LLaVA

Existing weighted clustering algorithms often heavily rely on specific parameters. Specifically, in addition to the number of clusters (k), several other parameters need to be manually tuned, which greatly limits their practical applicability. The fundamental issue lies in the fact that most weighted clustering methods derive feature weights through global iterations. To address this challenge, this paper introduces a novel weighted granular-ball structure, continually optimizing weights during the ball splitting process and restricting the calculation of local data point weights to the corresponding weighted granular-ball. We employ local iterations within this structure as an approximation to global weight calculations. This method eliminates the need for parameter tuning during the weight calculation process and incidentally addresses the “curse of dimensionality” in traditional granular-ball computing model. When applied to complex real-world datasets, this method accurately represents high-dimensional data, thereby improving clustering precision and extending the adaptability of the granular-ball computing model in high-dimensional spaces. Comprehensive experimental analysis demonstrates that our W-GBC algorithm performs well in terms of clustering results and competes strongly with baseline algorithms. The code has been released and is now available at https://github.com/xjnine/W-GBC.

Current data stream clustering algorithms face low efficiency in both the online and offline phases, and struggle to address the problem of cluster boundary overlap caused by concept drift. Specifically, in the online phase, the majority of existing data stream clustering algorithms require each newly arriving sample to be scanned and inserted into the appropriate micro-clusters. In offline clustering, algorithms typically require all sample points as input. Moreover, most data stream clustering algorithms struggle to effectively deal with the problem of cluster boundary overlap caused by the concept drift. To tackle these challenges, we use a granular-ball structure for the coarse-grained representation of data stream. This structure eliminates the need for computations on all data points in both the online and offline phases. Additionally, we introduce fuzziness into the granular-ball structure to resolve the issue of cluster boundary overlap caused by the concept drift. Experimental results on both synthetic and real-world datasets demonstrate that our approach achieves efficient and accurate clustering performance when compared to existing data stream clustering algorithms. Our source code is publicly available at https://github.com/xjnine/GBFuzzyStream.

The policies learned by humans in simple scenarios can be deployed in complex scenarios with the same task logic through limited feature alignment training, a process referred to as cognitive generalization or systematic generalization. Thus, a plausible conjecture is that unlocking cognitive generalization in DRL could enable effective generalization of policies from simple to complex scenarios through reward-agnostic fine-tuning. This would eliminate the need for designing reward functions in complex scenarios, thus reducing environment-building costs. In this paper, we propose a general framework to enhance the cognitive generalization ability of standard DRL methods. Our framework builds a cognitive latent space in a simple scenario, then segments the latent space to cluster samples with similar environmental influences into same subregion. During the fine-tuning in the complex scenario, the policy uses cognitive latent space to align the new sample with the same subregion sample collected from the simple scenario and approximates the rewards and Q values of the new samples for policy update. Based on this framework, we propose *Granular Ball Reinforcement Leaning* (GBRL), a practical algorithm via Variational Autoencoder (VAE) and Granular Ball Representation. GBRL achieves effective policy generalization on various difficult scenarios with the same task logic.

Deep learning has achieved outstanding performance in natural language processing, but actuality has witnessed its fragility against adversarial attacks. Synonyms-based attacks are most disastrous since their generated samples approximate raw inputs. Several countermeasures have been proposed in the literature, but the defense effectiveness is unsatisfactory because of the clumsy single-granularity synonyms clustering. To mitigate this dilemma, we propose a Granular-Ball Sample Enhancement-based defense Framework (GBSEF) for text adversarial attacks. Specifically, GBSEF first adopts an effective general synonyms clustering algorithm, which can adaptively adjust the granularity of synonym sets (i.e., granular-balls) for diverse datasets. Regarding each ball as a dot, the function consisting of most dots well fits the original data distribution, resulting in the relationships among words being well presented by the granular-balls. GBSEF then replaces each input word with the center vector of its subordinate ball, to construct robust samples preserving syntax and semantic information simultaneously. Finally, GBSEF combines a random substitution mechanism with granular-balls. This way can prompt GBSEF to take full advantage of the multi-granularity feature of granular-balls, to get more diverse valid samples. GBSEF obtains great performance through training on these samples. Abundant evaluations demonstrate the robustness and effectiveness of GBSEF against adversarial attacks, albeit with a slight performance decrease under normal scenarios without attacks. Meanwhile, GBSEF has good transferability against adversarial samples. Compared with state-of-art defense countermeasures, under multiple attacks on four neural network models (i.e., CNN, LSTM, Bi-LSTM, BERT), GBSEF always outperforms existing baselines.

Most natural language processing tasks rely on massive labeled data to train an outstanding neural network model. However, the label noise (i.e., wrong label) is inevitably introduced when annotating large-scale text datasets, which significantly degrades the performance of neural network models. To overcome this dilemma, we propose a novel Granular-B all based tRAINing framework, named GBRAIN, to realize robust coarse-grained representation learning, thus combating label noises in diverse text tasks. Specifically, considering that most samples in the dataset are precisely labeled, GBRAIN first proposes a dynamic granular-ball clustering algorithm to blend seamlessly into the traditional neural network model. A striking feature of the clustering algorithm is that it can adaptively group the embedding vectors of similar data into the same set (hereafter referred to as a granular-ball). The embedding vectors and labels of all samples from the same set will be coarse-grainedly represented by the center vector and the label of the granular-ball, respectively. Consequently, noise labels can be rectified through the labels of most of the labeled data. Moreover, we introduce a new gradient backpropagation mechanism compatible with our framework, which can help optimize coarse-grained embedding vectors with iterative training. Empirical results on text classification and name entity recognition tasks demonstrate that our proposal GBRAIN is indeed effective in contrast to the state-of-the-art baselines.

Manifold learning is essential for analyzing high-dimensional data, but it suffers from high time complexity. To address this, researchers proposed using anchors and constructing a similarity matrix to expedite eigen decomposition and reduce sparse consumption. However, randomly selected anchors fail to represent the data well, and using K-means for anchor generation is time-consuming. In this paper, we introduce Granular-ball (GB) into unsupervised manifold learning, presenting GB-USC and GB-USEC. By employing a coarse-to-fine approach, GB-USC generates high-quality anchors aligned with the data distribution. A bipartite graph is constructed between data points and anchors, enabling low-dimensional manifold embedding using transfer cut. GB-USEC combines multiple GB-USC clusters, generating consistent low-dimensional embeddings across dimensions and determining clustering results through voting. The experimental results show that compared with the state-of-the-art algorithm U-SPEC, GB-USC achieves the similar performance with the average running time of GB-USC is 33.96% less than that of U-SPEC for several million-level datasets. Additionally, our ensemble algorithm improves the clustering efficiency by an average of 29.19% compared with U-SENC.

In the real world, data distributions often exhibit multiple granularities. However, the majority of existing neighbor-based machine-learning methods rely on manually setting a single-granularity for neighbor relationships. These methods typically handle each data point using a single-granularity approach, which severely affects their accuracy and efficiency. This paper adopts a dual-pronged approach: it constructs a multi-granularity representation of the data using the granular-ball computing model, thereby boosting the algorithm's time efficiency. It leverages the multi-granularity representation of the data to create tailored, multi-granularity neighborhood relationships for different task scenarios, resulting in improved algorithmic accuracy. The experimental results convincingly demonstrate that the proposed multi-granularity neighbor relationship effectively enhances KNN classification and clustering methods.

On-the-fly Fine-grained sketch-based image retrieval (On-the-fly FG-SBIR) framework aim to break the barriers that sketch drawing requires excellent skills and is time-consuming. Considering such problems, a partial sketch with fewer strokes contains only the little local information, and the drawing process may show great difference among users, resulting in poor performance at the early retrieval. In this study, we developed a local-global representation learning (LGRL) method, in which we learn the representations for both the local and global regions of the partial sketch and its target photos. Specifically, we first designed a triplet network to learn the joint embedding space shared between the local and global regions of the entire sketch and its corresponding region of the photo. Then, we divided each partial sketch in the sketch-drawing episode into several local regions; Another learnable module following the triplet network was designed to learn the representations for the local regions of the partial sketch. Finally, by combining both the local and global regions of the sketches and photos, the final distance was determined. In the experiments, our method outperformed state-of-the-art baseline methods in terms of early retrieval efficiency on two publicly sketch-retrieval datasets and the practice test. Codes are available on:https://github.com/ddw2AIGROUP2CQUPT/LGRL.

In large-scale decision systems with high dimensions, constructing an efficient feature selection method via an uncertainty measure, has become a critical problem in fuzzy rough sets (FRS). However, the uncertainty method constructed through FRS for feature selection has the following limitations. 1) The composition of the uncertainty caused by fuzzy distance and similarity is neglected, which can not precisely evaluate the uncertainty. 2) The method of measuring uncertainty is to select all the sample for establishing a fuzzy similarity matrix, which leads to substantial time consumption. 3) The efficiency of selecting import features in a nonbatch manner is relatively low. Driven by this, both granular-ball (GB) computing and three-way approximations (TWA) are integrated to guide an uncertainty measure named multigranularity fuzzy entropy (MGFE), which is based on fuzzy distance and similarity, to improve the efficiency of feature selection. The MGFE is primarily recommended for measuring the uncertainty in multigranularity spaces. Therewith, the GB and TWA computing are integrated to compress the sample space to select representative sample. In addition, the MGFE is employed to assess the significance of the features in the representative sample space. Aided by the TWA, an efficient filter-wrapper feature selection with a three-way accelerator is successfully developed. Finally, related experiments illustrate the advancement of our proposed feature selection.s

Three-way decision with neighborhood rough sets (3WDNRS) is adept at addressing uncertain problems involving continuous data by configuring the neighborhood radius. However, on one hand, the inputs of 3WDNRS are individual neighborhood granules, which reduce the decision efficiency and generality; on other hand, the thresholds of 3WDNRS require prior knowledge to be approximately set in advance, making it difficult to apply in cases where such knowledge is unavailable. To address these issues, we introduce granular-ball computing (GBC) into 3WDNRS from the perspective of uncertainty. Firstly, we propose an enhanced granular-ball generation method based on DBSCAN called DBGBC. Subsequently, we present an improved granular-ball neighborhood rough sets model (GBNRS++) by combining DBGBC with a quality index. Furthermore, we construct a three-way classifier with granular-ball neighborhood rough sets (3WC-GBNRS++) based on the principle of minimum fuzziness loss. This approach provides an objective and efficient way to determine the thresholds. To further enhance classification accuracy, we design an adaptive granular-ball neighborhood within the subsequent classification process of 3WC-GBNRS++. Finally, experimental results demonstrate that, 3WC-GBNRS++ almost outperformed other comparison methods in terms of effectiveness and robustness, including 4 state-of-the-art granular-balls-based classifiers and 5 classical machine learning classifiers on 12 public benchmark datasets. Moreover, we discuss the limitations of our work and the outlook for future research.

This paper presents a novel framework for continual feature selection (CFS) in data preprocessing, particularly in the context of an open and dynamic environment where unknown classes may emerge. CFS encounters two primary challenges: the discovery of unknown knowledge and the transfer of known knowledge. To this end, we propose a GBCFS method, which combines the strengths of continual learning (CL) with granular-ball computing (GBC). The GBCFS method focuses on constructing a granular-ball knowledge base to detect unknown classes and facilitate the transfer of previously learned knowledge for further feature selection. GBCFS consists of two stages: initial learning and open learning. The former aims to establish an initial knowledge base through multi-granularity representation using granular balls. The latter utilizes prior granular-ball knowledge to identify unknowns, updates the knowledge base for granular-ball knowledge transfer, reinforces old knowledge, and integrates new knowledge. Subsequently, we devise an optimal feature subset mechanism that incorporates minimal new features into the existing optimal subset, often yielding superior results during each period. Extensive experimental results on public benchmark datasets demonstrate our method's superiority in terms of both effectiveness and efficiency compared to state-of-the-art feature selection methods.

Partial label learning (PLL) tackles scenarios where the unique ground-truth label of each sample is concealed within a candidate label set. Dimensionality reduction, considering labeling confidence estimation, has become a promising strategy to enhance the generalization performance of PLL models. However, current studies achieve dimensionality reduction, often relying on kNN-based labeling confidence estimation or disregarding potential labeling information. To address this issue, this paper proposes a novel Confidence-induced granular Partial label feature selection method using Dependency and Similarity (CPDS), which consists of two phases: Labeling Confidence Estimation (LCE) and Feature Selection (FS). For LCE, through granular ball computing, the feature space's similarity and the label space's correlation between the training data and the granular ball can be fused simultaneously, thereby effectively reconstructing more credible labeling confidence from candidate labels with more diverse semantic representation information. In the FS stage, by leveraging the LC with more diverse information, the proposed PLL neighborhood decision system further effectively combines feature dependency and label similarity to identify a feature subset with more discriminative capabilities, thereby achieving better performance for classification tasks. Among them, feature dependency effectively utilizes the dependency between neighborhoods and equivalence relations, while label similarity fully exploits the similarity between each sample and its neighbors. Extensive experiments show that CPDS significantly outperforms the compared approaches in most cases on nine controlled UCI datasets and five real-world datasets, demonstrating the superiority of the proposed method.

Traditional fuzzy set methods, designed around the finest granularity of inputs-individual points and their membership degrees-often struggle with inefficiencies and label noise. To overcome these challenges, we introduce granular-ball computing into the fuzzy set, creating the new granular-ball fuzzy set framework. This approach uses granular-ball inputs rather than single points, significantly reducing the number of entities and minimizing susceptibility to the noise affecting individual sample points. As a result, our framework enhances both efficiency and robustness compared to traditional methods and is applicable across various domains of fuzzy data processing. Furthermore, we apply this framework to fuzzy support vector machines (FSVMs), developing the Granular-ball Fuzzy Support Vector Machine (GBFSVM). Experimental tests on UCI benchmark datasets show that GBFSVM surpasses traditional models in efficiency and robustness.

Due to simplicity, K-means has become a widely used clustering method. However, its clustering result is seriously affected by the initial centers and the allocation strategy makes it hard to identify manifold clusters. Many improved K-means are proposed to accelerate it and improve the quality of initialize cluster centers, but few researchers pay attention to the shortcoming of K-means in discovering arbitrary-shaped clusters. Using graph distance (GD) to measure the dissimilarity between objects is a good way to solve this problem, but computing the GD is time-consuming. Inspired by the idea that granular ball uses a ball to represent the local data, we select representatives from a local neighborhood, called natural density peaks (NDPs). On the basis of NDPs, we propose a novel K-means algorithm for identifying arbitrary-shaped clusters, called NDP-Kmeans. It defines neighbor-based distance between NDPs and takes advantage of the neighbor-based distance to compute the GD between NDPs. Afterward, an improved K-means with high-quality initial centers and GD is used to cluster NDPs. Finally, each remaining object is assigned according to its representative. The experimental results show that our algorithms can not only recognize spherical clusters but also manifold clusters. Therefore, NDP-Kmeans has more advantages in detecting arbitrary-shaped clusters than other excellent algorithms.

Density peaks clustering algorithm (DP) has difficulty in clustering large-scale data, because it requires the distance matrix to compute the density and -distance for each object, which has time complexity. Granular ball (GB) is a coarse-grained representation of data. It is based on the fact that an object and its local neighbors have similar distribution and they have high possibility of belonging to the same class. It has been introduced into supervised learning by Xia et al. to improve the efficiency of supervised learning, such as support vector machine, -nearest neighbor classification, rough set, etc. Inspired by the idea of GB, we introduce it into unsupervised learning for the first time and propose a GB-based DP algorithm, called GB-DP. First, it generates GBs from the original data with an unsupervised partitioning method. Then, it defines the density of GBs, instead of the density of objects, according to the centers, radius, and distances between its members and centers, without setting any parameters. After that, it computes the distance between the centers of GBs as the distance between GBs and defines the -distance of GBs. Finally, it uses GBs' density and -distance to plot the decision graph, employs DP algorithm to cluster them, and expands the clustering result to the original data. Since there is no need to calculate the distance between any two objects and the number of GBs is far less than the scale of a data, it greatly reduces the running time of DP algorithm. By comparing with -means, ball -means, DP, DPC-KNN-PCA, FastDPeak, and DLORE-DP, GB-DP can get similar or even better clustering results in much less running time without setting any parameters. The source code is available at https://github.com/DongdongCheng/GB-DP.

Granular-ball computing (GBC) is an efficient, robust, and scalable learning method for granular computing. The granular ball (GB) generation method is based on GB computing. This article proposes a method for accelerating GB generation using division to replace k -means. It can significantly improve the efficiency of GB generation while ensuring an accuracy similar to that of the existing methods. In addition, a new adaptive method for GB generation is proposed by considering the elimination of the GB overlap and other factors. This makes the GB generation process parameter-free and completely adaptive in the true sense. In addition, this study first provides mathematical models for the GB covering. The experimental results on some real datasets demonstrate that the two proposed GB generation methods have accuracies similar to those of the existing method in most cases, while adaptiveness or acceleration is realized. All the codes were released in the open-source GBC library at https://www.cquptshuyinxia.com/GBC.html or https://github.com/syxiaa/gbc.

Hierarchical quotient space structure (HQSS), as a typical description of granular computing (GrC), focuses on hierarchically granulating fuzzy data and mining hidden knowledge. The key step of constructing HQSS is to transform the fuzzy similarity relation into fuzzy equivalence relation. However, on one hand, the transformation process has high time complexity. On the other hand, it is difficult to mine knowledge directly from fuzzy similarity relation due to its information redundancy, i.e., sparsity of effective information. Therefore, this article mainly focuses on proposing an efficient granulation approach for constructing HQSS by quickly extracting the effective value of fuzzy similarity relation. First, the effective value and effective position of fuzzy similarity relation are defined according to whether they could be retained in fuzzy equivalence relation. Second, the number and composition of effective values are presented to confirm that which elements are effective values. Based on these above theories, redundant information and sparse effective information in fuzzy similarity relation could be completely distinguished. Next, both isomorphism and similarity between two fuzzy similarity relations are researched based on the effective value. The isomorphism between two fuzzy equivalence relations is discussed based on the effective value. Then, the algorithm with low time complexity for extracting effective values of fuzzy similarity relation is introduced. On the basis, the algorithm for constructing HQSS is presented to realize efficient granulation of fuzzy data. The proposed algorithms could accurately extract effective information from the fuzzy similarity relation and construct the same HQSS with the fuzzy equivalence relation while greatly reducing the time complexity. Finally, relevant experiments on 15 UCI datasets, 3 UKB datasets, and 5 image datasets are shown and analyzed to verify the effectiveness and efficiency of the proposed algorithm.

In some specific scenarios, face sketch was used to identify a person. However, drawing a complete face sketch often needs skills and takes time, which hinder its widespread applicability in the practice. In this study, we proposed a new task named sketch less face image retrieval (SLFIR), in which the retrieval was carried out at each stroke and aim to retrieve the target face photo using a partial sketch with as few strokes as possible (see Fig. 1). Firstly, we developed a method to generate the data of sketch with drawing process, and opened such dataset; Secondly, we proposed a two-stage method as the baseline for SLFIR that (1) a triplet network, was first adopt to learn the joint embedding space shared between the complete sketch and its target face photo; (2) regarding the sketch drawing episode as a sequence, we designed a LSTM module to optimize the representation of the incomplete face sketch. Experiments indicate that the new framework can finish the retrieval using a partial or poor drawing sketch. (https://github.com/ddw2AIGROUP2CQUPT/SLFIR)

As one of the rapidly developing methodologies for dealing with complex problems in line with human cognition, granular computing has made significant achievements in knowledge discovery. Neighborhood classifier, as a typical description of granular computing, is an effective method for the classification of continuous data. However, in the phase of constructing neighborhood rules, the existing neighborhood classifiers are divided into the following two modes and both have defects: 1)the strategy driven by center:there are a lot of overlap and inclusion among neighborhood rules, that is, it needs to spend much time to reduce redundancy rules; and 2)the strategy driven by rule:there are many rules containing only one object, which cannot form an effective covering and would affect knowledge acquisition in the incremental environment. Therefore, in this article, fuzzy quotient space theory is introduced to construct neighborhood rules. Based on the optimal granularity of fuzzy quotient space, first, a neighborhood covering classifier, which has no redundant rules and could form the effective covering, is proposed without any artificial parameter. Second, comprehensively considering the knowledge purity and complexity, the quality measure of granularity is proposed, which guides the optimal granularity selection of hierarchical quotient space structure. Third, neighborhood rules are constructed in optimal granularity. Then, the offset of center is introduced to describe the membership degree of the test object to different neighborhood rules, and the neighborhood allocation strategy is proposed accordingly. Next, an algorithm for the neighborhood covering classifier based on these theories is proposed. Finally, experiments on 13 UCI datasets and three real datasets are carried out to verify the performance of the proposed classifier from four common classification indexes.

This paper presents a strong data-mining method based on a rough set, which can simultaneously realize feature selection, classification, and knowledge representation. Although a rough set, a popular method for feature selection, has good interpretability, it is not sufficiently efficient and accurate to deal with large-scale datasets with high dimensions, which prevents it from being immediately applied to real-world scenarios. To address the efficiency issue of a rough set, we discover the stability of the local redundancy (SLR) of attributes and propose a theorem to prove it rigorously. Based on SLR, only the parts of objects in the boundary region are partitioned when calculating outer significance, which further improves the efficiency of the rough set. With regard to the accuracy issue, we show that overfitting may lead to ineffectiveness of the rough set, especially when processing noise attributes. We then propose relative importance, a robust measurement for an attribute, to alleviate such overfitting issues. In this paper, we propose a novel rough-set framework that significantly improves the efficiency and accuracy of existing rough-set methods. We further develop our rough set framework by proposing a “rough concept tree” for knowledge representation and classification. Experimental results on public benchmark datasets show that our proposed framework achieves higher accuracy than seven state-of-the-art feature-selection methods. All the codes are available athttps://github.com/syxiaa/powerroughset.

Feature selection is an important preprocessing step in data mining and pattern recognition. The neighborhood rough set (NRS) model is a widely-used rough set model for feature selection on continuous data. All currently known NRS models are defined on a distance metric — mostly the euclidean distance metric — which invalidates the NRS models in scenarios wherein the euclidean distance is ineffective, for example, while considering differing attribute weights. We first introduce the concept of space division of granular-rectangular, and then construct the neighborhood radius in our method by describing the relationship between child and parent spaces, which avoids the use of a distance metric and reduces the search space for the neighborhood radius. This greatly improves both the accuracy and efficiency of NRS. In addition, the upper and lower approximations of the granular-rectangular rough sets (GRRSs) comprise equivalence classes; this results in better performance of GRRS in knowledge representation compared with the traditional NRS. Experimental results on public benchmark datasets reveal that our method, GRRS, achieves higher accuracy than ten popular and state-of-the-art feature-selection methods, including two NRS algorithms. Moreover, GRRS outperforms the established NRS algorithms regarding efficiency, including the state-of-the-art NRS algorithm, GBNRS. All code has been released as an open libary called GRRS:https://github.com/syxiaa/GRRS.

In order to solve the problem that the traditional spectral clustering algorithm is time-consuming and resource consuming when applied to large-scale data, resulting in poor clustering effect or even unable to cluster, this paper proposes a spectral clustering algorithm based on granular-ball(GBSC). The algorithm changes the construction method of the similarity matrix. Based on granular-ball, the size of the similarity matrix is greatly reduced, and the construction of the similarity matrix is more reasonable. Experimental results show that the proposed algorithm achieves better speedup ratio, less memory consumption and stronger anti noise performance while achieving similar clustering results to the traditional spectral clustering algorithm. Suppose the number of granular-balls is$m$,$n$is the number of points in the dataset, and$m< < n$, the time complexity of GBSC is$O(m^{3})$. It is proved that GBSC has good adaptability to large-scale datasets. All codes have been released athttps://github.com/xjnine/GBSC.

Granular computing, a new paradigm for solving large-scale and complex problems, has made significant progresses in knowledge discovery. Granular ball computing (GBC) is a novel granular computing method, which can rapidly generate scalable and robust information granules, that is, granular balls. However, a comprehensive index for measuring the performance of a granular ball does not exist. Furthermore, GBC lacks a mechanism to deal with dynamic decision systems. Therefore, in this study, the quality index of a granular ball is first formulated. Next, with this index, a novel granular ball rough sets model (GBRS) based on GBC is proposed. GBRS is more conducive to learning knowledge from uncertain datasets and more suited to incremental learning than the latest granular ball neighborhood rough sets model based on GBC. Subsequently, an incremental mechanism is introduced into GBRS, and two incremental learning models are developed for objects increasing in stream patterns and batch patterns, respectively. In the incremental learning process, three patterns of granular balls, that is, update, fusion, and split, were well studied when a set of objects was added to the decision system. Finally, to verify the effectiveness and efficiency, we apply GBRS and these two incremental learning models into classification tasks. Compared with four current state-of-the-art classification methods based on granular computing and four classical classifiers in machine learning, the proposed classifiers in this paper achieve higher classification accuracy as well as better efficiency on benchmark datasets.

This article presents a general sampling method, called granular-ball sampling (GBS), for classification problems by introducing the idea of granular computing. The GBS method uses some adaptively generated hyperballs to cover the data space, and the points on the hyperballs constitute the sampled data. GBS is the first sampling method that not only reduces the data size but also improves the data quality in noisy label classification. In addition, because the GBS method can be used to exactly describe the boundary, it can obtain almost the same classification accuracy as the results on the original datasets, and it can obtain an obviously higher classification accuracy than random sampling. Therefore, for the data reduction classification task, GBS is a general method that is not especially restricted by any specific classifier or dataset. Moreover, the GBS can be effectively used as an undersampling method for imbalanced classification. It has a time complexity that is close to O( N ), so it can accelerate most classifiers. These advantages make GBS powerful for improving the performance of classifiers. All codes have been released in the open source GBS library at http://www.cquptshuyinxia.com/GBS.html.

This paper presents a novel accelerated exact k-means called as "Ball k-means" by using the ball to describe each cluster, which focus on reducing the point-centroid distance computation. The "Ball k-means" can exactly find its neighbor clusters for each cluster, resulting distance computations only between a point and its neighbor clusters' centroids instead of all centroids. What's more, each cluster can be divided into "stable area" and "active area", and the latter one is further divided into some exact "annular area". The assignment of the points in the "stable area" is not changed while the points in each "annular area" will be adjusted within a few neighbor clusters. There are no upper or lower bounds in the whole process. Moreover, ball k-means uses ball clusters and neighbor searching along with multiple novel stratagems for reducing centroid distance computations. In comparison with the current state-of-the art accelerated exact bounded methods, the Yinyang algorithm and the Exponion algorithm, as well as other top-of-the-line tree-based and bounded methods, the ball k-means attains both higher performance and performs fewer distance calculations, especially for large-k problems. The faster speed, no extra parameters and simpler design of "Ball k-means" make it an all-around replacement of the naive k-means.

Image annotation aims to jointly predict multiple tags for an image. Although significant progress has been achieved, existing approaches usually overlook aligning specific labels and their corresponding regions due to the weak supervised information (i.e., "bag of labels" for regions), thus failing to explicitly exploit the discrimination from different classes. In this article, we propose the deep label-specific feature (Deep-LIFT) learning model to build the explicit and exact correspondence between the label and the local visual region, which improves the effectiveness of feature learning and enhances the interpretability of the model itself. Deep-LIFT extracts features for each label by aligning each label and its region. Specifically, Deep-LIFTs are achieved through learning multiple correlation maps between image convolutional features and label embeddings. Moreover, we construct two variant graph convolutional networks (GCNs) to further capture the interdependency among labels. Empirical studies on benchmark datasets validate that the proposed model achieves superior performance on multilabel classification over other existing state-of-the-art methods.

This article presents a simple sampling method, which is very easy to be implemented, for classification by introducing the idea of random space division, called "random space division sampling" (RSDS). It can extract the boundary points as the sampled result by efficiently distinguishing the label noise points, inner points, and boundary points. This makes it the first general sampling method for classification that not only can reduce the data size but also enhance the classification accuracy of a classifier, especially in the label-noisy classification. The "general" means that it is not restricted to any specific classifiers or datasets (regardless of whether a dataset is linear or not). Furthermore, the RSDS can online accelerate most classifiers because of its lower time complexity than most classifiers. Moreover, the RSDS can be used as an undersampling method for imbalanced classification. The experimental results on benchmark datasets demonstrate its effectiveness and efficiency. The code of the RSDS and comparison algorithms is available at: https://github.com/syxiaa/RSDS.

Recently, deep dictionary learning (DDL) has aroused attention due to its abilities of learning multiple different dictionaries and extracting multi-level abstract feature representations for samples. It has been applied to many intelligent recognition tasks, such as vehicle detection, traffic sign recognition and driver monitoring. Nevertheless, the off-the-shelf DDL-based methods ignore the essential structural information of data in multi-layer dictionary learning. The learned hierarchical data representations are less discriminative. To address this issue, we develop a new DDL framework, called the hierarchical graph augmented deep collaborative dictionary learning (HGDCDL). Firstly, we propose a new deep collaborative dictionary learning (DCDL) that applies collaborative representation to the deepest-level representation learning. Most importantly, equipped with a simple yet effective hierarchal graph construction mechanism, our HGDCDL uses the structure of data to regularize dictionary learning, and generates more informative dictionaries and discriminative representations at different levels. Extensive experiments show that our HGDCDL performs significantly better than the state-of-the-art shallow and deep representation learning methods for classification.

Feature reduction is an important aspect of Big Data analytics on today’s ever-larger datasets. Rough sets are a classical method widely applied in attribute reduction. Most rough set algorithms use theprioridomain knowledge of a dataset to process continuous attributes through using a membership function. Neighborhood rough sets (NRS) replace the membership function with the concept of neighborhoods, allowing NRS to handle scenarios where noa prioriknowledge is available. However, the neighborhood radius of each object in NRS is fixed, and the optimization of the radius depends on grid searching. This diminishes both the efficiency and effectiveness, leading to a time complexity of not lower than$O(N^2)$O(N2). To resolve these limitations, granular ball neighborhood rough sets (GBNRS), a novel NRS method with time complexity$O(N)$O(N), is proposed. GBNRS adaptively generates a different neighborhood for each object, resulting in greater generality and flexibility in comparison to standard NRS methods. GBNRS is compared with the current state-of-the-art NRS method, FARNeMF, and find that GBNRS obtains both higher performance and higher classification accuracy on public benchmark datasets. All code has been released in the open source GBNRS library athttp://www.cquptshuyinxia.com/GBNRS.html.

Mitigating label noise is a crucial problem in classification. Noise filtering is an effective method of dealing with label noise which does not need to estimate the noise rate or rely on any loss function. However, most filtering methods focus mainly on binary classification, leaving the more difficult counterpart problem of multiclass classification relatively unexplored. To remedy this deficit, we present a definition for label noise in a multiclass setting and propose a general framework for a novel label noise filtering learning method for multiclass classification. Two examples of noise filtering methods for multiclass classification, multiclass complete random forest (mCRF) and multiclass relative density, are derived from their binary counterparts using our proposed framework. In addition, to optimize the NI_threshold hyperparameter in mCRF, we propose two new optimization methods: a new voting cross-validation method and an adaptive method that employs a 2-means clustering algorithm. Furthermore, we incorporate SMOTE into our label noise filtering learning framework to handle the ubiquitous problem of imbalanced data in multiclass classification. We report experiments on both synthetic data sets and UCI benchmarks to demonstrate our proposed methods are highly robust to label noise in comparison with state-of-the-art baselines. All code and data results are available at https://github.com/syxiaa/Multiclass-Label-Noise-Filtering-Learning.

Multi-scale decision system (MDS) is an effective tool to describe hierarchical data in machine learning. Optimal scale combination (OSC) selection and attribute reduction are two key issues related to knowledge discovery in MDSs. However, searching for all OSCs may result in a combinatorial explosion, and the existing approaches typically incur excessive time consumption. In this study, searching for all OSCs is considered as an optimization problem with the scale space as the search space. Accordingly, a sequential three-way decision model of the scale space is established to reduce the search space by integrating three-way decision with the Hasse diagram. First, a novel scale combination is proposed to perform scale selection and attribute reduction simultaneously, and then an extended stepwise optimal scale selection (ESOSS) method is introduced to quickly search for a single local OSC on a subset of the scale space. Second, based on the obtained local OSCs, a sequential three-way decision model of the scale space is established to divide the search space into three pair-wise disjoint regions, namely the positive, negative, and boundary regions. The boundary region is regarded as a new search space, and it can be proved that a local OSC on the boundary region is also a global OSC. Therefore, all OSCs of a given MDS can be obtained by searching for the local OSCs on the boundary regions in a step-by-step manner. Finally, according to the properties of the Hasse diagram, a formula for calculating the maximal elements of a given boundary region is provided to alleviate space complexity. Accordingly, an efficient OSC selection algorithm is proposed to improve the efficiency of searching for all OSCs by reducing the search space. The experimental results demonstrate that the proposed method can significantly reduce computational time.

In recent years, the convolution neural network (CNN) has been successfully applied in numerous fields as a machine learning model. However, such neural models are still considered to be “black box” for most tasks. The fundamental issue underlying this problem is that the information and knowledge learned by a neural network during the training process are unknown and unpredictable. In this study, we attempted to design a partially understandable neural network through semantic embedding. Firstly, we selected several understandable feature extraction operators as expected information. Secondly, we embedded these operators into the hierarchical layers of a neural network at the beginning of its training process. Finally, these embedded operators were only involved in forward calculation and remained unchanged in the error back-propagation of the training process. We applied our method to the ResNet and DenseNet models in image classification tasks. In the experiments, our new models achieved almost the same performance as the original ones, but decreased performance was exhibited when shutting the embedded parts, and the features in the embedded parts were understandable. The experiments verified that the embedded parts not only contributed to the classification tasks, but also caused the neural network model to be partially understandable.

The existing noise detection methods required the classifiers or distance measurements or data overall distribution, and `curse of dimensionality' and other restrictions made them insufficiently effective in complex data, e.g., different attribute weights, high-dimensionality, containing feature noise, nonlinearity, etc. This is also the main reason that the existing noise filtering methods were not widely applied and formed an effective learning framework. To address this problem, we propose here a complete and efficient random forest method (CRF) specifically for the class noise detection by simulating the grid generation and expansion. The CRF is not based on distance measures or overall distribution or classifiers; besides, the voting mechanism makes it able to effectively process datasets containing feature noise. Furthermore, we introduce CRF based class noise filtering learning framework (CRF-NFL) and derive its mathematical model. The framework is then applied to many widely used classifiers including some state-of-the-art algorithms, e.g., k-means tree, GBDT, and XGBoost. Moreover, its parallelized is designed for large-scale data. The CRF-NFL show much better generalizability than the conventional classifiers and the relative density-based method, which is the most effective noise filtering method as far as we know. All research has formed an open source library, called CRF-NFL: http://www.cquptshuyinxia.com/CRF-NFL.html.

Class noise can cause overfitting of learning methods and deteriorate their generalizability. Although relative density can detect class noise effectively, it has a time complexity of O(N2) and a low efficiency. To address this problem, by introducing the granular computing into the relative density model, this paper proposes a Multi-Granularity Relative Density (MGRD) model for class noise detection. In an experiment, we tested the effect of parameters on its performance under classifiers. The experimental results on benchmark data sets demonstrated that it had a higher efficiency than conventional methods. In addition, it exhibited better generalizability in comparison with the conventional methods because of the good robustness of granular computing on many cases.

In the human cognition learning, the noise self-filtering filters the noise data by itself, making the human brain very robust. Although k-Nearest Neighbors (kNN) can decrease the affection of noise data by optimizing the parameter k, noise data still may deteriorate the learning results to an extent on various data. Therefore, this paper proposes the strategy for kNNs. Here, we formalize such training strategies in the context of kNNs, and they are called with “Noise Self-filtering k-Nearest Neighbors” (NSF-kNNs). As its name suggests, it is determined by the model itself based on what it has already learned, as oppose to some predefined heuristic criteria. We derive the mathematical model of the NSF-kNNs, which is an algorithm framework. The NSF-kNNs are compared with the exact kNNs and as far as we know the most efficient approximate kNN [1]. The results show the achievement of improvements in the robustness and generalizability on various data sets.