The graph-based clustering aims to utilize structural information from graphs to provide clustering solutions. However, many existing graph clustering methods separate graph construction from the learning of clustering results, and rely on the assumption of consistent feature importance, which often leads to suboptimal clustering outcomes. Anchor-based graph clustering offers an efficient and scalable solution for clustering tasks. Nevertheless, the need to manually specify the number of anchors limits its practicality. Motivated by these issues, this paper proposes a method called Multi-granularity Granular-ball Anchor Graph Clustering with self-weighting (MGAGC). The MGAGC utilizes granular-ball computing to adaptively generate granular-ball anchors based on the data distribution, where the number of granular-ball anchors is much smaller than the number of data samples. Then, by enabling interaction between fine-granularity sample points and coarse-granularity granular-ball anchors in a self-weighting feature space, the MGAGC integrates graph construction with the learning of clustering results. Extensive experiments are conducted on fourteen public datasets to compare the proposed MGAGC with nine classic or state-of-the-art baseline clustering methods. Experimental results show that MGAGC achieves an average ACC of 75.50% and an average NMI of 51.22%, outperforming other clustering methods by an average of 13.60% and 12.21%, respectively. Moreover, statistical test results indicate that its performance differences are statistically significant compared to most of the competing methods. Code is available at https://github.com/awaw-Liyely/2026-IPM-MGAGC . • Adaptive granular-ball anchors auto-counted for full data coverage. • Self-weighted features enable fine-coarse interaction for accurate similarity. • Unified graph-clustering via Laplacian rank gives direct cluster labels. • Experimental results show that the proposed model and algorithm perform well.

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.

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.

Multi-label classification represented by hierarchical classification (HC) plays an important role in current large-scale problems, which can acquire a more accurate expression of data that conforms to the human multi-granularity cognitive process. To compress the original dataset and simultaneously enhance the expressive force of models, selecting an appropriate granularity for approximately describing the classification is the main task in the rough set theory. Nevertheless, the current rough set theory merely concerns flat classification and encounters new problems when approximately describing HC. 1) There lacks a measure to correctly reflect misclassification in accordance with the hierarchical accuracy of HC on the training set. 2) There lacks a measure relying on the distribution of the dataset to reflect the difference between two distinct feature sets describing HC in generalization ability. To address the mentioned issues, this paper utilizes the knowledge distance to characterize HC and proposes a cost-sensitive granularity selection for HC. First, HC and features are respectively granulated according to hierarchical quotient space and neighborhood granular structures. Then, knowledge distance and its extended form are employed to formulate misclassification and test costs. On this basis, a cost-sensitive neighborhood granularity selection is presented for HC. Finally, we experimentally demonstrate the excellent performance of the proposed method in terms of efficiency and HC accuracy both in synthetic and real datasets.

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.

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.

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.

Aligning users across networks using graph representation learning has been found effective where the alignment is accomplished in a low-dimensional embedding space. Yet, highly precise alignment remains challenging, especially for nodes with long-range connectivity to labeled anchors. To alleviate this limitation, we propose WL-Align which employs a regularized representation learning framework to learn distinctive node representations. It extends the Weisfeiler-Lehman Isormorphism Test and learns the alignment in alternating phases of “across-network Weisfeiler-Lehman relabeling” and “proximity-preserving representation learning”. The across-network Weisfeiler-Lehman relabeling is achieved through iterating the anchor-based label propagation and a similarity-based hashing to exploit the known anchors’ connectivity to different nodes in an efficient and robust manner. The representation learning module preserves the second-order proximity within individual networks and is regularized by the across-network Weisfeiler-Lehman hash labels. Extensive experiments on real-world and synthetic datasets have demonstrated that our proposed WL-Align outperforms the state-of-the-art methods, achieving significant performance improvements in the “exact matching” scenario.

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.

A dilemma faced by classification is that the data is not collected at the same frequency in some applications. We investigate the mixed frequency data in a new way and recognize them as a special style of multi-view data, in which each view data is collected at a different sampling frequency. This paper proposes a discriminative dictionary pair learning method constrained by ordinal locality for mixed frequency data classification (shorted by DPLOL-MF). This method integrates synthesis dictionary and analysis dictionary into a dictionary pair, which not only improves computational cost caused by the ℓ0or ℓ1-norm constraint, but also can deal with the sampling frequency inconsistency. The DPLOL-MF utilizes a synthesis dictionary to learn class-specified reconstruction information and employs an analysis dictionary to generate coding coefficients by analyzing samples. Particularly, the ordinal locality preserving term is leveraged to constrain the atoms of dictionaries pair to further facilitate the learned dictionary pair to be more discriminative. Besides, we design a specific classification scheme for the inconsistent sample size of mixed frequency data. This paper illustrates a novel idea to solve the classification task of mixed frequency data and the experimental results demonstrate the effectiveness of the proposed method.

Machine understanding and thinking require prior knowledge consisting of explicit and implicit knowledge. The current knowledge base contains various explicit knowledge but not implicit knowledge. As part of implicit knowledge, the typical characteristics of the things referred to by the concept are available by concept cognition for knowledge graphs. Therefore, this paper attempts to realize concept cognition for knowledge graphs from the perspective of mining multigranularity decision rules. Specifically, (1) we propose a novel multigranularity three-way decision model that merges the ideas of multigranularity (i.e., from coarse granularity to fine granularity) and three-way decision (i.e., acceptance, rejection, and deferred decision). (2) Based on the multigranularity three-way decision model, an algorithm for mining multigranularity decision rules is proposed. (3) The monotonicity of positive or negative granule space ensured that the positive (or negative) granule space from coarser granularity does not need to participate in the three-classification process at a finer granularity, which accelerates the process of mining multigranularity decision rules. Moreover, the experimental results show that the multigranularity decision rule is better than the two-way decision rule, frequent decision rule and single granularity decision rule, and the monotonicity of positive or negative granule space can accelerate the process of mining multigranularity decision rules.

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.

Social network alignment aims at aligning person identities across social networks. Embedding based models have been shown effective for the alignment where the structural proximity preserving objective is typically adopted for the model training. With the observation that “overly-close” user embeddings are unavoidable for such models causing alignment inaccuracy, we propose a novel learning framework which tries to enforce the resulting embeddings to be more widely apart among the users via the introduction of carefully implanted pseudo anchors. We further proposed a meta-learning algorithm to guide the updating of the pseudo anchor embeddings during the learning process. The proposed intervention via the use of pseudo anchors and meta-learning allows the learning framework to be applicable to a wide spectrum of network alignment methods. We have incorporated the proposed learning framework into several state-of-the-art models. Our experimental results demonstrate its efficacy where the methods with the pseudo anchors implanted can outperform their counterparts without pseudo anchors by a fairly large margin, especially when there only exist very few labeled anchors.

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.

How to accurately predict unknown quality-of-service (QoS) data based on observed ones is a hot yet thorny issue in Web service-related applications. Recently, a latent factor (LF) model has shown its efficiency in addressing this issue owing to its high accuracy and scalability. An LF model can be improved by identifying user and service neighborhoods based on user and service geographical information. However, such information can be difficult to acquire in most applications with the considerations of information security, identity privacy, and commercial interests in a real system. Besides, the existing LF model-based QoS predictors mostly ignore the reliability of given QoS data where noises commonly exist to cause accuracy loss. To address the above issues, this paper proposes a data-characteristic-aware latent factor (DCALF) model to implement highly accurate QoS predictions, where ‘data-characteristic-aware’ indicates that it can appropriately implement QoS prediction according to the characteristics of given QoS data. Its main idea is two-fold: a) it detects the neighborhoods and noises of users and services based on the dense LFs extracted from the original sparse QoS data, b) it incorporates a density peaks-based clustering method into its modeling process for achieving the simultaneous detections of both neighborhoods and noises of QoS data. With such designs, it precisely represents the given QoS data in spite of their sparsity, thereby achieving highly accurate predictions for unknown ones. Experimental results on two QoS datasets generated by real-world Web services demonstrate that the proposed DCALF model outperforms state-of-the-art QoS predictors, making it highly competitive in addressing the issue of Web service selection and recommendation.

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.

A dilemma faced by classification is that the data is not collected at the same frequency in some applications. We investigate the mixed frequency data in a new way and recognize them as a special style of multi-view data, in which each view data is collected at a different sampling frequency. This article proposes a discriminative dictionary pair learning method constrained by ordinal locality for mixed frequency data classification (shorted by DPLOL-MF). This method integrates synthesis dictionary and analysis dictionary into a dictionary pair, which not only improves computational cost caused by the${\ell _0}$or${\ell _1}$-norm constraint, but also can deal with the sampling frequency inconsistency. The DPLOL-MF utilizes a synthesis dictionary to learn class-specified reconstruction information and employs an analysis dictionary to generate coding coefficients by analyzing samples. Particularly, the ordinal locality preserving term is leveraged to constrain the atoms of dictionaries pair to further facilitate the learned dictionary pair to be more discriminative. Besides, we design a specific classification scheme for the inconsistent sample size of mixed frequency data. This paper illustrates a novel idea to solve the classification task of mixed frequency data and the experimental results demonstrate the effectiveness of the proposed method.

The existing multi-view clustering algorithms require that a sample in a view is completely or partially mapped onto one or more samples in a different corresponding view. However, this requirement could not be satisfied in many practical applications. Fortunately, there is a common cognition that the graph structure formed from each view should be as consistent as possible. Thus, this paper proposes a novel multi-view clustering method for unknown mapping relationships between cross-view samples based on the framework of non-negative matrix factorization, as an attempt to solve this problem. The objective function is designed by effectively building reconstruction error terms, local structural constraint terms, and cross-view mapping loss terms by exploring cross-view relationships. The experimental results show that the proposed method not only performs well to reveal the real mapping relationships between cross-view samples but also outperforms the comparison algorithms on the obtained clustering results.

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.

Aluminum alloy is widely used in transportation, catering, industry, sports, health and other fields, because of their excellent high specific strength and corrosion resistance. Aluminum industry has been an important mainstay industry of a national economy. In the process of electrolytic aluminum, the superheat degree is a very important production target. When an electrolysis cell is working in the appropriate superheat degree state, the life of cell is prolonged and the amounts of aluminum released will enhanced. However, to measure the superheat degree is very difficult and the measured results cannot timely feedback to the process of production. To address the problem, a soft sensing prediction model of superheat degree is proposed in this paper, in which some new concepts such as the decay function of data weight, the credibility of a rule and the rule tree are introduced. Basically speaking, the processing of the soft sensing prediction model is mainly based on the rough set data analysis method and a tree data structure. The static rules are obtained from the history data by using the attribute reduction and value reduction method in the rough sets. The rule tree is updated timely based on the incremental data set accordingly. The effectiveness of the proposed model is verified with the aluminum production data provided by Shandong Weiqiao Aluminum Electrolysis limited company in China.

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.

Rule induction method based on rough set theory (RST) has received much attention recently since it may generate a minimal set of rules from the decision system for real-life applications by using of attribute reduction and approximations. The decision system may vary with time, e.g., the variation of objects, attributes and attribute values. The reduction and approximations of the decision system may alter on Attribute Values' Coarsening and Refining (AVCR), a kind of variation of attribute values, which results in the alteration of decision rules simultaneously. This paper aims for dynamic maintenance of decision rules w.r.t. AVCR. The definition of minimal discernibility attribute set is proposed firstly, which aims to improve the efficiency of attribute reduction in RST. Then, principles of updating decision rules in case of AVCR are discussed. Furthermore, the rough set-based methods for updating decision rules in the inconsistent decision system are proposed. The complexity analysis and extensive experiments on UCI data sets have verified the effectiveness and efficiency of the proposed methods.

With the development of Web technology and it is applied in education, Web-based learning support systems (WLSSs) have been adopted all over the world. This paper presents a formal evaluation model for WLSSs based on the method of fuzzy integrated evaluation. We concentrate on the commonly factors and elements that ensure and contribute to the learning course. The model is comprehensive and objective, so that it can be used to evaluate all WLSSs. Based on the proposed model, some WLSSs are evaluated and compared with each other. Some further research issues are also discussed.

Rough set (RS) is a valid theory to deal with imprecise, uncertain, and vague information. It has been applied successfully since it was developed by Professor Z. Pawlak in 1982 in such fields as machine learning, data mining, intelligent data analyzing, control algorithm acquiring, etc. The greatest advantage of the RS is its great ability to compute the reductions of information systems. Many researchers have done a lot of work in developing efficient algorithms to compute useful reductions of information systems. There also are some researchers working on the relationship between rough entropy and information entropy. They have developed some efficient reduction algorithms based on conditional information entropy. In this article, the relationship of the definitions of rough reduction in algebra view and information view is studied. Some relationships such as inclusion relationship under some conditions and equivalence relationship under some other conditions are presented. The inclusion relationship between the attribute importance defined in algebra view and information view is presented also. Some efficient heuristic reduction algorithms can be developed further using these results. © 2003 Wiley Periodicals, Inc.

The problem of representing and processing logical knowledge using a neural network is discussed. A novel neuron model, a triple-valued logical neuron (TLN) is presented. There are two kinds of TLNs, triple-valued “logical and” neuron (TLN-AND) and triple-valued “logical or” neuron (TLN-OR). A multiple-layer neural network (TLNN) made up of TLNs can implement a triple-valued logical inference system. TLNN can thus form a base for representing logical knowledge using neural networks. ©1999 John Wiley & Sons, Inc.