Multimodal Sentiment Analysis (MSA) with incomplete data has gained significant attention recently.Existing studies focus on optimizing model structures to handle modality missingness, but models still face challenges in robustness when dealing with uncertain missingness.To this end, we propose a data-centric robust multimodal sentiment analysis method, Proxy-Driven Robust Multimodal Fusion (P-RMF).First, we map unimodal data to the latent space of Gaussian distributions to capture core features and structure, thereby learn stable modality representation.Then, we combine the quantified modality intrinsic uncertainty to learn stable multimodal joint representation (i.e., proxy modality), which is further enhanced through multi-layer dynamic cross-modal injection to increase its diversity.Extensive experimental results show that P-RMF outperforms existing models in noise resistance and achieves state-of-the-art performance on multiple benchmark datasets.

Category-level object understanding has progressed, but generalized part perception remains underexplored. This paper introduces GASEM, a framework for Generalizable and Actionable Parts GAPart Segmentation and pose Estimation via object Motion perception. GASEM utilizes point-wise motion data from observed point clouds and cross-perspective alignment to learn object motion using a scene flow model. It features a segmentation proposal architecture for GAPart segmentation and an Normalized Object Coordinate Space(NPCS) branch for pose estimation. Additionally, a reinforcement learning agent is trained for robust GAPart manipulation in both simulations and real-world environments. Experiments on the GAPartNet dataset show GASEM outperforms state-of-the-art methods. This work promises advancements in embodied intelligence applications like robot-object interaction and generalizable manipulation. Codes are available at https://github.com/Zirconium233/GASEM.

Most clustering validity indexes (CVIs) for fuzzy clustering are based upon the fuzzy c-means (FCMs) algorithm, and the effect of these CVIs is limited due to the "uniform effect" of FCM. Besides, main existing CVIs have the problems of incompleteness characterization of separateness and weak performance for noisy datasets. To address these challenges, the multi-granularity fusion (MGF) index is proposed. First, MGF synthetically considers the FCM, possibilistic fuzzy c-means and kernel-based FCM algorithms, which is more comprehensive than just considering FCM. Second, we add a perturbation to the sum of the partition matrix as the fuzzy cardinality and combine it with the fuzzy weighted distance, which are helpful to grasp the compactness. Third, four elements are considered together to characterize the separateness, incorporating the minimum distance, the maximum distance, the mean distance, and the sample variance of cluster center, where the last one can make the separateness unbiased from the macroscopic perspective. Besides, the convergence of MGF is proved. Finally, we test MGF for five algorithms on 36 datasets comparing with 14 CVIs, validating the accuracy and stability of MGF. It is observed that MGF can get superior results than other CVIs, especially for high-dimensional datasets and noisy datasets.

Determining the optimal number of clusters in cluster analysis without prior knowledge remains a critical and challenging task. Existing methods often depend on calculating clustering validity indices (CVIs), which increases complexity and may reduce efficiency. Furthermore, different CVIs frequently suggest varying optimal cluster numbers, complicating the selection process. To address these challenges, we propose a novel clustering algorithm, self-regulating possibilistic C-means (PCM) with high-density points (SR-PCM-HDP), which simplifies cluster number determination while improving clustering efficiency. First, the density-based knowledge extraction (DBKE) method is introduced to estimate an appropriate initial cluster number and identify high-density points. DBKE enhances the density peak clustering (DPC) algorithm by removing the need for a predefined density radius. Second, SR-PCM-HDP refines the clustering process by incorporating a parameter to balance the interactions between high-density points and cluster centers, reducing sensitivity to initial configurations and accelerating convergence. Third, the parameter adjustment mechanism in classical PCM is redefined to enable adaptive updates during SR-PCM-HDP iterations. This mechanism facilitates the gradual elimination of obsolete clusters and iterative cluster formation. The theoretical foundations of the SR-PCM-HDP cluster elimination mechanism are rigorously established. Experimental results validate the accuracy and effectiveness of SR-PCM-HDP in determining cluster numbers and ensuring clustering validity, particularly for datasets with overlapping or imbalanced distributions. Comparisons are conducted against 13 state-of-the-art algorithms, including fuzzy clustering, possibilistic clustering, and CVI-based cluster determination methods.

The Bandler-Kohout subproduct (BKS) method acts as one of the two representative fuzzy relational inference (FRI) strategies. Observing the BKS method using constraint modeling, two fuzzy implications, respectively, produce expression to the factors of inference mechanism and rule base. However, these two factors normally reflect different connotations from the perspectives of artificial intelligence applications and logical meaning. Enlightened by such idea, in this study, we propose and investigate the differently implicational BKS (DBKS) method. Initially, main properties of DBKS are validated. The reversibility and interpolativity of DBKS are proved under certain conditions. The equivalent relationship is verified between interpolativity and continuity for DBKS. The robustness of DBKS is confirmed from both the similarity and the extensional hull. Posteriorly, the computational performance of DBKS is analyzed. In DBKS, the preservation of the indistinguishability holds for input fuzzy sets, and it is proved that the first-aggregate-then-infer (FATI) reasoning strategy of DBKS is equivalent to the first-infer-then-aggregate (FITA) one. To improve the computational efficiency, the hierarchical DBKS method is presented. In addition, the fuzzy system is established on the strength of the DBKS method, the singleton fuzzifier and the centroid defuzzifier. Its response function is analyzed and a universal approximator is built by the fuzzy system via DBKS. At the end, we compare the results of DBKS with BKS by virtue of two examples in affective computing. It is discovered that DBKS can create superior forms of FRI in comparison to those produced by BKS.

Multi-view attributed graphs (MVAGs) provide rich structural and attribute information, but existing clustering methods struggle to jointly exploit multi-view attributes and multiple graph structures. Moreover, they often focus on either visible view collaboration or hidden feature extraction, failing to capture the synergy between the two. To address these challenges, we propose ITF-MVFC (Multi-View Fuzzy Clustering with Intrinsic and Topological Features), a novel clustering model designed for MVAGs. ITF-MVFC first constructs proximity matrices from topological connections and then introduces a Double Visible-Hidden Feature Extraction (DVHFE) mechanism based on non-negative matrix factorization (NMF). This extracts both intrinsic and topological visible-hidden feature representations. To enhance sparsity and interpretability, we further employ network lasso regularization, enabling effective cooperative learning between intrinsic and topological views. Finally, a fuzzy clustering objective function is established to integrate these multi-view representations. Experiments on synthetic, real-world, and large size datasets show that ITF-MVFC consistently outperforms state-of-the-art clustering methods on both external metrics and internal validation indices across multiple datasets.

In current granular clustering algorithms, numeric representatives were selected by users or an ordinary strategy, which seemed simple; meanwhile, weight settings for granular data could not adequately express their structural characteristics. Aiming at these problems, in this study, a new scheme called a granular weighted kernel fuzzy clustering (GWKFC) algorithm is put forward. We propose the representative selection and granularity generation (RSGG) algorithm enlightened by the density peak clustering (DPC) algorithm. We build interval and triangular granular data on the strength of numeric representatives obtained by RSGG under the principle of justifiable granularity (PJG), in which we establish some combinations of functions and boundary constraints and prove their properties. Furthermore, we present a novel distance formula via the kernel function for granular data and design new weights to affect the coverage and specificity of granular data. In addition, based upon these factors, we come up with the GWKFC algorithm of granular clustering, and its performance with different granularity is assessed. To sum up, a macro framework involving granular modeling, granular clustering, and assessment has been set up. Lastly, the GWKFC algorithm and ten other granular clustering algorithms are compared by experiments on some artificial and UCI datasets together with datasets with large data or those of high dimensionality. It is found that the GWKFC algorithm can provide better granular clustering results by contrast with other algorithms. The originality is embodied as follows. First, we improve the previous density radius and present the RSGG algorithm to acquire numeric representatives. Second, we propose a new strategy to determine granular data boundaries and further obtain novel weights enlightened by the idea of volume. Lastly, we employ the kernel function to calculate the distance between granular data, which has a stronger spatial division ability than the previous Euclidean distance.

Multimodal sentiment analysis (MSA) aims to integrate multiple modalities of information to better understand human sentiment. The current research mainly focuses on conducting multimodal fusion, which neglects the under-optimized modal representations generated by the imbalance of unimodal performances in joint learning. Moreover, the size of labeled datasets limits the generalization ability of existing supervised models. To address the above issues, this paper proposes a knowledge-enhanced self-supervised balanced representation approach (KEBR). First, a text-based cross-modal fusion method (TCMF) is constructed, which injects the non-verbal information from the videos into the semantic representation of text to enhance the multimodal representation of text. Then, a multimodal cosine constrained loss (MCC) is designed to constrain the fusion of non-verbal information in joint learning to balance the representation. Finally, with the help of sentiment knowledge and non-verbal information, KEBR conducts sentiment word masking and sentiment intensity prediction. Experimental results show that KEBR outperforms the baseline.

Depression is a prevalent and severe mental illness that significantly impacts patients’ physical health and daily life. Recent studies have focused on multimodal depression assessment, aiming to objectively and conveniently evaluate depression using multimodal data. However, existing methods based on audio–visual modalities struggle to capture the dynamic variations in depression clues and cannot fully explore multimodal data over a long time. In addition, they rely heavily on insufficient single-stage multimodal fusion, which limits the accuracy of depression assessment. To address these limitations, we propose a novel parallel multiscale bridge fusion network (PMBFN) for audio–visual depression assessment. PMBFN comprehensively captures subtle multilevel dynamic changes in depression expression through parallel multiscale dynamic convolutions and long short-term memories (LSTMs) and effectively solves the problem of long-term audio–visual sequence information loss by using spatiotemporal attention pooling modules. Furthermore, the multimodal bridge fusion module is proposed in PMBFN to achieve multistage interactive recursive multimodal fusion, enhancing the expressive capacity of multimodal depression-related features to improve the accuracy of assessment. Extensive experiments on the DAIC-WOZ and E-DAIC datasets demonstrate that our method outperforms current state-of-the-art methods and clearly shows our method's effectiveness eventually.

In existing granular clustering algorithms, the design of coverage and specificity does not fully capture the inherent structural characteristics of granular data together with the optimization issue, and the current weight setting for the granular data is not sufficient. To address these problems, in this study, the trapezoidal information granule, which is rarely studied before, is concentrated, and we come up with a novel granular clustering algorithm called the weighted possibilistic fuzzy c-means algorithm for trapezoidal granularity (WPFCM-T). Firstly, under the acknowledged principle of justifiable granularity, novel functions of coverage and specificity are designed for trapezoidal information granules, considering the internal characteristics of such granules. The idea of particle swarm optimization (PSO) is exploited to upgrade the established granular data, and then the trapezoidal information granule construction (TIGC) method is proposed to realize granular modeling. Secondly, an exponential weight is constructed with regard to coverage and specificity, while a novel distance via α-cuts is given. The possibilistic fuzzy c-means (PFCM) structure is introduced into granular clustering, in which the new weight and distance are integrated, resulting in the proposed WPFCM-T algorithm. Thirdly, the reconstruction criterion is studied to evaluate granular clustering, and hence an overall framework including granular modeling, clustering and evaluation is constructed. Lastly, through experiments completed on artificial datasets, UCI datasets, large datasets, high-dimensional datasets, and noisy datasets, WPFCMT has superior granular data reconstruction ability by contrast with other granular clustering algorithms, indicating that the granular clustering performance of WPFCM-T is better than the others.

The introduction of domain knowledge opens new horizons to fuzzy clustering. Then knowledge-driven and data-driven fuzzy clustering methods come into being. To address the challenges of inadequate extraction mechanism and imperfect fusion mode in such class of methods, we propose the Knowledge-induced Multiple Kernel Fuzzy Clustering (KMKFC) algorithm. First, to extract knowledge points better, the Relative Density-based Knowledge Extraction (RDKE) method is proposed to extract high-density knowledge points close to cluster centers of real data structure, and provide initialized cluster centers. Moreover, the multiple kernel mechanism is introduced to improve the adaptability of clustering algorithm and map data to high-dimensional space, so as to better discover the differences between the data and obtain superior clustering results. Second, knowledge points generated by RDKE are integrated into KMKFC through a knowledge-influence matrix to guide the iterative process of KMKFC. Third, we also provide a strategy of automatically obtaining knowledge points, and thus propose the RDKE with Automatic knowledge acquisition (RDKE-A) method and the corresponding KMKFC-A algorithm. Then we prove the convergence of KMKFC and KMKFC-A. Finally, experimental studies demonstrate that the KMKFC and KMKFC-A algorithms perform better than thirteen comparison algorithms with regard to four evaluation indexes and the convergence speed.

The existing clustering validity indexes (CVIs) show some difficulties to produce the correct cluster number when some cluster centers are close to each other, and the separation processing mechanism appears simple. The results are imperfect in case of noisy data sets. For this reason, in this study, we come up with a novel CVI for fuzzy clustering, referred to as the triple center relation (TCR) index. The originality of this index is twofold. On the one hand, a new fuzzy cardinality is built on the strength of the maximum membership degree, and a novel compactness formula is constructed by combining it with the within-class weighted squared error sum. On the other hand, starting from the minimum distance between different cluster centers, the mean distance as well as the sample variance of cluster centers in the statistical sense are further integrated. These three factors are combined by means of product to form a triple characterization of the relationship between cluster centers, and hence a 3-D expression pattern of separability is formed. Subsequently, the TCR index is put forward by combining the compactness formula with the separability expression pattern. By virtue of the degenerate structure of hard clustering, we show an important property of the TCR index. Finally, based on the fuzzy C -means (FCMs) clustering algorithm, experimental studies were conducted on 36 data sets (incorporating artificial and UCI data sets, images, the Olivetti face database). For comparative purposes, 10 CVIs were also considered. It has been found that the proposed TCR index performs best in finding the correct cluster number, and has excellent stability.

Knowledge-based clustering algorithms can improve traditional clustering models by introducing domain knowledge to identify the underlying data structure. While there have been several approaches to clustering with the guidance of knowledge tidbits, most of them mainly focus on numeric knowledge without considering the uncertain nature of information. To capture the uncertainty of information, pure numeric knowledge tidbits are expanded to knowledge granules in this article. Then, two questions arise: how to obtain granular knowledge and how to use those knowledge granules in clustering. To the end, a novel knowledge extraction and granulation (KEG) method and a granular knowledge-based fuzzy clustering model are proposed in this study. First, inspired by the concept of natural neighbors, an automatic KEG is developed. In KEG, high-density points are filtered from the dataset and then merged with their natural neighbors to form several dense areas, i.e., granular knowledge. Furthermore, the granular knowledge expressed by interval or triangular numbers is leveraged into the clustering algorithm, which is the framework of fuzzy clustering with granular knowledge. To concretize this model into clustering algorithms, the classical fuzzy C-Means clustering algorithm has been selected to incorporate the granular knowledge produced by KEG. Then, the corresponding fuzzy C-Means clustering with interval knowledge granules (IKG-FCM) and triangular knowledge granules (TKG-FCM) are proposed. Experiments on synthetic and real-world datasets demonstrate that IKG-FCM and TKG-FCM always achieve better clustering performance with less time cost, especially on imbalanced data, compared with state-of-the-art algorithms.

The Bandler-Kohout subproduct (BKS) method is one of the two widely acknowledged fuzzy relational inference (FRI) schemes. The previous works related to its stability and robustness mainly concentrated on how the output values were changed with perturbation parameters of input values. However, the works on estimating oscillation bounds of output values with regard to varying limits of input, are lacking. In this study, we investigate the oscillation-bound estimation of perturbations for BKS. First, the BKS output variation scopes are acquired for interval perturbation, where the R -implication, ( S, N )-implication, QL-implication, and t -norm implication are adopted. Second, in allusion to the more sophisticated problem of the fuzzy reasoning chain with BKS, the oscillation bounds of BKS output resulting from input interval perturbation are offered. Third, we construct the upper and lower bounds of BKS output deviation originated in the simple perturbation of the input fuzzy set, in which the situations of one rule and multiple rules are both dissected. Finally, the stable properties of all these BKS strategies are confirmed. It is emphasized that interval perturbation and simple perturbation are more general ways to give expression describing the robustness issue, and the obtained oscillation bounds also deliver more detailed characterization of the output deviation along with the input perturbation. This study further validates the sound properties of the BKS method.

Under interval-valued fuzzy environment, based on the differently implicational idea and hierarchical inference mechanism, the interval-valued universal triple I algorithm is put forward. To begin with, the interval-valued fuzzy implications and related residual pairs are researched. Furthermore, the interval-valued universal triple I principles are proposed, and the optimal solutions of the interval-valued universal triple I algorithm are achieved from the viewpoints of residual pairs together with the R-implications, and the corresponding hierarchical inference mode is established, meanwhile the reversible properties of the interval-valued universal triple I algorithm are proved. Finally, it is verified by examples that the interval-valued universal triple I algorithm performs better than the interval-valued triple I algorithm.

Task partition is a critical problem of collaborative conceptual design. Aiming at the shortage that current task partition methods don't accord to innovative functional reasoning that is the kernel process and essence embodiment of conceptual design, a new task partition method for function tree according to innovative functional reasoning is proposed. To begin with, the concept of task module is proposed as the basic unit of task pre-partition before task module pre-partition algorithm that generates initial task modules is put forward. Furthermore, based on analyzing and gaining three basic constraint relationships: including, independent and innovative conflict relationship, M- TPG (module-driven task precedence graph) generated from the former two relationships is introduced into this field as the basic tool of task management. Lastly, task partition algorithm based on M-TPG with three basic principles for innovation is given. The new method is derived from clustering of microcosmic elements of innovative functional reasoning and conflicted task modules, which can obtain deeper cohesiveness and more reasonable results.