Feiping Nie

Junyun Cui, Xiaoyu Shen, Feiping Nie et al.

Legal judgment prediction (LJP) applies Natural Language Processing (NLP) techniques to predict judgment results based on fact descriptions automatically. Recently, large-scale public datasets and advances in NLP research have led to increasing interest in LJP. Despite a clear gap between machine and human performance, impressive results have been achieved in various benchmark datasets. In this paper, to address the current lack of comprehensive survey of existing LJP tasks, datasets, models and evaluations, (1) we analyze 31 LJP datasets in 6 languages, present their construction process and define a classification method of LJP with 3 different attributes; (2) we summarize 14 evaluation metrics under four categories for different outputs of LJP tasks; (3) we review 12 legal-domain pretrained models in 3 languages and highlight 3 major research directions for LJP; (4) we show the state-of-art results for 8 representative datasets from different court cases and discuss the open challenges. This paper can provide up-to-date and comprehensive reviews to help readers understand the status of LJP. We hope to facilitate both NLP researchers and legal professionals for further joint efforts in this problem.

Feiping Nie, Jitao Lu, Danyang Wu et al.

Normalized-Cut (N-Cut) is a famous model of spectral clustering. The traditional N-Cut solvers are two-stage: 1) calculating the continuous spectral embedding of normalized Laplacian matrix; 2) discretization via $K$-means or spectral rotation. However, this paradigm brings two vital problems: 1) two-stage methods solve a relaxed version of the original problem, so they cannot obtain good solutions for the original N-Cut problem; 2) solving the relaxed problem requires eigenvalue decomposition, which has $\mathcal{O}(n^3)$ time complexity ($n$ is the number of nodes). To address the problems, we propose a novel N-Cut solver designed based on the famous coordinate descent method. Since the vanilla coordinate descent method also has $\mathcal{O}(n^3)$ time complexity, we design various accelerating strategies to reduce the time complexity to $\mathcal{O}(|E|)$ ($|E|$ is the number of edges). To avoid reliance on random initialization which brings uncertainties to clustering, we propose an efficient initialization method that gives deterministic outputs. Extensive experiments on several benchmark datasets demonstrate that the proposed solver can obtain larger objective values of N-Cut, meanwhile achieving better clustering performance compared to traditional solvers.

Yongbo Yu, Weizhong Yu, Feiping Nie et al.

The self-attention mechanism in Transformer architecture, invariant to sequence order, necessitates positional embeddings to encode temporal order in time series prediction. We argue that this reliance on positional embeddings restricts the Transformer's ability to effectively represent temporal sequences, particularly when employing longer lookback windows. To address this, we introduce an innovative approach that combines Pyramid RNN embeddings(PRE) for univariate time series with the Transformer's capability to model multivariate dependencies. PRE, utilizing pyramidal one-dimensional convolutional layers, constructs multiscale convolutional features that preserve temporal order. Additionally, RNNs, layered atop these features, learn multiscale time series representations sensitive to sequence order. This integration into Transformer models with attention mechanisms results in significant performance enhancements. We present the PRformer, a model integrating PRE with a standard Transformer encoder, demonstrating state-of-the-art performance on various real-world datasets. This performance highlights the effectiveness of our approach in leveraging longer lookback windows and underscores the critical role of robust temporal representations in maximizing Transformer's potential for prediction tasks. Code is available at this repository: \url{https://github.com/usualheart/PRformer}.

Feiping Nie, Hong Chen, Rong Wang et al.

This paper presents an algorithm to solve the Soft k-Means problem globally. Unlike Fuzzy c-Means, Soft k-Means (SkM) has a matrix factorization-type objective and has been shown to have a close relation with the popular probability decomposition-type clustering methods, e.g., Left Stochastic Clustering (LSC). Though some work has been done for solving the Soft k-Means problem, they usually use an alternating minimization scheme or the projected gradient descent method, which cannot guarantee global optimality since the non-convexity of SkM. In this paper, we present a sufficient condition for a feasible solution of Soft k-Means problem to be globally optimal and show the output of the proposed algorithm satisfies it. Moreover, for the Soft k-Means problem, we provide interesting discussions on stability, solutions non-uniqueness, and connection with LSC. Then, a new model, named Minimal Volume Soft k-Means (MVSkM), is proposed to address the solutions non-uniqueness issue. Finally, experimental results support our theoretical results.

Liangchen Liu, Qiuhong Ke, Chaojie Li et al.

Spectral clustering is an effective methodology for unsupervised learning. Most traditional spectral clustering algorithms involve a separate two-step procedure and apply the transformed new representations for the final clustering results. Recently, much progress has been made to utilize the non-negative feature property in real-world data and to jointly learn the representation and clustering results. However, to our knowledge, no previous work considers a unified model that incorporates the important multi-view information with those properties, which severely limits the performance of existing methods. In this paper, we formulate a novel clustering model, which exploits the non-negative feature property and, more importantly, incorporates the multi-view information into a unified joint learning framework: the unified multi-view orthonormal non-negative graph based clustering framework (Umv-ONGC). Then, we derive an effective three-stage iterative solution for the proposed model and provide analytic solutions for the three sub-problems from the three stages. We also explore, for the first time, the multi-model non-negative graph-based approach to clustering data based on deep features. Extensive experiments on three benchmark data sets demonstrate the effectiveness of the proposed method.

Da Zhang, Bingyu Li, Zhiyuan Zhao et al.

Time series analysis plays a vital role in fields such as finance, healthcare, industry, and meteorology, underpinning key tasks including classification, forecasting, and anomaly detection. Although deep learning models have achieved remarkable progress in these areas in recent years, constructing an efficient, multi-task compatible, and generalizable unified framework for time series analysis remains a significant challenge. Existing approaches are often tailored to single tasks or specific data types, making it difficult to simultaneously handle multi-task modeling and effectively integrate information across diverse time series types. Moreover, real-world data are often affected by noise, complex frequency components, and multi-scale dynamic patterns, which further complicate robust feature extraction and analysis. To ameliorate these challenges, we propose FusAD, a unified analysis framework designed for diverse time series tasks. FusAD features an adaptive time-frequency fusion mechanism, integrating both Fourier and Wavelet transforms to efficiently capture global-local and multi-scale dynamic features. With an adaptive denoising mechanism, FusAD automatically senses and filters various types of noise, highlighting crucial sequence variations and enabling robust feature extraction in complex environments. In addition, the framework integrates a general information fusion and decoding structure, combined with masked pre-training, to promote efficient learning and transfer of multi-granularity representations. Extensive experiments demonstrate that FusAD consistently outperforms state-of-the-art models on mainstream time series benchmarks for classification, forecasting, and anomaly detection tasks, while maintaining high efficiency and scalability. Code is available at https://github.com/zhangda1018/FusAD.

Jinghui Yuan, Weijin Jiang, Zhe Cao et al.

Ensemble learning is a method that leverages weak learners to produce a strong learner. However, obtaining a large number of base learners requires substantial time and computational resources. Therefore, it is meaningful to study how to achieve the performance typically obtained with many base learners using only a few. We argue that to achieve this, it is essential to enhance both classification performance and generalization ability during the ensemble process. To increase model accuracy, each weak base learner needs to be more efficiently integrated. It is observed that different base learners exhibit varying levels of accuracy in predicting different classes. To capitalize on this, we introduce confidence tensors $\tilde{\mathbfΘ}$ and $\tilde{\mathbfΘ}_{rst}$ signifies the degree of confidence that the $t$-th base classifier assigns the sample to class $r$ while it actually belongs to class $s$. To the best of our knowledge, this is the first time an evaluation of the performance of base classifiers across different classes has been proposed. The proposed confidence tensor compensates for the strengths and weaknesses of each base classifier in different classes, enabling the method to achieve superior results with a smaller number of base learners. To enhance generalization performance, we design a smooth and convex objective function that leverages the concept of margin, making the strong learner more discriminative. Furthermore, it is proved that in gradient matrix of the loss function, the sum of each column's elements is zero, allowing us to solve a constrained optimization problem using gradient-based methods. We then compare our algorithm with random forests of ten times the size and other classical methods across numerous datasets, demonstrating the superiority of our approach.

Jinghui Yuan, Chusheng Zeng, Fangyuan Xie et al.

Clustering is a fundamental task in machine learning and data science, and similarity graph-based clustering is an important approach within this domain. Doubly stochastic symmetric similarity graphs provide numerous benefits for clustering problems and downstream tasks, yet learning such graphs remains a significant challenge. Marcus theorem states that a strictly positive symmetric matrix can be transformed into a doubly stochastic symmetric matrix by diagonal matrices. However, in clustering, learning sparse matrices is crucial for computational efficiency. We extend Marcus theorem by proposing the Marcus mapping, which indicates that certain sparse matrices can also be transformed into doubly stochastic symmetric matrices via diagonal matrices. Additionally, we introduce rank constraints into the clustering problem and propose the Doubly Stochastic Adaptive Neighbors Clustering algorithm based on the Marcus Mapping (ANCMM). This ensures that the learned graph naturally divides into the desired number of clusters. We validate the effectiveness of our algorithm through extensive comparisons with state-of-the-art algorithms. Finally, we explore the relationship between the Marcus mapping and optimal transport. We prove that the Marcus mapping solves a specific type of optimal transport problem and demonstrate that solving this problem through Marcus mapping is more efficient than directly applying optimal transport methods.

Guanxiong He, Jie Wang, Liaoyuan Tang et al.

Federated clustering addresses the critical challenge of extracting patterns from decentralized, unlabeled data. However, it is hampered by the flaw that current approaches are forced to accept a compromise between performance and privacy: \textit{transmitting embedding representations risks sensitive data leakage, while sharing only abstract cluster prototypes leads to diminished model accuracy}. To resolve this dilemma, we propose Structural Privacy-Preserving Federated Graph Clustering (SPP-FGC), a novel algorithm that innovatively leverages local structural graphs as the primary medium for privacy-preserving knowledge sharing, thus moving beyond the limitations of conventional techniques. Our framework operates on a clear client-server logic; on the client-side, each participant constructs a private structural graph that captures intrinsic data relationships, which the server then securely aggregates and aligns to form a comprehensive global graph from which a unified clustering structure is derived. The framework offers two distinct modes to suit different needs. SPP-FGC is designed as an efficient one-shot method that completes its task in a single communication round, ideal for rapid analysis. For more complex, unstructured data like images, SPP-FGC+ employs an iterative process where clients and the server collaboratively refine feature representations to achieve superior downstream performance. Extensive experiments demonstrate that our framework achieves state-of-the-art performance, improving clustering accuracy by up to 10\% (NMI) over federated baselines while maintaining provable privacy guarantees.

Feiping Nie, Zhezheng Hao, Rong Wang

Support Vector Machine (SVM) stands out as a prominent machine learning technique widely applied in practical pattern recognition tasks. It achieves binary classification by maximizing the "margin", which represents the minimum distance between instances and the decision boundary. Although many efforts have been dedicated to expanding SVM for multi-class case through strategies such as one versus one and one versus the rest, satisfactory solutions remain to be developed. In this paper, we propose a novel method for multi-class SVM that incorporates pairwise class loss considerations and maximizes the minimum margin. Adhering to this concept, we embrace a new formulation that imparts heightened flexibility to multi-class SVM. Furthermore, the correlations between the proposed method and multiple forms of multi-class SVM are analyzed. The proposed regularizer, akin to the concept of "margin", can serve as a seamless enhancement over the softmax in deep learning, providing guidance for network parameter learning. Empirical evaluations demonstrate the effectiveness and superiority of our proposed method over existing multi-classification methods.Code is available at https://github.com/zz-haooo/M3SVM.

Xinjie Shen, Danyang Wu, Jitao Lu et al.

How to utilize the pseudo labels has always been a research hotspot in machine learning. However, most methods use pseudo labels as supervised training, and lack of valid assessing for their accuracy. Moreover, applications of pseudo labels in graph neural networks (GNNs) oversee the difference between graph learning and other machine learning tasks such as message passing mechanism. Aiming to address the first issue, we found through a large number of experiments that the pseudo labels are more accurate if they are selected by not overlapping partial labels and defined as negative node pairs relations. Therefore, considering the extraction based on pseudo and partial labels, negative edges are constructed between two nodes by the negative pseudo partial labels extraction (NP$^2$E) module. With that, a signed graph are built containing highly accurate pseudo labels information from the original graph, which effectively assists GNN in learning at the message-passing level, provide one solution to the second issue. Empirical results about link prediction and node classification tasks on several benchmark datasets demonstrate the effectiveness of our method. State-of-the-art performance is achieved on the both tasks.

Xilai Li, Wuyang Liu, Xiaosong Li et al.

Multi-modality image fusion (MMIF) combines complementary information from different image modalities to provide a more comprehensive and objective interpretation of scenes. However, existing MMIF methods lack the ability to resist different weather interferences in real-world scenes, preventing them from being useful in practical applications such as autonomous driving. To bridge this research gap, we proposed an all-weather MMIF model. Achieving effective multi-tasking in this context is particularly challenging due to the complex and diverse nature of weather conditions. A key obstacle lies in the 'black box' nature of current deep learning architectures, which restricts their multi-tasking capabilities. To overcome this, we decompose the network into two modules: a fusion module and a restoration module. For the fusion module, we introduce a learnable low-rank representation model to decompose images into low-rank and sparse components. This interpretable feature separation allows us to better observe and understand images. For the restoration module, we propose a physically-aware clear feature prediction module based on an atmospheric scattering model that can deduce variations in light transmittance from both scene illumination and reflectance. We also construct a large-scale multi-modality dataset with 100,000 image pairs across rain, haze, and snow conditions, covering various degradation levels and diverse scenes to thoroughly evaluate image fusion methods in adverse weather. Experimental results in both real-world and synthetic scenes show that the proposed algorithm excels in detail recovery and multi-modality feature extraction. The code is available at https://github.com/ixilai/AWFusion.

Da Zhang, Bingyu Li, Zhuyuan Zhao et al.

As multimodal data proliferates across diverse real-world applications, leveraging heterogeneous information such as texts and timestamps for accurate time series forecasting (TSF) has become a critical challenge. While diffusion models demonstrate exceptional performance in generation tasks, their application to TSF remains largely confined to modeling single-modality numerical sequences, overlooking the abundant cross-modal signals inherent in complex heterogeneous data. To address this gap, we propose UniDiff, a unified diffusion framework for multimodal time series forecasting. To process the numerical sequence, our framework first tokenizes the time series into patches, preserving local temporal dynamics by mapping each patch to an embedding space via a lightweight MLP. At its core lies a unified and parallel fusion module, where a single cross-attention mechanism adaptively weighs and integrates structural information from timestamps and semantic context from texts in one step, enabling a flexible and efficient interplay between modalities. Furthermore, we introduce a novel classifier-free guidance mechanism designed for multi-source conditioning, allowing for decoupled control over the guidance strength of textual and temporal information during inference, which significantly enhances model robustness. Extensive experiments on real-world benchmark datasets across eight domains demonstrate that the proposed UniDiff model achieves state-of-the-art performance.

Jinghui Yuan, Hao Chen, Renwei Luo et al.

Ensemble learning has achieved remarkable success in machine learning, but its reliance on numerous base learners limits its application in resource-constrained environments. This paper introduces an innovative "Margin-Maximizing Fine-Grained Ensemble Method" that achieves performance surpassing large-scale ensembles by meticulously optimizing a small number of learners and enhancing generalization capability. We propose a novel learnable confidence matrix, quantifying each classifier's confidence for each category, precisely capturing category-specific advantages of individual learners. Furthermore, we design a margin-based loss function, constructing a smooth and partially convex objective using the logsumexp technique. This approach improves optimization, eases convergence, and enables adaptive confidence allocation. Finally, we prove that the loss function is Lipschitz continuous, based on which we develop an efficient gradient optimization algorithm that simultaneously maximizes margins and dynamically adjusts learner weights. Extensive experiments demonstrate that our method outperforms traditional random forests using only one-tenth of the base learners and other state-of-the-art ensemble methods.

Jinghui Yuan, Fangyuan Xie, Feiping Nie et al.

The indicator matrix plays an important role in machine learning, but optimizing it is an NP-hard problem. We propose a new relaxation of the indicator matrix and prove that this relaxation forms a manifold, which we call the Relaxed Indicator Matrix Manifold (RIM manifold). Based on Riemannian geometry, we develop a Riemannian toolbox for optimization on the RIM manifold. Specifically, we provide several methods of Retraction, including a fast Retraction method to obtain geodesics. We point out that the RIM manifold is a generalization of the double stochastic manifold, and it is much faster than existing methods on the double stochastic manifold, which has a complexity of \( \mathcal{O}(n^3) \), while RIM manifold optimization is \( \mathcal{O}(n) \) and often yields better results. We conducted extensive experiments, including image denoising, with millions of variables to support our conclusion, and applied the RIM manifold to Ratio Cut, we provide a rigorous convergence proof and achieve clustering results that outperform the state-of-the-art methods. Our Code in \href{https://github.com/Yuan-Jinghui/Riemannian-Optimization-on-Relaxed-Indicator-Matrix-Manifold}{here}.

Danyang Wu, Xinjie Shen, Jitao Lu et al.

Existing multigraph convolution methods either ignore the cross-view interaction among multiple graphs, or induce extremely high computational cost due to standard cross-view polynomial operators. To alleviate this problem, this paper proposes a Simple MultiGraph Convolution Networks (SMGCN) which first extracts consistent cross-view topology from multigraphs including edge-level and subgraph-level topology, then performs polynomial expansion based on raw multigraphs and consistent topologies. In theory, SMGCN utilizes the consistent topologies in polynomial expansion rather than standard cross-view polynomial expansion, which performs credible cross-view spatial message-passing, follows the spectral convolution paradigm, and effectively reduces the complexity of standard polynomial expansion. In the simulations, experimental results demonstrate that SMGCN achieves state-of-the-art performance on ACM and DBLP multigraph benchmark datasets. Our codes are available at https://github.com/frinkleko/SMGCN.

Jinghui Yuan, Jiaxuan Zou, Shuo Wang et al.

Matrix-based optimizers have demonstrated immense potential in training Large Language Models (LLMs), however, designing an ideal optimizer remains a formidable challenge. A superior optimizer must satisfy three core desiderata: efficiency, achieving Muon-like preconditioning to accelerate optimization; stability, strictly adhering to the scale-invariance inherent in neural networks; and speed, minimizing computational overhead. While existing methods address these aspects to varying degrees, they often fail to unify them, either incurring prohibitive computational costs like Muon, or allowing radial jitters that compromise stability like RMNP. To bridge this gap, we propose Nora, an optimizer that rigorously satisfies all three requirements. Nora achieves training stability by explicitly stabilizing weight norms and angular velocities through row-wise momentum projection onto the orthogonal complement of the weights. Simultaneously, by leveraging the block-diagonal dominance of the Transformer Hessian, Nora effectively approximates structured preconditioning while maintaining an optimal computational complexity of $\mathcal{O}(mn)$. Furthermore, we prove that Nora is a scalable optimizer and establish its corresponding scaling theorems. With a streamlined implementation requiring only two lines of code, our preliminary experiments validate Nora as an efficient and highly promising optimizer for large-scale training.

Feiping Nie, Yitao Song, Wei Chang et al.

In the graph-based semi-supervised learning, the Green-function method is a classical method that works by computing the Green's function in the graph space. However, when applied to large graphs, especially those sparse ones, this method performs unstably and unsatisfactorily. We make a detailed analysis on it and propose a novel method from the perspective of optimization. On fully connected graphs, the method is equivalent to the Green-function method and can be seen as another interpretation with physical meanings, while on non-fully connected graphs, it helps to explain why the Green-function method causes a mess on large sparse graphs. To solve this dilemma, we propose a workable approach to improve our proposed method. Unlike the original method, our improved method can also apply two accelerating techniques, Gaussian Elimination, and Anchored Graphs to become more efficient on large graphs. Finally, the extensive experiments prove our conclusions and the efficiency, accuracy, and stability of our improved Green's function method.

Fangyuan Xie, Jinghui Yuan, Feiping Nie et al.

Min cut is an important graph partitioning method. However, current solutions to the min cut problem suffer from slow speeds, difficulty in solving, and often converge to simple solutions. To address these issues, we relax the min cut problem into a dual-bounded constraint and, for the first time, treat the min cut problem as a dual-bounded nonlinear optimal transport problem. Additionally, we develop a method for solving dual-bounded nonlinear optimal transport based on the Frank-Wolfe method (abbreviated as DNF). Notably, DNF not only solves the size constrained min cut problem but is also applicable to all dual-bounded nonlinear optimal transport problems. We prove that for convex problems satisfying Lipschitz smoothness, the DNF method can achieve a convergence rate of \(\mathcal{O}(\frac{1}{t})\). We apply the DNF method to the min cut problem and find that it achieves state-of-the-art performance in terms of both the loss function and clustering accuracy at the fastest speed, with a convergence rate of \(\mathcal{O}(\frac{1}{\sqrt{t}})\). Moreover, the DNF method for the size constrained min cut problem requires no parameters and exhibits better stability.

Feiping Nie, Shenfei Pei, Zengwei Zheng et al.

We propose a Greedy strategy to solve the problem of Graph Cut, called GGC. It starts from the state where each data sample is regarded as a cluster and dynamically merges the two clusters which reduces the value of the global objective function the most until the required number of clusters is obtained, and the monotonicity of the sequence of objective function values is proved. To reduce the computational complexity of GGC, only mergers between clusters and their neighbors are considered. Therefore, GGC has a nearly linear computational complexity with respect to the number of samples. Also, unlike other algorithms, due to the greedy strategy, the solution of the proposed algorithm is unique. In other words, its performance is not affected by randomness. We apply the proposed method to solve the problem of normalized cut which is a widely concerned graph cut problem. Extensive experiments show that better solutions can often be achieved compared to the traditional two-stage optimization algorithm (eigendecomposition + k-means), on the normalized cut problem. In addition, the performance of GGC also has advantages compared to several state-of-the-art clustering algorithms.

Xueyuan Xu, Fulin Wei, Tianyuan Jia et al.

In the last decade, embedded multi-label feature selection methods, incorporating the search for feature subsets into model optimization, have attracted considerable attention in accurately evaluating the importance of features in multi-label classification tasks. Nevertheless, the state-of-the-art embedded multi-label feature selection algorithms based on least square regression usually cannot preserve sufficient discriminative information in multi-label data. To tackle the aforementioned challenge, a novel embedded multi-label feature selection method, termed global redundancy and relevance optimization in orthogonal regression (GRROOR), is proposed to facilitate the multi-label feature selection. The method employs orthogonal regression with feature weighting to retain sufficient statistical and structural information related to local label correlations of the multi-label data in the feature learning process. Additionally, both global feature redundancy and global label relevancy information have been considered in the orthogonal regression model, which could contribute to the search for discriminative and non-redundant feature subsets in the multi-label data. The cost function of GRROOR is an unbalanced orthogonal Procrustes problem on the Stiefel manifold. A simple yet effective scheme is utilized to obtain an optimal solution. Extensive experimental results on ten multi-label data sets demonstrate the effectiveness of GRROOR.

Da Zhang, Bingyu Li, Zhiyuan Zhao et al.

Time series classification (TSC) is crucial in numerous real-world applications, such as environmental monitoring, medical diagnosis, and posture recognition. TSC tasks require models to effectively capture discriminative information for accurate class identification. Although deep learning architectures excel at capturing temporal dependencies, they often suffer from high computational cost, sensitivity to noise perturbations, and susceptibility to overfitting on small-scale datasets. To address these challenges, we propose FAIM, a lightweight Frequency-Aware Interactive Mamba model. Specifically, we introduce an Adaptive Filtering Block (AFB) that leverages Fourier Transform to extract frequency-domain features from time series data. The AFB incorporates learnable adaptive thresholds to dynamically suppress noise and employs element-wise coupling of global and local semantic adaptive filtering, enabling in-depth modeling of the synergy among different frequency components. Furthermore, we design an Interactive Mamba Block (IMB) to facilitate efficient multi-granularity information interaction, balancing the extraction of fine-grained discriminative features and comprehensive global contextual information, thereby endowing FAIM with powerful and expressive representations for TSC tasks. Additionally, we incorporate a self-supervised pre-training mechanism to enhance FAIM's understanding of complex temporal patterns and improve its robustness across various domains and high-noise scenarios. Extensive experiments on multiple benchmarks demonstrate that FAIM consistently outperforms existing state-of-the-art (SOTA) methods, achieving a superior trade-off between accuracy and efficiency and exhibits outstanding performance.

Lixiang Xu, Xianwei Ding, Xin Yuan et al.

Knowledge Tracing (KT) involves monitoring the changes in a student's knowledge over time by analyzing their past responses, with the goal of predicting future performance. However, most existing methods primarily focus on feature enhancement, while overlooking the deficiencies in cognitive representation and the ability to express cognition-issues often caused by interference from non-cognitive factors such as slipping and guessing. This limitation hampers the ability to capture the continuity and coherence of the student's cognitive process. As a result, many methods may introduce more prediction bias and modeling costs due to their inability to maintain cognitive continuity and coherence. Based on the above discussion, we propose the Cognitive Representation Dynamic Programming based Knowledge Tracing (CRDP-KT) model. This model em ploys a dynamic programming algorithm to optimize cognitive representations based on the difficulty of the questions and the performance intervals between them. This approach ensures that the cognitive representation aligns with the student's cognitive patterns, maintaining overall continuity and coherence. As a result, it provides more accurate and systematic input features for subsequent model training, thereby minimizing distortion in the simulation of cognitive states. Additionally, the CRDP-KT model performs partitioned optimization of cognitive representations to enhance the reliability of the optimization process. Furthermore, it improves its ability to express the student's cognition through a weighted fusion of optimized record representations and re lationships learned from a bipartite graph. Finally, experiments conducted on three public datasets validate the effectiveness of the proposed CRDP-KT model.

Guanzhou Lan, Yuqi Yang, Anup Teejo Mathew et al.

Goal-conditioned dynamic manipulation is inherently challenging due to complex system dynamics and stringent task constraints, particularly in deformable object scenarios characterized by high degrees of freedom and underactuation. Prior methods often simplify the problem to low-speed or 2D settings, limiting their applicability to real-world 3D tasks. In this work, we explore 3D goal-conditioned rope manipulation as a representative challenge. To mitigate data scarcity, we introduce a novel simulation framework and benchmark grounded in reduced-order dynamics, which enables compact state representation and facilitates efficient policy learning. Building on this, we propose Dynamics Informed Diffusion Policy (DIDP), a framework that integrates imitation pretraining with physics-informed test-time adaptation. First, we design a diffusion policy that learns inverse dynamics within the reduced-order space, enabling imitation learning to move beyond naïve data fitting and capture the underlying physical structure. Second, we propose a physics-informed test-time adaptation scheme that imposes kinematic boundary conditions and structured dynamics priors on the diffusion process, ensuring consistency and reliability in manipulation execution. Extensive experiments validate the proposed approach, demonstrating strong performance in terms of accuracy and robustness in the learned policy.

Feiping Nie, Yitao Song, Jingjing Xue et al.

We propose the DPSM method, a density-based node clustering approach that automatically determines the number of clusters and can be applied in both data space and graph space. Unlike traditional density-based clustering methods, which necessitate calculating the distance between any two nodes, our proposed technique determines density through a propagation process, thereby making it suitable for a graph space. In DPSM, nodes are partitioned into small clusters based on propagated density. The partitioning technique has been proved to be sound and complete. We then extend the concept of spectral clustering from individual nodes to these small clusters, while introducing the CluCut measure to guide cluster merging. This measure is modified in various ways to account for cluster properties, thus provides guidance on when to terminate the merging process. Various experiments have validated the effectiveness of DOSM and the accuracy of these conclusions.

Qiang Chen, Weizhong Yu, Feiping Nie et al.

Fuzzy clustering algorithms can be roughly categorized into two main groups: Fuzzy C-Means (FCM) based methods and mixture model based methods. However, for almost all existing FCM based methods, how to automatically selecting proper membership degree hyper-parameter values remains a challenging and unsolved problem. Mixture model based methods, while circumventing the difficulty of manually adjusting membership degree hyper-parameters inherent in FCM based methods, often have a preference for specific distributions, such as the Gaussian distribution. In this paper, we propose a novel FCM based clustering model that is capable of automatically learning an appropriate membership degree hyper-parameter value and handling data with non-Gaussian clusters. Moreover, by removing the graph embedding regularization, the proposed FCM model can degenerate into the simplified generalized Gaussian mixture model. Therefore, the proposed FCM model can be also seen as the generalized Gaussian mixture model with graph embedding. Extensive experiments are conducted on both synthetic and real-world datasets to demonstrate the effectiveness of the proposed model.

Haorui Xiang, Zhichang Wu, Guoxu Li et al.

Ordinal regression is a specialized supervised problem where the labels show an inherent order. The order distinguishes it from normal multi-class problem. Support Vector Ordinal Regression, as an outstanding ordinal regression model, is widely used in many ordinal regression tasks. However, like most supervised learning algorithms, the design of SVOR is based on the assumption that the training data are real and reliable, which is difficult to satisfy in real-world data. In many practical applications, outliers are frequently present in the training set, potentially leading to misguide the learning process, such that the performance is non-optimal. In this paper, we propose a novel capped $\ell_{p}$-norm loss function that is theoretically robust to both light and heavy outliers. The capped $\ell_{p}$-norm loss can help the model detect and eliminate outliers during training process. Adhering to this concept, we introduce a new model, Capped $\ell_{p}$-Norm Support Vector Ordinal Regression(CSVOR), that is robust to outliers. CSVOR uses a weight matrix to detect and eliminate outliers during the training process to improve the robustness to outliers. Moreover, a Re-Weighted algorithm algorithm which is illustrated convergence by our theoretical results is proposed to effectively minimize the corresponding problem. Extensive experimental results demonstrate that our model outperforms state-of-the-art(SOTA) methods, particularly in the presence of outliers.

Lei Xu, Lei Chen, Rong Wang et al.

Feature selection (FS) plays an important role in machine learning, which extracts important features and accelerates the learning process. In this paper, we propose a deep FS method that simultaneously conducts feature selection and differentiable $ k $-NN graph learning based on the Dirichlet Energy. The Dirichlet Energy identifies important features by measuring their smoothness on the graph structure, and facilitates the learning of a new graph that reflects the inherent structure in new feature subspace. We employ Optimal Transport theory to address the non-differentiability issue of learning $ k $-NN graphs in neural networks, which theoretically makes our method applicable to other graph neural networks for dynamic graph learning. Furthermore, the proposed framework is interpretable, since all modules are designed algorithmically. We validate the effectiveness of our model with extensive experiments on both synthetic and real-world datasets.

Bo Jiang, Fei Xu, Ziyan Zhang et al.

To alleviate the local receptive issue of GCN, Transformers have been exploited to capture the long range dependences of nodes for graph data representation and learning. However, existing graph Transformers generally employ regular self-attention module for all node-to-node message passing which needs to learn the affinities/relationships between all node's pairs, leading to high computational cost issue. Also, they are usually sensitive to graph noises. To overcome this issue, we propose a novel graph Transformer architecture, termed Anchor Graph Transformer (AGFormer), by leveraging an anchor graph model. To be specific, AGFormer first obtains some representative anchors and then converts node-to-node message passing into anchor-to-anchor and anchor-to-node message passing process. Thus, AGFormer performs much more efficiently and also robustly than regular node-to-node Transformers. Extensive experiments on several benchmark datasets demonstrate the effectiveness and benefits of proposed AGFormer.

Peican Zhu, Xin Hou, Keke Tang et al.

Along with the flourish of the information age, massive amounts of data are generated day by day. Due to the large-scale and high-dimensional characteristics of these data, it is often difficult to achieve better decision-making in practical applications. Therefore, an efficient big data analytics method is urgently needed. For feature engineering, feature selection seems to be an important research content in which is anticipated to select "excellent" features from candidate ones. Different functions can be realized through feature selection, such as dimensionality reduction, model effect improvement, and model performance improvement. In many classification tasks, researchers found that data seem to be usually close to each other if they are from the same class; thus, local compactness is of great importance for the evaluation of a feature. In this manuscript, we propose a fast unsupervised feature selection method, named as, Compactness Score (CSUFS), to select desired features. To demonstrate the efficiency and accuracy, several data sets are chosen with extensive experiments being performed. Later, the effectiveness and superiority of our method are revealed through addressing clustering tasks. Here, the performance is indicated by several well-known evaluation metrics, while the efficiency is reflected by the corresponding running time. As revealed by the simulation results, our proposed algorithm seems to be more accurate and efficient compared with existing algorithms.

Kun Song, Junwei Han, Gong Cheng et al.

In this paper, we reveal that metric learning would suffer from serious inseparable problem if without informative sample mining. Since the inseparable samples are often mixed with hard samples, current informative sample mining strategies used to deal with inseparable problem may bring up some side-effects, such as instability of objective function, etc. To alleviate this problem, we propose a novel distance metric learning algorithm, named adaptive neighborhood metric learning (ANML). In ANML, we design two thresholds to adaptively identify the inseparable similar and dissimilar samples in the training procedure, thus inseparable sample removing and metric parameter learning are implemented in the same procedure. Due to the non-continuity of the proposed ANML, we develop an ingenious function, named \emph{log-exp mean function} to construct a continuous formulation to surrogate it, which can be efficiently solved by the gradient descent method. Similar to Triplet loss, ANML can be used to learn both the linear and deep embeddings. By analyzing the proposed method, we find it has some interesting properties. For example, when ANML is used to learn the linear embedding, current famous metric learning algorithms such as the large margin nearest neighbor (LMNN) and neighbourhood components analysis (NCA) are the special cases of the proposed ANML by setting the parameters different values. When it is used to learn deep features, the state-of-the-art deep metric learning algorithms such as Triplet loss, Lifted structure loss, and Multi-similarity loss become the special cases of ANML. Furthermore, the \emph{log-exp mean function} proposed in our method gives a new perspective to review the deep metric learning methods such as Prox-NCA and N-pairs loss. At last, promising experimental results demonstrate the effectiveness of the proposed method.

Wei Chang, Feiping Nie, Rong Wang et al.

Multi-task learning has been observed by many researchers, which supposes that different tasks can share a low-rank common yet latent subspace. It means learning multiple tasks jointly is better than learning them independently. In this paper, we propose two novel multi-task learning formulations based on two regularization terms, which can learn the optimal shared latent subspace by minimizing the exactly $k$ minimal singular values. The proposed regularization terms are the more tight approximations of rank minimization than trace norm. But it's an NP-hard problem to solve the exact rank minimization problem. Therefore, we design a novel re-weighted based iterative strategy to solve our models, which can tactically handle the exact rank minimization problem by setting a large penalizing parameter. Experimental results on benchmark datasets demonstrate that our methods can correctly recover the low-rank structure shared across tasks, and outperform related multi-task learning methods.

Rong Wang, Yihang Lu, Qianrong Zhang et al.

In recent years, hyperspectral anomaly detection (HAD) has become an active topic and plays a significant role in military and civilian fields. As a classic HAD method, the collaboration representation-based detector (CRD) has attracted extensive attention and in-depth research. Despite the good performance of the CRD method, its computational cost mainly arising from the sliding dual window strategy is too high for wide applications. Moreover, it takes multiple repeated tests to determine the size of the dual window, which needs to be reset once the dataset changes and cannot be identified in advance with prior knowledge. To alleviate this problem, we proposed a novel ensemble and random collaborative representation-based detector (ERCRD) for HAD, which comprises two closely related stages. Firstly, we process the random sub-sampling on CRD (RCRD) to gain several detection results instead of the sliding dual window strategy, which significantly reduces the computational complexity and makes it more feasible in practical applications. Secondly, ensemble learning is employed to refine the multiple results of RCRD, which act as various "experts" providing abundant complementary information to better target different anomalies. Such two stages form an organic and theoretical detector, which can not only improve the accuracy and stability of HAD methods but also enhance its generalization ability. Experiments on four real hyperspectral datasets exhibit the accuracy and efficiency of this proposed ERCRD method compared with ten state-of-the-art HAD methods.

Zhengxin Li, Feiping Nie, Jintang Bian et al.

In the field of data mining, how to deal with high-dimensional data is an inevitable problem. Unsupervised feature selection has attracted more and more attention because it does not rely on labels. The performance of spectral-based unsupervised methods depends on the quality of constructed similarity matrix, which is used to depict the intrinsic structure of data. However, real-world data contain a large number of noise samples and features, making the similarity matrix constructed by original data cannot be completely reliable. Worse still, the size of similarity matrix expands rapidly as the number of samples increases, making the computational cost increase significantly. Inspired by principal component analysis, we propose a simple and efficient unsupervised feature selection method, by combining reconstruction error with $l_{2,p}$-norm regularization. The projection matrix, which is used for feature selection, is learned by minimizing the reconstruction error under the sparse constraint. Then, we present an efficient optimization algorithm to solve the proposed unsupervised model, and analyse the convergence and computational complexity of the algorithm theoretically. Finally, extensive experiments on real-world data sets demonstrate the effectiveness of our proposed method.

Caixia Yan, Xiaojun Chang, Minnan Luo et al.

Linear discriminant analysis (LDA) is a popular technique to learn the most discriminative features for multi-class classification. A vast majority of existing LDA algorithms are prone to be dominated by the class with very large deviation from the others, i.e., edge class, which occurs frequently in multi-class classification. First, the existence of edge classes often makes the total mean biased in the calculation of between-class scatter matrix. Second, the exploitation of l2-norm based between-class distance criterion magnifies the extremely large distance corresponding to edge class. In this regard, a novel self-weighted robust LDA with l21-norm based pairwise between-class distance criterion, called SWRLDA, is proposed for multi-class classification especially with edge classes. SWRLDA can automatically avoid the optimal mean calculation and simultaneously learn adaptive weights for each class pair without setting any additional parameter. An efficient re-weighted algorithm is exploited to derive the global optimum of the challenging l21-norm maximization problem. The proposed SWRLDA is easy to implement, and converges fast in practice. Extensive experiments demonstrate that SWRLDA performs favorably against other compared methods on both synthetic and real-world datasets, while presenting superior computational efficiency in comparison with other techniques.

Xuesong Wang, Lina Yao, Xianzhi Wang et al.

Neural Processes (NPs) families encode distributions over functions to a latent representation, given context data, and decode posterior mean and variance at unknown locations. Since mean and variance are derived from the same latent space, they may fail on out-of-domain tasks where fluctuations in function values amplify the model uncertainty. We present a new member named Neural Processes with Position-Relevant-Only Variances (NP-PROV). NP-PROV hypothesizes that a target point close to a context point has small uncertainty, regardless of the function value at that position. The resulting approach derives mean and variance from a function-value-related space and a position-related-only latent space separately. Our evaluation on synthetic and real-world datasets reveals that NP-PROV can achieve state-of-the-art likelihood while retaining a bounded variance when drifts exist in the function value.

Zhe Liu, Yun Li, Lina Yao et al.

Conventional multi-view clustering methods seek for a view consensus through minimizing the pairwise discrepancy between the consensus and subviews. However, the pairwise comparison cannot portray the inter-view relationship precisely if some of the subviews can be further agglomerated. To address the above challenge, we propose the agglomerative analysis to approximate the optimal consensus view, thereby describing the subview relationship within a view structure. We present Agglomerative Neural Network (ANN) based on Constrained Laplacian Rank to cluster multi-view data directly while avoiding a dedicated postprocessing step (e.g., using K-means). We further extend ANN with learnable data space to handle data of complex scenarios. Our evaluations against several state-of-the-art multi-view clustering approaches on four popular datasets show the promising view-consensus analysis ability of ANN. We further demonstrate ANN's capability in analyzing complex view structures and extensibility in our case study and explain its robustness and effectiveness of data-driven modifications.

Di Hu, Zheng Wang, Haoyi Xiong et al.

Associating sound and its producer in complex audiovisual scene is a challenging task, especially when we are lack of annotated training data. In this paper, we present a flexible audiovisual model that introduces a soft-clustering module as the audio and visual content detector, and regards the pervasive property of audiovisual concurrency as the latent supervision for inferring the correlation among detected contents. To ease the difficulty of audiovisual learning, we propose a novel curriculum learning strategy that trains the model from simple to complex scene. We show that such ordered learning procedure rewards the model the merits of easy training and fast convergence. Meanwhile, our audiovisual model can also provide effective unimodal representation and cross-modal alignment performance. We further deploy the well-trained model into practical audiovisual sound localization and separation task. We show that our localization model significantly outperforms existing methods, based on which we show comparable performance in sound separation without referring external visual supervision. Our video demo can be found at https://youtu.be/kuClfGG0cFU.

Xia Wu, Xueyuan Xu, Jianhong Liu et al.

Effective features can improve the performance of a model, which can thus help us understand the characteristics and underlying structure of complex data. Previous feature selection methods usually cannot keep more local structure information. To address the defects previously mentioned, we propose a novel supervised orthogonal least square regression model with feature weighting for feature selection. The optimization problem of the objection function can be solved by employing generalized power iteration (GPI) and augmented Lagrangian multiplier (ALM) methods. Experimental results show that the proposed method can more effectively reduce the feature dimensionality and obtain better classification results than traditional feature selection methods. The convergence of our iterative method is proved as well. Consequently, the effectiveness and superiority of the proposed method are verified both theoretically and experimentally.

Jinglin Xu, Junwei Han, Mingliang Xu et al.

Clustering is an effective technique in data mining to group a set of objects in terms of some attributes. Among various clustering approaches, the family of K-Means algorithms gains popularity due to simplicity and efficiency. However, most of existing K-Means based clustering algorithms cannot deal with outliers well and are difficult to efficiently solve the problem embedded the $L_0$-norm constraint. To address the above issues and improve the performance of clustering significantly, we propose a novel clustering algorithm, named REFCMFS, which develops a $L_{2,1}$-norm robust loss as the data-driven item and imposes a $L_0$-norm constraint on the membership matrix to make the model more robust and sparse flexibly. In particular, REFCMFS designs a new way to simplify and solve the $L_0$-norm constraint without any approximate transformation by absorbing $\|\cdot\|_0$ into the objective function through a ranking function. These improvements not only make REFCMFS efficiently obtain more promising performance but also provide a new tractable and skillful optimization method to solve the problem embedded the $L_0$-norm constraint. Theoretical analyses and extensive experiments on several public datasets demonstrate the effectiveness and rationality of our proposed REFCMFS method.

Feiping Nie, Zhanxuan Hu, Xiaoqian Wang et al.

This work aims at solving the problems with intractable sparsity-inducing norms that are often encountered in various machine learning tasks, such as multi-task learning, subspace clustering, feature selection, robust principal component analysis, and so on. Specifically, an Iteratively Re-Weighted method (IRW) with solid convergence guarantee is provided. We investigate its convergence speed via numerous experiments on real data. Furthermore, in order to validate the practicality of IRW, we use it to solve a concrete robust feature selection model with complicated objective function. The experimental results show that the model coupled with proposed optimization method outperforms alternative methods significantly.

Feiping Nie, Hua Wang, Zheng Wang et al.

As one of the most popular linear subspace learning methods, the Linear Discriminant Analysis (LDA) method has been widely studied in machine learning community and applied to many scientific applications. Traditional LDA minimizes the ratio of squared L2-norms, which is sensitive to outliers. In recent research, many L1-norm based robust Principle Component Analysis methods were proposed to improve the robustness to outliers. However, due to the difficulty of L1-norm ratio optimization, so far there is no existing work to utilize sparsity-inducing norms for LDA objective. In this paper, we propose a novel robust linear discriminant analysis method based on the L1,2-norm ratio minimization. Minimizing the L1,2-norm ratio is a much more challenging problem than the traditional methods, and there is no existing optimization algorithm to solve such non-smooth terms ratio problem. We derive a new efficient algorithm to solve this challenging problem, and provide a theoretical analysis on the convergence of our algorithm. The proposed algorithm is easy to implement, and converges fast in practice. Extensive experiments on both synthetic data and nine real benchmark data sets show the effectiveness of the proposed robust LDA method.

Feiping Nie, Jing Li, Xuelong Li

Exploiting different representations, or views, of the same object for better clustering has become very popular these days, which is conventionally called multi-view clustering. Generally, it is essential to measure the importance of each individual view, due to some noises, or inherent capacities in description. Many previous works model the view importance as weight, which is simple but effective empirically. In this paper, instead of following the traditional thoughts, we propose a new weight learning paradigm in context of multi-view clustering in virtue of the idea of re-weighted approach, and we theoretically analyze its working mechanism. Meanwhile, as a carefully achieved example, all of the views are connected by exploring a unified Laplacian rank constrained graph, which will be a representative method to compare with other weight learning approaches in experiments. Furthermore, the proposed weight learning strategy is much suitable for multi-view data, and it can be naturally integrated with many existing clustering learners. According to the numerical experiments, the proposed intrinsic weight learning approach is proved effective and practical to use in multi-view clustering.

Lai Tian, Feiping Nie, Xuelong Li

This paper presents new algorithms to solve the feature-sparsity constrained PCA problem (FSPCA), which performs feature selection and PCA simultaneously. Existing optimization methods for FSPCA require data distribution assumptions and are lack of global convergence guarantee. Though the general FSPCA problem is NP-hard, we show that, for a low-rank covariance, FSPCA can be solved globally (Algorithm 1). Then, we propose another strategy (Algorithm 2) to solve FSPCA for the general covariance by iteratively building a carefully designed proxy. We prove theoretical guarantees on approximation and convergence for the new algorithms. Experimental results show the promising performance of the new algorithms compared with the state-of-the-arts on both synthetic and real-world datasets.

Di Hu, Dong Wang, Xuelong Li et al.

Visual-to-auditory sensory substitution devices can assist the blind in sensing the visual environment by translating the visual information into a sound pattern. To improve the translation quality, the task performances of the blind are usually employed to evaluate different encoding schemes. In contrast to the toilsome human-based assessment, we argue that machine model can be also developed for evaluation, and more efficient. To this end, we firstly propose two distinct cross-modal perception model w.r.t. the late-blind and congenitally-blind cases, which aim to generate concrete visual contents based on the translated sound. To validate the functionality of proposed models, two novel optimization strategies w.r.t. the primary encoding scheme are presented. Further, we conduct sets of human-based experiments to evaluate and compare them with the conducted machine-based assessments in the cross-modal generation task. Their highly consistent results w.r.t. different encoding schemes indicate that using machine model to accelerate optimization evaluation and reduce experimental cost is feasible to some extent, which could dramatically promote the upgrading of encoding scheme then help the blind to improve their visual perception ability.

Fei Wang, Zhongheng Li, Fang He et al.

The AdaBoost algorithm has the superiority of resisting overfitting. Understanding the mysteries of this phenomena is a very fascinating fundamental theoretical problem. Many studies are devoted to explaining it from statistical view and margin theory. In this paper, we illustrate it from feature learning viewpoint, and propose the AdaBoost+SVM algorithm, which can explain the resistant to overfitting of AdaBoost directly and easily to understand. Firstly, we adopt the AdaBoost algorithm to learn the base classifiers. Then, instead of directly weighted combination the base classifiers, we regard them as features and input them to SVM classifier. With this, the new coefficient and bias can be obtained, which can be used to construct the final classifier. We explain the rationality of this and illustrate the theorem that when the dimension of these features increases, the performance of SVM would not be worse, which can explain the resistant to overfitting of AdaBoost.

Di Hu, Feiping Nie, Xuelong Li

Multiple modalities can provide more valuable information than single one by describing the same contents in various ways. Hence, it is highly expected to learn effective joint representation by fusing the features of different modalities. However, previous methods mainly focus on fusing the shallow features or high-level representations generated by unimodal deep networks, which only capture part of the hierarchical correlations across modalities. In this paper, we propose to densely integrate the representations by greedily stacking multiple shared layers between different modality-specific networks, which is named as Dense Multimodal Fusion (DMF). The joint representations in different shared layers can capture the correlations in different levels, and the connection between shared layers also provides an efficient way to learn the dependence among hierarchical correlations. These two properties jointly contribute to the multiple learning paths in DMF, which results in faster convergence, lower training loss, and better performance. We evaluate our model on three typical multimodal learning tasks, including audiovisual speech recognition, cross-modal retrieval, and multimodal classification. The noticeable performance in the experiments demonstrates that our model can learn more effective joint representation.

Di Hu, Feiping Nie, Xuelong Li

The conventional supervised hashing methods based on classification do not entirely meet the requirements of hashing technique, but Linear Discriminant Analysis (LDA) does. In this paper, we propose to perform a revised LDA objective over deep networks to learn efficient hashing codes in a truly end-to-end fashion. However, the complicated eigenvalue decomposition within each mini-batch in every epoch has to be faced with when simply optimizing the deep network w.r.t. the LDA objective. In this work, the revised LDA objective is transformed into a simple least square problem, which naturally overcomes the intractable problems and can be easily solved by the off-the-shelf optimizer. Such deep extension can also overcome the weakness of LDA Hashing in the limited linear projection and feature learning. Amounts of experiments are conducted on three benchmark datasets. The proposed Deep LDA Hashing shows nearly 70 points improvement over the conventional one on the CIFAR-10 dataset. It also beats several state-of-the-art methods on various metrics.

Zhanxuan Hu, Feiping Nie, Rong Wang et al.

Low rank regularization, in essence, involves introducing a low rank or approximately low rank assumption for matrix we aim to learn, which has achieved great success in many fields including machine learning, data mining and computer version. Over the last decade, much progress has been made in theories and practical applications. Nevertheless, the intersection between them is very slight. In order to construct a bridge between practical applications and theoretical research, in this paper we provide a comprehensive survey for low rank regularization. We first review several traditional machine learning models using low rank regularization, and then show their (or their variants) applications in solving practical issues, such as non-rigid structure from motion and image denoising. Subsequently, we summarize the regularizers and optimization methods that achieve great success in traditional machine learning tasks but are rarely seen in solving practical issues. Finally, we provide a discussion and comparison for some representative regularizers including convex and non-convex relaxations. Extensive experimental results demonstrate that non-convex regularizers can provide a large advantage over the nuclear norm, the regularizer widely used in solving practical issues.

Di Hu, Feiping Nie, Xuelong Li

The seen birds twitter, the running cars accompany with noise, etc. These naturally audiovisual correspondences provide the possibilities to explore and understand the outside world. However, the mixed multiple objects and sounds make it intractable to perform efficient matching in the unconstrained environment. To settle this problem, we propose to adequately excavate audio and visual components and perform elaborate correspondence learning among them. Concretely, a novel unsupervised audiovisual learning model is proposed, named as \Deep Multimodal Clustering (DMC), that synchronously performs sets of clustering with multimodal vectors of convolutional maps in different shared spaces for capturing multiple audiovisual correspondences. And such integrated multimodal clustering network can be effectively trained with max-margin loss in the end-to-end fashion. Amounts of experiments in feature evaluation and audiovisual tasks are performed. The results demonstrate that DMC can learn effective unimodal representation, with which the classifier can even outperform human performance. Further, DMC shows noticeable performance in sound localization, multisource detection, and audiovisual understanding.