Xuhui Huang

Graph Based Semi-supervised Non-negative Matrix Factorization for Document Clustering

Non-negative matrix factorization (NMF) approximates a non-negative matrix by the product of two low-rank matrices and achieves good performance in clustering. Recently, semi-supervised NMF (SS-NMF) further improves the performance by incorporating part of the labels of few samples into NMF. In this paper, we proposed a novel graph based SS-NMF (GSS-NMF). For each sample, GSS-NMF minimizes its distances to the same labeled samples and maximizes the distances against different labeled samples to incorporate the discriminative information. Since both labeled and unlabeled samples are embedded in the same reduced dimensional space, the discriminative information from the labeled samples is successfully transferred to the unlabeled samples, and thus it greatly improves the clustering performance. Since the traditional multiplicative update rule converges slowly, we applied the well-known projected gradient method to optimizing GSS-NMF and the proposed algorithm can be applied to optimizing other manifold regularized NMF efficiently. Experimental results on two popular document datasets, i.e., Reuters21578 and TDT-2, show that GSS-NMF outperforms the representative SS-NMF algorithms.

Symmetric Non-negative Matrix Factorization Based Link Partition Method for Overlapping Community Detection

Partitioning links rather than nodes is effective in overlapping community detection (OCD) on complex networks. However, it consumes high CPU and memory overheads because the volume of links is huge especially when the network is rather complex. In this paper, we proposes a symmetric non-negative matrix factorization (SNMF) based link partition method called SNMF-Link to overcome this deficiency. In particular, SNMF-Link represents data in a lower-dimensional space spanned by the node-link incidence matrix. By solving a lighter SNMF problem, SNMF-Link learns the clustering indicators of each links. Since traditional multiplicative update rule (MUR) based optimization algorithm for SNMF suffers from slow convergence, we applied the augmented Lagrangian method (ALM) to efficiently optimize SNMF. Experimental results show that SNMF-Link is much more efficient than the representative clustering algorithms without reducing the OCD performance.

Correntropy supervised non-negative matrix factorization

Non-negative matrix factorization (NMF) is a powerful dimension reduction method and has been widely used in many pattern recognition and computer vision problems. However, conventional NMF methods are neither robust enough as their loss functions are sensitive to outliers, nor discriminative because they completely ignore labels in a dataset. In this paper, we proposed a correntropy supervised NMF (CSNMF) to simultaneously overcome aforementioned deficiencies. In particular, CSNMF maximizes the correntropy between the data matrix and its reconstruction in low-dimensional space to inhibit outliers during learning the subspace, and narrows the minimizes the distances between coefficients of any two samples with the same class labels to enhance the subsequent classification performance. To solve CSNMF, we developed a multiplicative update rules and theoretically proved its convergence. Experimental results on popular face image datasets verify the effectiveness of CSNMF comparing with NMF, its supervised variants, and its robustified variants.

Overlapping community detection via link partition of asymmetric weighted graph

Link partition clusters edges of a complex network to discover its overlapping communities. Due to Its effectiveness, link partition has attracted much attentions from the network science community. However, since link partition assigns each edge of a network to unique community, it cannot detect the disjoint communities. To overcome this deficiency, this paper proposes a link partition on asymmetric weighted graph (LPAWG) method for detecting overlapping communities. Particularly, LPAWG divides each edge into two parts to distinguish the roles of connected nodes. This strategy biases edges to a specific node and helps assigning each node to its affiliated community. Since LPAWG introduces more edges than those in the original network, it cannot efficiently detect communities from some networks with relative large amount of edges. We therefore aggregate the line graph of LPAWG to shrink its scale. Experimental results of community detection on both synthetic datasets and the realworld networks show the effectiveness of LPAWG comparing with the representative methods.

Attention Focused Spatial Pyramid Pooling for Boxless Action Recognition in Still Images.

Existing approaches for still image based action recognition rely heavily on bounding boxes and could be restricted to specific applications with bounding boxes available. Thus, exploring the boxless action recognition in still images is very challenging for lack of any supervised knowledge. To address this issue, we propose an attention focused spatial pyramid pooling (SPP) network (AttSPP-net) free from the bounding boxes by jointly integrating the soft attention mechanism and SPP into a convolutional neural network. Particularly, soft attention mechanism automatically indicates relevant image regions to be an action. Besides, AttSPP-net further exploits SPP to boost the robustness to action deformation by capturing spatial structures among image pixels. Experiments on two public action recognition benchmark datasets including PASCAL VOC 2012 and Stanford-40 demonstrate that AttSPP-net can achieve promising results and even outweighs some methods based on ground-truth bounding boxes, and provides an alternative way towards practical applications.

Two-Dimensional Euler PCA for Face Recognition

Principal component analysis (PCA) projects data on the directions with maximal variances. Since PCA is quite effective in dimension reduction, it has been widely used in computer vision. However, conventional PCA suffers from following deficiencies: 1) it spends much computational costs to handle high-dimensional data, and 2) it cannot reveal the nonlinear relationship among different features of data. To overcome these deficiencies, this paper proposes an efficient two-dimensional Euler PCA (2D-ePCA) algorithm. Particularly, 2D-ePCA learns projection matrix on the 2D pixel matrix of each image without reshaping it into 1D long vector, and uncovers nonlinear relationships among features by mapping data onto complex representation. Since such 2D complex representation induces much smaller kernel matrix and principal subspaces, 2D-ePCA costs much less computational overheads than Euler PCA on large-scale dataset. Experimental results on popular face datasets show that 2D-ePCA outperforms the representative algorithms in terms of accuracy, computational overhead, and robustness.

Non-negative Low-Rank and Group-Sparse Matrix Factorization

Non-negative matrix factorization (NMF) has been a popular data analysis tool and has been widely applied in computer vision. However, conventional NMF methods cannot adaptively learn grouping structure from a dataset. This paper proposes a non-negative low-rank and group-sparse matrix factorization (NLRGS) method to overcome this deficiency. Particularly, NLRGS captures the relationships among examples by constraining rank of the coefficients meanwhile identifies the grouping structure via group sparsity regularization. By both constraints, NLRGS boosts NMF in both classification and clustering. However, NLRGS is difficult to be optimized because it needs to deal with the low-rank constraint. To relax such hard constraint, we approximate the low-rank constraint with the nuclear norm and then develop an optimization algorithm for NLRGS in the frame of augmented Lagrangian method(ALM). Experimental results of both face recognition and clustering on four popular face datasets demonstrate the effectiveness of NLRGS in quantities.

Single image defogging with single and multiple hybrid scattering model.

Image defogging (IDF) removes influences of fogs from an image to improve its quality. Since defogged images can significantly boost the performance of subsequent processing, IDF has attracted many attentions from the computer vision community. However, existing IDF algorithms are built on the assumption that light is scattered once by a grain. Since such assumption is violated if images are contaminated by dense haze or heavy fog, traditional IDF algorithms often fail in this situation. In this paper, we propose a hybrid image defogging (HIDF) algorithm to overcome this deficiency. In particular, HIDF applies the single scattering physics model (SSPM) to pixels dominated by single scattering of light, and applies the multiple scattering physics model (MSPM) to remaining pixels. To distinguish two types of pixels, HIDF utilizes the optical thickness of corresponding pixels. If optical thickness is smaller than a threshold that determines whether the single scattering or the multiple scattering dominates, HIDF applies the SSPM, and HIDF applies the MSPM otherwise. Experimental results on several popular foggy images demonstrate that HIDF competes with the state-of-the-art algorithms, and show the promise of HIDF for defogging heavily foggy images.

Nonnegative Constrained Graph Based Canonical Correlation Analysis for Multi-view Feature Learning

Understanding and analyzing multi-view data is a fundamental research topic of feature learning for a wide range of practical applications such as image classification. Canonical correlation analysis (CCA) is a popular unsupervised method of analyzing multi-view data, which captures common subspace of two groups of variable sets by maximizing the correlations between them. However, traditional CCA ignores the underlying geometric structure within dataset, which shows great power in describing data distribution, and thus fails in some tasks such as classification. To handle this limitation, this paper proposes an improved CCA variant of Nonnegative Constrained Graph regularized CCA (NCGCCA). Specifically, we improve CCA to NCGCCA with the following two contributions. Firstly, we develop a nonnegative constrained graph based self-representation to explore the underlying group-wise structure within dataset. Secondly, based on the proposed informative representation, we offer a graph embedding schema to incorporate the underlying structure into CCA. Experiments of image classification on four face datasets including Yale, ORL, UMIST, and YaleB demonstrate the efficacy of NCGCCA compared with existing baseline CCA methods.

Stacked Marginal Time Warping for Temporal Alignment

Time warping is the popular technique of temporally aligning two sequences and has successfully applied in temporal alignment tasks such as activity recognition. However, existing time warping methods suffer from limited representation ability because aligning process is performed on either raw sequences or the projected lower-dimensional features. In this paper, we propose a stacked time warping framework (STW) to learn layer-wise representation for temporal alignment in a stacked structure. By using this structure, STW gives higher flexibility than existing methods meanwhile unifies them into a deep architecture. Based on the proposed STW framework, we explore a stacked marginal time warping (SMTW) method by using marginal stacked denoising autoencoder (mSDA) as the regularization term which enables SMTW to marginalize out noises and learn layer-wise non-linear representations with the effective closed-form solution. Benefitting from the incorporation of mSDA, SMTW achieves better alignment performance and keeps comparable time efficiency with regular time warping methods. Experiments on both synthetic data and practical human activity recognition datasets demonstrate that SMTW is superior to the state-of-the-art time warping methods in quantity.