arXiv subjects

Chun-Guang Li

Publications and source records attributed to Chun-Guang Li.

28 records · Page 2Linked to original sources

arXiv2020

Is an Affine Constraint Needed for Affine Subspace Clustering?

Subspace clustering methods based on expressing each data point as a linear combination of other data points have achieved great success in computer vision applications such as motion segmentation, face and digit clustering. In face clustering, the subspaces are linear and subspace clustering methods can be applied directly. In motion segmentation, the subspaces are affine and an additional affine constraint on the coefficients is often enforced. However, since affine subspaces can always be embedded into linear subspaces of one extra dimension, it is unclear if the affine constraint is really necessary. This paper shows, both theoretically and empirically, that when the dimension of the ambient space is high relative to the sum of the dimensions of the affine subspaces, the affine constraint has a negligible effect on clustering performance. Specifically, our analysis provides conditions that guarantee the correctness of affine subspace clustering methods both with and without the affine constraint, and shows that these conditions are satisfied for high-dimensional data. Underlying our analysis is the notion of affinely independent subspaces, which not only provides geometrically interpretable correctness conditions, but also clarifies the relationships between existing results for affine subspace clustering.

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arXiv2020

Stochastic Sparse Subspace Clustering

State-of-the-art subspace clustering methods are based on self-expressive model, which represents each data point as a linear combination of other data points. By enforcing such representation to be sparse, sparse subspace clustering is guaranteed to produce a subspace-preserving data affinity where two points are connected only if they are from the same subspace. On the other hand, however, data points from the same subspace may not be well-connected, leading to the issue of over-segmentation. We introduce dropout to address the issue of over-segmentation, which is based on randomly dropping out data points in self-expressive model. In particular, we show that dropout is equivalent to adding a squared $\ell_2$ norm regularization on the representation coefficients, therefore induces denser solutions. Then, we reformulate the optimization problem as a consensus problem over a set of small-scale subproblems. This leads to a scalable and flexible sparse subspace clustering approach, termed Stochastic Sparse Subspace Clustering, which can effectively handle large scale datasets. Extensive experiments on synthetic data and real world datasets validate the efficiency and effectiveness of our proposal.

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arXiv2019

Self-Supervised Convolutional Subspace Clustering Network

Subspace clustering methods based on data self-expression have become very popular for learning from data that lie in a union of low-dimensional linear subspaces. However, the applicability of subspace clustering has been limited because practical visual data in raw form do not necessarily lie in such linear subspaces. On the other hand, while Convolutional Neural Network (ConvNet) has been demonstrated to be a powerful tool for extracting discriminative features from visual data, training such a ConvNet usually requires a large amount of labeled data, which are unavailable in subspace clustering applications. To achieve simultaneous feature learning and subspace clustering, we propose an end-to-end trainable framework, called Self-Supervised Convolutional Subspace Clustering Network (S$^2$ConvSCN), that combines a ConvNet module (for feature learning), a self-expression module (for subspace clustering) and a spectral clustering module (for self-supervision) into a joint optimization framework. Particularly, we introduce a dual self-supervision that exploits the output of spectral clustering to supervise the training of the feature learning module (via a classification loss) and the self-expression module (via a spectral clustering loss). Our experiments on four benchmark datasets show the effectiveness of the dual self-supervision and demonstrate superior performance of our proposed approach.

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arXiv2018

On Geometric Analysis of Affine Sparse Subspace Clustering

Sparse subspace clustering (SSC) is a state-of-the-art method for segmenting a set of data points drawn from a union of subspaces into their respective subspaces. It is now well understood that SSC produces subspace-preserving data affinity under broad geometric conditions but suffers from a connectivity issue. In this paper, we develop a novel geometric analysis for a variant of SSC, named affine SSC (ASSC), for the problem of clustering data from a union of affine subspaces. Our contributions include a new concept called affine independence for capturing the arrangement of a collection of affine subspaces. Under the affine independence assumption, we show that ASSC is guaranteed to produce subspace-preserving affinity. Moreover, inspired by the phenomenon that the $\ell_1$ regularization no longer induces sparsity when the solution is nonnegative, we further show that subspace-preserving recovery can be achieved under much weaker conditions for all data points other than the extreme points of samples from each subspace. In addition, we confirm a curious observation that the affinity produced by ASSC may be subspace-dense---which could guarantee the subspace-preserving affinity of ASSC to produce correct clustering under rather weak conditions. We validate the theoretical findings on carefully designed synthetic data and evaluate the performance of ASSC on several real data sets.

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arXiv2018

Constrained Sparse Subspace Clustering with Side-Information

Subspace clustering refers to the problem of segmenting high dimensional data drawn from a union of subspaces into the respective subspaces. In some applications, partial side-information to indicate "must-link" or "cannot-link" in clustering is available. This leads to the task of subspace clustering with side-information. However, in prior work the supervision value of the side-information for subspace clustering has not been fully exploited. To this end, in this paper, we present an enhanced approach for constrained subspace clustering with side-information, termed Constrained Sparse Subspace Clustering plus (CSSC+), in which the side-information is used not only in the stage of learning an affinity matrix but also in the stage of spectral clustering. Moreover, we propose to estimate clustering accuracy based on the partial side-information and theoretically justify the connection to the ground-truth clustering accuracy in terms of the Rand index. We conduct experiments on three cancer gene expression datasets to validate the effectiveness of our proposals.

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arXiv2018

Dual Attention Matching Network for Context-Aware Feature Sequence based Person Re-Identification

Typical person re-identification (ReID) methods usually describe each pedestrian with a single feature vector and match them in a task-specific metric space. However, the methods based on a single feature vector are not sufficient enough to overcome visual ambiguity, which frequently occurs in real scenario. In this paper, we propose a novel end-to-end trainable framework, called Dual ATtention Matching network (DuATM), to learn context-aware feature sequences and perform attentive sequence comparison simultaneously. The core component of our DuATM framework is a dual attention mechanism, in which both intra-sequence and inter-sequence attention strategies are used for feature refinement and feature-pair alignment, respectively. Thus, detailed visual cues contained in the intermediate feature sequences can be automatically exploited and properly compared. We train the proposed DuATM network as a siamese network via a triplet loss assisted with a de-correlation loss and a cross-entropy loss. We conduct extensive experiments on both image and video based ReID benchmark datasets. Experimental results demonstrate the significant advantages of our approach compared to the state-of-the-art methods.

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arXiv2017

Structured Sparse Subspace Clustering: A Joint Affinity Learning and Subspace Clustering Framework

Subspace clustering refers to the problem of segmenting data drawn from a union of subspaces. State-of-the-art approaches for solving this problem follow a two-stage approach. In the first step, an affinity matrix is learned from the data using sparse or low-rank minimization techniques. In the second step, the segmentation is found by applying spectral clustering to this affinity. While this approach has led to state-of-the-art results in many applications, it is sub-optimal because it does not exploit the fact that the affinity and the segmentation depend on each other. In this paper, we propose a joint optimization framework --- Structured Sparse Subspace Clustering (S$^3$C) --- for learning both the affinity and the segmentation. The proposed S$^3$C framework is based on expressing each data point as a structured sparse linear combination of all other data points, where the structure is induced by a norm that depends on the unknown segmentation. Moreover, we extend the proposed S$^3$C framework into Constrained Structured Sparse Subspace Clustering (CS$^3$C) in which available partial side-information is incorporated into the stage of learning the affinity. We show that both the structured sparse representation and the segmentation can be found via a combination of an alternating direction method of multipliers with spectral clustering. Experiments on a synthetic data set, the Extended Yale B data set, the Hopkins 155 motion segmentation database, and three cancer data sets demonstrate the effectiveness of our approach.

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arXiv2016

Oracle Based Active Set Algorithm for Scalable Elastic Net Subspace Clustering

State-of-the-art subspace clustering methods are based on expressing each data point as a linear combination of other data points while regularizing the matrix of coefficients with $\ell_1$, $\ell_2$ or nuclear norms. $\ell_1$ regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no connections between points from different subspaces) under broad theoretical conditions, but the clusters may not be connected. $\ell_2$ and nuclear norm regularization often improve connectivity, but give a subspace-preserving affinity only for independent subspaces. Mixed $\ell_1$, $\ell_2$ and nuclear norm regularizations offer a balance between the subspace-preserving and connectedness properties, but this comes at the cost of increased computational complexity. This paper studies the geometry of the elastic net regularizer (a mixture of the $\ell_1$ and $\ell_2$ norms) and uses it to derive a provably correct and scalable active set method for finding the optimal coefficients. Our geometric analysis also provides a theoretical justification and a geometric interpretation for the balance between the connectedness (due to $\ell_2$ regularization) and subspace-preserving (due to $\ell_1$ regularization) properties for elastic net subspace clustering. Our experiments show that the proposed active set method not only achieves state-of-the-art clustering performance, but also efficiently handles large-scale datasets.

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arXiv2015

HEp-2 Cell Classification via Fusing Texture and Shape Information

Indirect Immunofluorescence (IIF) HEp-2 cell image is an effective evidence for diagnosis of autoimmune diseases. Recently computer-aided diagnosis of autoimmune diseases by IIF HEp-2 cell classification has attracted great attention. However the HEp-2 cell classification task is quite challenging due to large intra-class variation and small between-class variation. In this paper we propose an effective and efficient approach for the automatic classification of IIF HEp-2 cell image by fusing multi-resolution texture information and richer shape information. To be specific, we propose to: a) capture the multi-resolution texture information by a novel Pairwise Rotation Invariant Co-occurrence of Local Gabor Binary Pattern (PRICoLGBP) descriptor, b) depict the richer shape information by using an Improved Fisher Vector (IFV) model with RootSIFT features which are sampled from large image patches in multiple scales, and c) combine them properly. We evaluate systematically the proposed approach on the IEEE International Conference on Pattern Recognition (ICPR) 2012, IEEE International Conference on Image Processing (ICIP) 2013 and ICPR 2014 contest data sets. The experimental results for the proposed methods significantly outperform the winners of ICPR 2012 and ICIP 2013 contest, and achieve comparable performance with the winner of the newly released ICPR 2014 contest.

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arXiv2015

Dynamic texture and scene classification by transferring deep image features

Dynamic texture and scene classification are two fundamental problems in understanding natural video content. Extracting robust and effective features is a crucial step towards solving these problems. However the existing approaches suffer from the sensitivity to either varying illumination, or viewpoint changing, or even camera motion, and/or the lack of spatial information. Inspired by the success of deep structures in image classification, we attempt to leverage a deep structure to extract feature for dynamic texture and scene classification. To tackle with the challenges in training a deep structure, we propose to transfer some prior knowledge from image domain to video domain. To be specific, we propose to apply a well-trained Convolutional Neural Network (ConvNet) as a mid-level feature extractor to extract features from each frame, and then form a representation of a video by concatenating the first and the second order statistics over the mid-level features. We term this two-level feature extraction scheme as a Transferred ConvNet Feature (TCoF). Moreover we explore two different implementations of the TCoF scheme, i.e., the \textit{spatial} TCoF and the \textit{temporal} TCoF, in which the mean-removed frames and the difference between two adjacent frames are used as the inputs of the ConvNet, respectively. We evaluate systematically the proposed spatial TCoF and the temporal TCoF schemes on three benchmark data sets, including DynTex, YUPENN, and Maryland, and demonstrate that the proposed approach yields superior performance.

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