arXiv subjects

Guangcan Liu

Publications and source records attributed to Guangcan Liu.

36 records · Page 2Linked to original sources

arXiv2019

Flexible Auto-weighted Local-coordinate Concept Factorization: A Robust Framework for Unsupervised Clustering

Concept Factorization (CF) and its variants may produce inaccurate representation and clustering results due to the sensitivity to noise, hard constraint on the reconstruction error and pre-obtained approximate similarities. To improve the representation ability, a novel unsupervised Robust Flexible Auto-weighted Local-coordinate Concept Factorization (RFA-LCF) framework is proposed for clustering high-dimensional data. Specifically, RFA-LCF integrates the robust flexible CF by clean data space recovery, robust sparse local-coordinate coding and adaptive weighting into a unified model. RFA-LCF improves the representations by enhancing the robustness of CF to noise and errors, providing a flexible constraint on the reconstruction error and optimizing the locality jointly. For robust learning, RFA-LCF clearly learns a sparse projection to recover the underlying clean data space, and then the flexible CF is performed in the projected feature space. RFA-LCF also uses a L2,1-norm based flexible residue to encode the mismatch between the recovered data and its reconstruction, and uses the robust sparse local-coordinate coding to represent data using a few nearby basis concepts. For auto-weighting, RFA-LCF jointly preserves the manifold structures in the basis concept space and new coordinate space in an adaptive manner by minimizing the reconstruction errors on clean data, anchor points and coordinates. By updating the local-coordinate preserving data, basis concepts and new coordinates alternately, the representation abilities can be potentially improved. Extensive results on public databases show that RFA-LCF delivers the state-of-the-art clustering results compared with other related methods.

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arXiv2019

Robust Subspace Clustering with Compressed Data

Dimension reduction is widely regarded as an effective way for decreasing the computation, storage and communication loads of data-driven intelligent systems, leading to a growing demand for statistical methods that allow analysis (e.g., clustering) of compressed data. We therefore study in this paper a novel problem called compressive robust subspace clustering, which is to perform robust subspace clustering with the compressed data, and which is generated by projecting the original high-dimensional data onto a lower-dimensional subspace chosen at random. Given only the compressed data and sensing matrix, the proposed method, row space pursuit (RSP), recovers the authentic row space that gives correct clustering results under certain conditions. Extensive experiments show that RSP is distinctly better than the competing methods, in terms of both clustering accuracy and computational efficiency.

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arXiv2019

Learning Structured Twin-Incoherent Twin-Projective Latent Dictionary Pairs for Classification

In this paper, we extend the popular dictionary pair learning (DPL) into the scenario of twin-projective latent flexible DPL under a structured twin-incoherence. Technically, a novel framework called Twin-Projective Latent Flexible DPL (TP-DPL) is proposed, which minimizes the twin-incoherence constrained flexibly-relaxed reconstruction error to avoid the possible over-fitting issue and produce accurate reconstruction. In this setting, our TP-DPL integrates the twin-incoherence based latent flexible DPL and the joint embedding of codes as well as salient features by twin-projection into a unified model in an adaptive neighborhood-preserving manner. As a result, TP-DPL unifies the salient feature extraction, representation and classification. The twin-incoherence constraint on codes and features can explicitly ensure high intra-class compactness and inter-class separation over them. TP-DPL also integrates the adaptive weighting to preserve the local neighborhood of the coefficients and salient features within each class explicitly. For efficiency, TP-DPL uses Frobenius-norm and abandons the costly l0/l1-norm for group sparse representation. Another byproduct is that TP-DPL can directly apply the class-specific twin-projective reconstruction residual to compute the label of data. Extensive results on public databases show that TP-DPL can deliver the state-of-the-art performance.

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arXiv2019

Kernel-Induced Label Propagation by Mapping for Semi-Supervised Classification

Kernel methods have been successfully applied to the areas of pattern recognition and data mining. In this paper, we mainly discuss the issue of propagating labels in kernel space. A Kernel-Induced Label Propagation (Kernel-LP) framework by mapping is proposed for high-dimensional data classification using the most informative patterns of data in kernel space. The essence of Kernel-LP is to perform joint label propagation and adaptive weight learning in a transformed kernel space. That is, our Kernel-LP changes the task of label propagation from the commonly-used Euclidean space in most existing work to kernel space. The motivation of our Kernel-LP to propagate labels and learn the adaptive weights jointly by the assumption of an inner product space of inputs, i.e., the original linearly inseparable inputs may be mapped to be separable in kernel space. Kernel-LP is based on existing positive and negative LP model, i.e., the effects of negative label information are integrated to improve the label prediction power. Also, Kernel-LP performs adaptive weight construction over the same kernel space, so it can avoid the tricky process of choosing the optimal neighborhood size suffered in traditional criteria. Two novel and efficient out-of-sample approaches for our Kernel-LP to involve new test data are also presented, i.e., (1) direct kernel mapping and (2) kernel mapping-induced label reconstruction, both of which purely depend on the kernel matrix between training set and testing set. Owing to the kernel trick, our algorithms will be applicable to handle the high-dimensional real data. Extensive results on real datasets demonstrate the effectiveness of our approach.

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arXiv2019

Robust Unsupervised Flexible Auto-weighted Local-Coordinate Concept Factorization for Image Clustering

We investigate the high-dimensional data clustering problem by proposing a novel and unsupervised representation learning model called Robust Flexible Auto-weighted Local-coordinate Concept Factorization (RFA-LCF). RFA-LCF integrates the robust flexible CF, robust sparse local-coordinate coding and the adaptive reconstruction weighting learning into a unified model. The adaptive weighting is driven by including the joint manifold preserving constraints on the recovered clean data, basis concepts and new representation. Specifically, our RFA-LCF uses a L2,1-norm based flexible residue to encode the mismatch between clean data and its reconstruction, and also applies the robust adaptive sparse local-coordinate coding to represent the data using a few nearby basis concepts, which can make the factorization more accurate and robust to noise. The robust flexible factorization is also performed in the recovered clean data space for enhancing representations. RFA-LCF also considers preserving the local manifold structures of clean data space, basis concept space and the new coordinate space jointly in an adaptive manner way. Extensive comparisons show that RFA-LCF can deliver enhanced clustering results.

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arXiv2019

Scalable Block-Diagonal Locality-Constrained Projective Dictionary Learning

We propose a novel structured discriminative block-diagonal dictionary learning method, referred to as scalable Locality-Constrained Projective Dictionary Learning (LC-PDL), for efficient representation and classification. To improve the scalability by saving both training and testing time, our LC-PDL aims at learning a structured discriminative dictionary and a block-diagonal representation without using costly l0/l1-norm. Besides, it avoids extra time-consuming sparse reconstruction process with the well-trained dictionary for new sample as many existing models. More importantly, LC-PDL avoids using the complementary data matrix to learn the sub-dictionary over each class. To enhance the performance, we incorporate a locality constraint of atoms into the DL procedures to keep local information and obtain the codes of samples over each class separately. A block-diagonal discriminative approximation term is also derived to learn a discriminative projection to bridge data with their codes by extracting the special block-diagonal features from data, which can ensure the approximate coefficients to associate with its label information clearly. Then, a robust multiclass classifier is trained over extracted block-diagonal codes for accurate label predictions. Experimental results verify the effectiveness of our algorithm.

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arXiv2019

Joint Label Prediction based Semi-Supervised Adaptive Concept Factorization for Robust Data Representation

Constrained Concept Factorization (CCF) yields the enhanced representation ability over CF by incorporating label information as additional constraints, but it cannot classify and group unlabeled data appropriately. Minimizing the difference between the original data and its reconstruction directly can enable CCF to model a small noisy perturbation, but is not robust to gross sparse errors. Besides, CCF cannot preserve the manifold structures in new representation space explicitly, especially in an adaptive manner. In this paper, we propose a joint label prediction based Robust Semi-Supervised Adaptive Concept Factorization (RS2ACF) framework. To obtain robust representation, RS2ACF relaxes the factorization to make it simultaneously stable to small entrywise noise and robust to sparse errors. To enrich prior knowledge to enhance the discrimination, RS2ACF clearly uses class information of labeled data and more importantly propagates it to unlabeled data by jointly learning an explicit label indicator for unlabeled data. By the label indicator, RS2ACF can ensure the unlabeled data of the same predicted label to be mapped into the same class in feature space. Besides, RS2ACF incorporates the joint neighborhood reconstruction error over the new representations and predicted labels of both labeled and unlabeled data, so the manifold structures can be preserved explicitly and adaptively in the representation space and label space at the same time. Owing to the adaptive manner, the tricky process of determining the neighborhood size or kernel width can be avoided. Extensive results on public databases verify that our RS2ACF can deliver state-of-the-art data representation, compared with other related methods.

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arXiv2019

Differentiable Linearized ADMM

Recently, a number of learning-based optimization methods that combine data-driven architectures with the classical optimization algorithms have been proposed and explored, showing superior empirical performance in solving various ill-posed inverse problems, but there is still a scarcity of rigorous analysis about the convergence behaviors of learning-based optimization. In particular, most existing analyses are specific to unconstrained problems but cannot apply to the more general cases where some variables of interest are subject to certain constraints. In this paper, we propose Differentiable Linearized ADMM (D-LADMM) for solving the problems with linear constraints. Specifically, D-LADMM is a K-layer LADMM inspired deep neural network, which is obtained by firstly introducing some learnable weights in the classical Linearized ADMM algorithm and then generalizing the proximal operator to some learnable activation function. Notably, we rigorously prove that there exist a set of learnable parameters for D-LADMM to generate globally converged solutions, and we show that those desired parameters can be attained by training D-LADMM in a proper way. To the best of our knowledge, we are the first to provide the convergence analysis for the learning-based optimization method on constrained problems.

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arXiv2018

Matrix Recovery with Implicitly Low-Rank Data

In this paper, we study the problem of matrix recovery, which aims to restore a target matrix of authentic samples from grossly corrupted observations. Most of the existing methods, such as the well-known Robust Principal Component Analysis (RPCA), assume that the target matrix we wish to recover is low-rank. However, the underlying data structure is often non-linear in practice, therefore the low-rankness assumption could be violated. To tackle this issue, we propose a novel method for matrix recovery in this paper, which could well handle the case where the target matrix is low-rank in an implicit feature space but high-rank or even full-rank in its original form. Namely, our method pursues the low-rank structure of the target matrix in an implicit feature space. By making use of the specifics of an accelerated proximal gradient based optimization algorithm, the proposed method could recover the target matrix with non-linear structures from its corrupted version. Comprehensive experiments on both synthetic and real datasets demonstrate the superiority of our method.

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arXiv2017

Detection of Moving Object in Dynamic Background Using Gaussian Max-Pooling and Segmentation Constrained RPCA

Due to its efficiency and stability, Robust Principal Component Analysis (RPCA) has been emerging as a promising tool for moving object detection. Unfortunately, existing RPCA based methods assume static or quasi-static background, and thereby they may have trouble in coping with the background scenes that exhibit a persistent dynamic behavior. In this work, we shall introduce two techniques to fill in the gap. First, instead of using the raw pixel-value as features that are brittle in the presence of dynamic background, we devise a so-called Gaussian max-pooling operator to estimate a "stable-value" for each pixel. Those stable-values are robust to various background changes and can therefore distinguish effectively the foreground objects from the background. Then, to obtain more accurate results, we further propose a Segmentation Constrained RPCA (SC-RPCA) model, which incorporates the temporal and spatial continuity in images into RPCA. The inference process of SC-RPCA is a group sparsity constrained nuclear norm minimization problem, which is convex and easy to solve. Experimental results on seven videos from the CDCNET 2014 database show the superior performance of the proposed method.

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arXiv2014

A Latent Clothing Attribute Approach for Human Pose Estimation

As a fundamental technique that concerns several vision tasks such as image parsing, action recognition and clothing retrieval, human pose estimation (HPE) has been extensively investigated in recent years. To achieve accurate and reliable estimation of the human pose, it is well-recognized that the clothing attributes are useful and should be utilized properly. Most previous approaches, however, require to manually annotate the clothing attributes and are therefore very costly. In this paper, we shall propose and explore a \emph{latent} clothing attribute approach for HPE. Unlike previous approaches, our approach models the clothing attributes as latent variables and thus requires no explicit labeling for the clothing attributes. The inference of the latent variables are accomplished by utilizing the framework of latent structured support vector machines (LSSVM). We employ the strategy of \emph{alternating direction} to train the LSSVM model: In each iteration, one kind of variables (e.g., human pose or clothing attribute) are fixed and the others are optimized. Our extensive experiments on two real-world benchmarks show the state-of-the-art performance of our proposed approach.

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arXiv2014

Unified Structured Learning for Simultaneous Human Pose Estimation and Garment Attribute Classification

In this paper, we utilize structured learning to simultaneously address two intertwined problems: human pose estimation (HPE) and garment attribute classification (GAC), which are valuable for a variety of computer vision and multimedia applications. Unlike previous works that usually handle the two problems separately, our approach aims to produce a jointly optimal estimation for both HPE and GAC via a unified inference procedure. To this end, we adopt a preprocessing step to detect potential human parts from each image (i.e., a set of "candidates") that allows us to have a manageable input space. In this way, the simultaneous inference of HPE and GAC is converted to a structured learning problem, where the inputs are the collections of candidate ensembles, the outputs are the joint labels of human parts and garment attributes, and the joint feature representation involves various cues such as pose-specific features, garment-specific features, and cross-task features that encode correlations between human parts and garment attributes. Furthermore, we explore the "strong edge" evidence around the potential human parts so as to derive more powerful representations for oriented human parts. Such evidences can be seamlessly integrated into our structured learning model as a kind of energy function, and the learning process could be performed by standard structured Support Vector Machines (SVM) algorithm. However, the joint structure of the two problems is a cyclic graph, which hinders efficient inference. To resolve this issue, we compute instead approximate optima by using an iterative procedure, where in each iteration the variables of one problem are fixed. In this way, satisfactory solutions can be efficiently computed by dynamic programming. Experimental results on two benchmark datasets show the state-of-the-art performance of our approach.

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arXiv2014

Recovery of Coherent Data via Low-Rank Dictionary Pursuit

The recently established RPCA method provides us a convenient way to restore low-rank matrices from grossly corrupted observations. While elegant in theory and powerful in reality, RPCA may be not an ultimate solution to the low-rank matrix recovery problem. Indeed, its performance may not be perfect even when data are strictly low-rank. This is because conventional RPCA ignores the clustering structures of the data which are ubiquitous in modern applications. As the number of cluster grows, the coherence of data keeps increasing, and accordingly, the recovery performance of RPCA degrades. We show that the challenges raised by coherent data (i.e., the data with high coherence) could be alleviated by Low-Rank Representation (LRR), provided that the dictionary in LRR is configured appropriately. More precisely, we mathematically prove that if the dictionary itself is low-rank then LRR is immune to the coherence parameter which increases with the underlying cluster number. This provides an elementary principle for dealing with coherent data. Subsequently, we devise a practical algorithm to obtain proper dictionaries in unsupervised environments. Our extensive experiments on randomly generated matrices verify our claims.

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arXiv2014

Advancing Matrix Completion by Modeling Extra Structures beyond Low-Rankness

A well-known method for completing low-rank matrices based on convex optimization has been established by Cand{è}s and Recht. Although theoretically complete, the method may not entirely solve the low-rank matrix completion problem. This is because the method captures only the low-rankness property which gives merely a rough constraint that the data points locate on some low-dimensional subspace, but generally ignores the extra structures which specify in more detail how the data points locate on the subspace. Whenever the geometric distribution of the data points is not uniform, the coherence parameters of data might be large and, accordingly, the method might fail even if the latent matrix we want to recover is fairly low-rank. To better handle non-uniform data, in this paper we propose a method termed Low-Rank Factor Decomposition (LRFD), which imposes an additional restriction that the data points must be represented as linear combinations of the bases in a dictionary constructed or learnt in advance. We show that LRFD can well handle non-uniform data, provided that the dictionary is configured properly: We mathematically prove that if the dictionary itself is low-rank then LRFD is immune to the coherence parameters which might be large on non-uniform data. This provides an elementary principle for learning the dictionary in LRFD and, naturally, leads to a practical algorithm for advancing matrix completion. Extensive experiments on randomly generated matrices and motion datasets show encouraging results.

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arXiv2014

Blind Image Deblurring by Spectral Properties of Convolution Operators

In this paper, we study the problem of recovering a sharp version of a given blurry image when the blur kernel is unknown. Previous methods often introduce an image-independent regularizer (such as Gaussian or sparse priors) on the desired blur kernel. We shall show that the blurry image itself encodes rich information about the blur kernel. Such information can be found through analyzing and comparing how the spectrum of an image as a convolution operator changes before and after blurring. Our analysis leads to an effective convex regularizer on the blur kernel which depends only on the given blurry image. We show that the minimizer of this regularizer guarantees to give good approximation to the blur kernel if the original image is sharp enough. By combining this powerful regularizer with conventional image deblurring techniques, we show how we could significantly improve the deblurring results through simulations and experiments on real images. In addition, our analysis and experiments help explaining a widely accepted doctrine; that is, the edges are good features for deblurring.

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arXiv2014

Exact Subspace Segmentation and Outlier Detection by Low-Rank Representation

In this work, we address the following matrix recovery problem: suppose we are given a set of data points containing two parts, one part consists of samples drawn from a union of multiple subspaces and the other part consists of outliers. We do not know which data points are outliers, or how many outliers there are. The rank and number of the subspaces are unknown either. Can we detect the outliers and segment the samples into their right subspaces, efficiently and exactly? We utilize a so-called {\em Low-Rank Representation} (LRR) method to solve this problem, and prove that under mild technical conditions, any solution to LRR exactly recovers the row space of the samples and detect the outliers as well. Since the subspace membership is provably determined by the row space, this further implies that LRR can perform exact subspace segmentation and outlier detection, in an efficient way.

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arXiv2012

Robust Recovery of Subspace Structures by Low-Rank Representation

In this work we address the subspace recovery problem. Given a set of data samples (vectors) approximately drawn from a union of multiple subspaces, our goal is to segment the samples into their respective subspaces and correct the possible errors as well. To this end, we propose a novel method termed Low-Rank Representation (LRR), which seeks the lowest-rank representation among all the candidates that can represent the data samples as linear combinations of the bases in a given dictionary. It is shown that LRR well solves the subspace recovery problem: when the data is clean, we prove that LRR exactly captures the true subspace structures; for the data contaminated by outliers, we prove that under certain conditions LRR can exactly recover the row space of the original data and detect the outlier as well; for the data corrupted by arbitrary errors, LRR can also approximately recover the row space with theoretical guarantees. Since the subspace membership is provably determined by the row space, these further imply that LRR can perform robust subspace segmentation and error correction, in an efficient way.

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arXiv2010

Closed-Form Solutions to A Category of Nuclear Norm Minimization Problems

It is an efficient and effective strategy to utilize the nuclear norm approximation to learn low-rank matrices, which arise frequently in machine learning and computer vision. So the exploration of nuclear norm minimization problems is gaining much attention recently. In this paper we shall prove that the following Low-Rank Representation (LRR) \cite{icml_2010_lrr,lrr_extention} problem: {eqnarray*} \min_{Z} \norm{Z}_*, & {s.t.,} & X=AZ, {eqnarray*} has a unique and closed-form solution, where $X$ and $A$ are given matrices. The proof is based on proving a lemma that allows us to get closed-form solutions to a category of nuclear norm minimization problems.

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