Dansong Cheng

LRSR: Low-Rank-Sparse representation for subspace clustering

Abstract High-dimensional data in the real world often resides in low-dimensional subspaces. The state-of-the-art methods for subspace segmentation include Low Rank Representation (LRR) and Sparse Representation (SR). The former seeks the global lowest rank representation but restrictively assumes the independence among subspaces, whereas the latter seeks the clustering of disjoint or overlapped subspaces through locality measure, which may cause failure in the case of large noises. To this end, a Low Rank subspace Sparse Representation framework, hereafter referred to as LRSR, is proposed in this paper to recover and segment embedding subspaces simultaneously. Three major contributions can be claimed in this paper: First, a clean dictionary is constructed by optimizing its nuclear norm, low-rank-sparse coefficient matrix obtained using linearized alternating direction method (LADM). Second, both the convergence proof and the complexity analysis are given to prove the effectiveness and efficiency of our proposed LRSR algorithm. Third, the experiments on synthetic data and two benchmark datasets further verify that the LRSR enjoys the capability of clustering disjoint subspaces as well as the robustness against large noises, thanks to its considerations of both global and local subspace information. Therefore, it has been demonstrated in this research that our proposed LRSR algorithm outperforms the state-of-the-art subspace clustering methods, verified by both theoretical analysis and the empirical studies.

Active contour driven by multi-scale local binary fitting and Kullback-Leibler divergence for image segmentation

Image segmentation is an important processing in many applications such as image retrieval and computer vision. One of the most successful models for image segmentation is the level set methods which are based on local context. The methods, though comparatively effective in segmenting images with inhomogeneous intensity, are considerably computation-intensive and at the risk of falling into local minima in the convergence of the active contour energy function. To address the issues, we propose a region-based level set method, called KL-MLBF, which is based on the multi-scale local binary fitting (MLBF) and the Kullback-Leibler (KL) divergence. We first apply the multi-scale theory to the local binary fitting model to build MLBF. Then the energy term measured by KL divergence between regions to be segmented is incorporated into the energy function of MLBF. KL-MLBF utilizes the between-cluster distance and the adaptive kernel function selection strategy to formulate the energy function. Being more robust to the initial location of the contour than the classical segmentation models, KL-MLBF can deal with blurry boundaries and noise problems. The results of experiments on synthetic and real images have shown that KL-MLBF can improve the effectiveness of segmentation while ensuring the accuracy by accelerating the minimization of the energy function.

Double-noise-dual-problem approach to the augmented Lagrange multiplier method for robust principal component analysis

Robust principal component analysis (RPCA) is one of the most useful tools to recover a low-rank data component from the superposition of a sparse component. The augmented Lagrange multiplier (ALM) method enjoys the highest accuracy among all the approaches to the RPCA. However, it still suffers from two problems, namely, a brutal force initialization phase resulting in low convergence speed and ignorance of other types of noise resulting in low accuracy. To this end, this paper proposes a double-noise, dual-problem approach to the augmented Lagrange multiplier method, referred to as DNDP-ALM, for robust principal component analysis. Firstly, the original ALM method considers sparse noise only, ignoring Gaussian noise, which generally exists in real-world data. In our proposed DNDP-ALM, the data consist of low-rank component, sparse component and Gaussian noise component, with RPCA problem converted to convex optimization. Secondly, the original ALM uses a rough initialization of multipliers, leading to more work of iterative calculation and lower calculation accuracy. In our proposed DNDP-ALM, the initialization is carried out by solving a dual problem to obtain the optimal multiplier. The experimental results show that the proposed approach super-performs in solving robust principal component analysis problems in terms of speed and accuracy, compared to the state-of-the-art techniques.

A global-local affinity matrix model via EigenGap for graph-based subspace clustering

We propose a Global-Local Affinity Matrix Model for Graph-based Subspace Clustering.We propose a criterion called Fractional Eigenvalues Sum (FEVS) for global scheme.Our proposed model is solved by Alternative Direction Method (ADM).We evaluates our proposed model on low-dimensional data.The GLAM model has excellent performance on face clustering and motion segmentation. In this paper, we address the spectral clustering problem by effectively constructing an affinity matrix with a large EigenGap. Although the faultless Block-Diagonal structure is highly in demand for accurate spectral clustering, the relaxed Block-Diagonal affinity matrix with a large EigenGap is more effective and easier to obtain. A global EigenGap scheme is proposed by utilizing the Fractional Eigenvalues Sum (FEVS) penalty of maximizing top eigenvalues and minimizing the residual. The closed-form solution of the FEVS term and the proximity term is also presented. We then propose a Global-Local Affinity Matrix model that integrates the global EigenGap with local pairwise distance measure for graph construction. Furthermore, we also combine the state-of-the-art subspace recovery methods such as LRR and RSIM with our proposed model to learn an effective affinity matrix for high dimensional data. To the best of our knowledge, this is the first research that attempts to pursue such a relaxed Block-Diagonal structure with a large EigenGap. Extensive experiments on face clustering and motion segmentation clearly demonstrate the significant advantages of the novel methods.

An advanced total variation model in H-1 space for image inpainting

Image inpainting is to restore a damaged image with missing information – a fundamental problem and a hot research area in image processing. Many approaches, both geometry oriented and texture oriented, have been proposed on inpainting such as total variation (TV), Criminisi algorithm, etc. However, these approaches suffer from either limitations such as only suitable for small areas (cracks), staircase effect (discontinuity), or inefficient (time-consuming) to search the best matched patch (for filling-in). In this paper we propose a novel approach based on partial differential equation (PDE) and isophotes direction, named as Isophotes-TV-H-1. A corrupted image is first decomposed into two parts: the cartoon (smooth parts and edges of the image) and the texture. The cartoon part is inpainted through Isophotes- TV-H-1 while the texture part is done by an enhanced Criminisi algorithm which reduces the searching time for match and gives more reasonable match patches. The results of experiments on several images have demonstrated that, compared to existing methods, the proposed solution can recover the texture (of the damaged region) better, suppress error propagation and solve the problem of intensity discontinuity.

Sign correlation subspace for face alignment

Face alignment is an essential task for facial performance capture and expression analysis. Current methods such as random subspace supervised descent method, stage-wise relational dictionary and coarse-to-fine shape searching can ease multi-pose face alignment problem, but no method can deal with the multiple local minima problem directly. In this paper, we propose a sign correlation subspace method for domain partition in only one reduced low-dimensional subspace. Unlike previous methods, we analyze the sign correlation between features and shapes and project both of them into a mutual sign correlation subspace. Each pair of projected shape and feature keeps their signs consistent in each dimension of the subspace, so that each hyper octant holds the condition that one general descent exists. Then a set of general descents are learned from the samples in different hyperoctants. Requiring only the feature projection for domain partition, our proposed method is effective for face alignment. We have validated our approach with the public face datasets which include a range of poses. The validation results show that our method can reveal their latent relationships to poses. The comparison with state-of-the-art methods demonstrates that our method outperforms them, especially in uncontrolled conditions with various poses, while enjoying the comparable speed.

Image segmentation based on multi-region multi-scale local binary fitting and Kullback–Leibler divergence

The inhomogeneity of intensity and the noise of image are the two major obstacles to accurate image segmentation by region-based level set models. To provide a more general solution to these challenges and address the difficulty of image segmentation methods to handle an arbitrary number of regions, we propose a region-based multi-phase level set method, which is based on the multi-scale local binary fitting (MLBF) and the Kullback–Leibler (KL) divergence, called KL–MMLBF. We first apply the multi-scale theory and multi-phase level set framework to the local binary fitting model to build the multi-region multi-scale local binary fitting (MMLBF). Then the energy term measured by KL divergence between regions to be segmented is incorporated into the energy function of MMLBF. KL–MMLBF utilizes the between-cluster distance and the adaptive kernel function selection strategy to formulate the energy function. Being more robust to the initial location of the contour than the classical segmentation models, KL–MMLBF can deal with blurry boundaries and noise problems. The results of experiments on synthetic and medical images have shown that KL–MMLBF can improve the effectiveness of segmentation while ensuring the accuracy by accelerating this minimization of this energy function and the model has achieved better segmentation results in terms of both accuracy and efficiency to analyze the multi-region image.

A differential privacy noise dynamic allocation algorithm for big multimedia data

An advanced differential privacy algorithm is proposed in this paper to solve the problem of non-uniformity faced with two-dimensional big multimedia data, such as images. Traditional privacy-preserving algorithms partition a spatial data space into grids and then add noise to each grid at same scale. Such a treatment increases relative errors and reduces accuracy. To address this issue, a differential privacy noise dynamic allocation algorithm is proposed based on the standard deviation circle radius hereafter referred to as SDC-DP algorithm. In our proposed algorithm, the intensity of privacy-preserving needs is defined by the divergence of each grid which is calculated by the standard deviation circle radius. The different scale of noise is mixed dynamically into count query results for each grid on the privacy-preserving needs. Experimental results show that the SDC-DP can effectively reduce the relative errors and improve accuracies, compared to the state-of-the-art techniques.

Low-Rank-Sparse Subspace Representation for Robust Regression

Learning robust regression model from high-dimensional corrupted data is an essential and difficult problem in many practical applications. The state-of-the-art methods have studied low-rank regression models that are robust against typical noises (like Gaussian noise and out-sample sparse noise) or outliers, such that a regression model can be learned from clean data lying on underlying subspaces. However, few of the existing low-rank regression methods can handle the outliers/noise lying on the sparsely corrupted disjoint subspaces. To address this issue, we propose a low-rank-sparse subspace representation for robust regression, hereafter referred to as LRS-RR in this paper. The main contribution include the following: (1) Unlike most of the existing regression methods, we propose an approach with two phases of low-rank-sparse subspace recovery and regression optimization being carried out simultaneously,(2) we also apply the linearized alternating direction method with adaptive penalty to solved the formulated LRS-RR problem and prove the convergence of the algorithm and analyze its complexity, (3) we demonstrate the efficiency of our method for the high-dimensional corrupted data on both synthetic data and two benchmark datasets against several state-of-the-art robust methods.

Intelligent pancreatitis diagnosis-based on relevance vector machine

Medical diagnostic decision is a fundamental uncertainty event, people always wanted to have an intelligent method approach to this activity. Relevance vector machine is a machine learning method under sparse Bayesian framework, tentatively be applied to help doctors make diagnose diseases decisions. This article for example with the diagnosis of pancreatitis, through the patients basic information, symptoms with relevance vector machine, determines the severity of patient illness; and compared with the support vector machine and BP neural network. Experiments with relevance vector machine show that the error rate was 22.41%, which is better than support vector machine (24.14%) and BP neural network (25.86%); while the number of relevance vector machine is less than that of support vector. It is illustrated that relevance vector machine is better than both of todays more out-of art methods to diagnose disease in terms of intelligence. It also shows the relevance vector machine has some potential for development in the field of intelligent diagnosis of disease.