Sparse approximation

About: Sparse approximation is a research topic. Over the lifetime, 18037 publications have been published within this topic receiving 497739 citations. The topic is also known as: Sparse approximation.

Sequence-based prediction of protein-protein interactions using weighted sparse representation model combined with global encoding

Abstract: Proteins are the important molecules which participate in virtually every aspect of cellular function within an organism in pairs. Although high-throughput technologies have generated considerable protein-protein interactions (PPIs) data for various species, the processes of experimental methods are both time-consuming and expensive. In addition, they are usually associated with high rates of both false positive and false negative results. Accordingly, a number of computational approaches have been developed to effectively and accurately predict protein interactions. However, most of these methods typically perform worse when other biological data sources (e.g., protein structure information, protein domains, or gene neighborhoods information) are not available. Therefore, it is very urgent to develop effective computational methods for prediction of PPIs solely using protein sequence information. In this study, we present a novel computational model combining weighted sparse representation based classifier (WSRC) and global encoding (GE) of amino acid sequence. Two kinds of protein descriptors, composition and transition, are extracted for representing each protein sequence. On the basis of such a feature representation, novel weighted sparse representation based classifier is introduced to predict protein interaction class. When the proposed method was evaluated with the PPIs data of S. cerevisiae, Human and H. pylori, it achieved high prediction accuracies of 96.82, 97.66 and 92.83 % respectively. Extensive experiments were performed for cross-species PPIs prediction and the prediction accuracies were also very promising. To further evaluate the performance of the proposed method, we then compared its performance with the method based on support vector machine (SVM). The results show that the proposed method achieved a significant improvement. Thus, the proposed method is a very efficient method to predict PPIs and may be a useful supplementary tool for future proteomics studies.

Sparsity Preserving Discriminant Projections with Applications to Face Recognition

Abstract: Dimensionality reduction is extremely important for understanding the intrinsic structure hidden in high-dimensional data. In recent years, sparse representation models have been widely used in dimensionality reduction. In this paper, a novel supervised learning method, called Sparsity Preserving Discriminant Projections (SPDP), is proposed. SPDP, which attempts to preserve the sparse representation structure of the data and maximize the between-class separability simultaneously, can be regarded as a combiner of manifold learning and sparse representation. Specifically, SPDP first creates a concatenated dictionary by classwise PCA decompositions and learns the sparse representation structure of each sample under the constructed dictionary using the least square method. Secondly, a local between-class separability function is defined to characterize the scatter of the samples in the different submanifolds. Then, SPDP integrates the learned sparse representation information with the local between-class relationship to construct a discriminant function. Finally, the proposed method is transformed into a generalized eigenvalue problem. Extensive experimental results on several popular face databases demonstrate the feasibility and effectiveness of the proposed approach.

Metasample-Based Sparse Representation for Tumor Classification

Abstract: A reliable and accurate identification of the type of tumors is crucial to the proper treatment of cancers. In recent years, it has been shown that sparse representation (SR) by l_1-norm minimization is robust to noise, outliers and even incomplete measurements, and SR has been successfully used for classification. This paper presents a new SR-based method for tumor classification using gene expression data. A set of metasamples are extracted from the training samples, and then an input testing sample is represented as the linear combination of these metasamples by l_1-regularized least square method. Classification is achieved by using a discriminating function defined on the representation coefficients. Since l_1-norm minimization leads to a sparse solution, the proposed method is called metasample-based SR classification (MSRC). Extensive experiments on publicly available gene expression data sets show that MSRC is efficient for tumor classification, achieving higher accuracy than many existing representative schemes.

Image deblocking via sparse representation

Abstract: Image compression based on block-based Discrete Cosine Transform (BDCT) inevitably produces annoying blocking artifacts because each block is transformed and quantized independently. This paper proposes a new deblocking method for BDCT compressed images based on sparse representation. To remove blocking artifacts, we obtain a general dictionary from a set of training images using the K-singular value decomposition (K-SVD) algorithm, which can effectively describe the content of an image. Then, an error threshold for orthogonal matching pursuit (OMP) is automatically estimated to use the dictionary for image deblocking by the compression factor of compressed image. Consequently, blocking artifacts are significantly reduced by the obtained dictionary and the estimated error threshold. Experimental results indicate that the proposed method is very effective in dealing with the image deblocking problem from compressed images.

A subdivision-based algorithm for the sparse resultant

Abstract: Multivariate resultants generalize the Sylvester resultant of two polynomials and characterize the solvability of a polynomial system. They also reduce the computation of all common roots to a problem in linear algebra. We propose a determinantal formula for the sparse resultant of an arbitrary system of n + 1 polynomials in n variables. This resultant generalizes the classical one and has significantly lower degree for polynomials that are sparse in the sense that their mixed volume is lower than their Bezout number. Our algorithm uses a mixed polyhedral subdivision of the Minkowski sum of the Newton polytopes in order to construct a Newton matrix. Its determinant is a nonzero multiple of the sparse resultant and the latter equals the GCD of at most n + 1 such determinants. This construction implies a restricted version of an effective sparse Nullstellensatz. For an arbitrary specialization of the coefficients, there are two methods that use one extra variable and yield the sparse resultant. This is the first algorithm to handle the general case with complexity polynomial in the resultant degree and simply exponential in n. We conjecture its extension to producing an exact rational expression for the sparse resultant.