Low-Rank Sparse Preserving Projections for Dimensionality Reduction

Abstract

Learning an efficient projection to map high-dimensional data into a lower dimensional space is a rather challenging task in the community of pattern recognition and computer vision. Manifold learning is widely applied because it can disclose the intrinsic geometric structure of data. However, it only concerns the geometric structure and may lose its effectiveness in case of corrupted data. To address this challenge, we propose a novel dimensionality reduction method by combining the manifold learning and low-rank sparse representation, termed low-rank sparse preserving projections (LSPP), which can simultaneously preserve the intrinsic geometric structure and learn a robust representation to reduce the negative effects of corruptions. Therefore, LSPP is advantageous to extract robust features. Because the formulated LSPP problem has no closed-form solution, we use the linearized alternating direction method with adaptive penalty and eigen-decomposition to obtain the optimal projection. The convergence of LSPP is proven, and we also analyze its complexity. To validate the effectiveness and robustness of LSPP in feature extraction and dimensionality reduction, we make a critical comparison between LSPP and a series of related dimensionality reduction methods. The experimental results demonstrate the effectiveness of LSPP.

Application of Sparse Representation in Bioinformatics

“…Low-rank sparse representation models have been applied in many fields ( Cheng et al, 2016 ; Chen et al, 2017 ; Zhang et al, 2017 ; Brbic and Kopriva, 2018 ; Chen et al, 2018 ; Xie et al, 2018 ; Yuanyuan et al, 2018 ; Zeng et al, 2018 ; Ding et al, 2019 ; Shen et al, 2019 ; Zhang et al, 2019 ; Li et al, 2020 ; Wu and Yu, 2021 ), which demonstrate high superiority, particularly in terms of dimensionality reduction and subspace segmentation. Considering existing analysis methods, introduce a low-rank sparse representation model for gene expression profile data analysis, several new methods for feature selection and feature extraction of gene expression profile data based on low-rank sparse representation models are explored, and they are applied to gene expression profile clustering and classification.…”

A Tensor-Based Submodule Clustering for 2D Images Using $$l_{\frac{1}{2}}$$-Induced Tensor Nuclear Norm Minimization

“…Supervised approaches, on one hand, necessitate higher computational time because they rely on prior data label-ing and training [4]. On the other hand, unlabeled data are mostly flexible and easy [5]. In light of this, clustering is an unsupervised data grouping approach in which objects are classified based on similarity inherent in the data [6,7].…”

Multiset Canonical Correlations Analysis With Global Structure Preservation

“…In this paper we propose a novel multi-view data dimension reduction method: multiset canonical correlations analysis based on low-rank representation (LRMCCA), which protects both the local structure and the global structure of sample points. First, we perform low-rank representation [32]- [37] of the data, spontaneously learn the low-rank representation matrix of the sample points in each view. Then, to maintain the global structure [35] of the data, we construct the cross-view similarity matrix by using the low-rank representation matrix, so that we can get the similarity between the sample points, including all sample points in cross views.…”