Low-Rank Representation Based On Local Geometry Embedding

With the development of information acquisition and Internet technology,we need to involve all kinds of multimedia information in our daily life.Although these multimedia data make our lives more convenient and colorful,it also brings many new challenges to the field of machine learning:(1)the internal structure of data is becoming more and more complex,and its complexity is expanding at an explosive speed;(2)most of the data obtained are unlabeled samples.Subspace learning can be applied to a variety of different types of data,and the above problems can be solved by learning new representations of samples.As a type of unsupervised subspace learning algorithm,low-rank representation captures the global information of the data by exploring the original subspace structure of the data,learns richer and more effective features of the sample data,and improves the performance of machine learning tasks based on the new representation.At present,low-rank representations and their improved algorithms have been successfully used in many fields,including clustering,retrieval,and classification.Based on the in-depth study of low-rank representation algorithms,the main contributions of this paper are as follows:1.Graph-Hessian Principal Component Analysis algorithm(GHPCA)and Graph-Hessian Robust Principal Component Analysis algorithm(GHRPCA)are proposed.Compared with Laplacian regularization,Hessian regularization can correctly use the inherent local geometry of the data manifold,correctly reflect the positional relationship between samples,and obtain richer structural information.This paper conducts image clustering experiments in the handwritten digital dataset USPS,the face dataset YALE and the object recognition dataset COIL-20.Experimental results prove that the GHPCA and GHRPCA algorithms are better than other related algorithms,including: PCA,RPCA,GLPCA,RPCAG.2.A general framework based on the spectral graph filter is proposed and applied to Lat LRR,and the Graph Convolution Latent Low-Rank Representation algorithm(GCLat LRR)is proposed.In GCLat LRR,the feature manifold of the data is used to construct a spectral graph filter,and the filter is introduced into Lat LRR as a "shared subspace".The knowledge learned from the observed data can be transferred to the hidden data to make the hidden effect more real and effective.Specifically,the data is reconstructed into a weighted combination of graph structure information after passing through the filter,so that the model can obtain rich feature manifold local geometric information and improve the authenticity of the learned subspace.In addition,in order to prove the universality of the proposed framework,a graph convolution Lat LRR model based on data manifold(GCLat LRR-DM)is proposed.Extensive experiments on several popular datasets validate that the proposed method outperforms other related algorithms in subspace clustering and feature extraction.