Feature Extraction And Clustering For High-dimensional Data Based On Graph Learning

In recent years,data acquisition technology has been increasingly refined and diversified.Human beings have collected quantitative single-view and multi-view data which have high dimensionality.On the one hand,these high dimensional data provide us more complete descriptions of things or phenomena,but on the other hand,the high dimensionality usually leads to some problems,such as ”curse of dimensionality”,which makes traditional data processing methods fail to reveal the knowledge from the data.How to design effective algorithms for high dimensional data becomes an important research topic in machine learning,pattern recognition,data mining and computer vision.In this paper,we focus on dimensionality reduction and clustering.Main contributions of this paper are listed as following:(1)Single-view feature extraction based on graph learningTraditional graph-based feature extraction methods have two separated steps: constructing a graph matrix and extracting features,which makes low-dimensional representations lack a reasonable feedback to the graph construction.In this paper,we propose an unsupervised single-view feature extraction method which conducts feature extraction and graph matrix construction simultaneously.By designing an interaction term between the low-dimensional representations and the graph matrix and adding a constraint on the graph,the proposed algorithm learns a transformation matrix and a graph matrix with an ideal clustering structure simultaneously.(2)Multi-view feature extraction based on graph learningTraditional multi-view feature extraction methods need an additional parameter to learn view weight factors and the common graph matrices they construct do not contain structure information.In this paper,we propose an unsupervised multi-view feature extraction method which learns a common graph matrix and a transformation matrix.By designing a view weight leaning strategy without an additional parameter,the proposed algorithm conducts feature extraction,graph matrix construction and view weight learning simultaneously.(3)Multi-view subspace clustering based on graph learningMost existing multi-view subspace clustering methods ignore the different importance among views when learning self-representation matrices.In this paper,we propose a robust multi-view subspace clustering method with a common self-representation matrix.The proposed method distinguishes the importance among views and features when learning the common self-representation matrix.The algorithm has view weight learning strategy and feature weight learning strategy,which enhances the robustness of the graph matrix constructed by the common representation matrix.