Low-rank Constraint Based Classification And Feature Analysis Approaches

With the rapid development of computer technology, the real world has witnessed an exponential increase in the existing data from multiple modalities. This has generated great advances on how to process massive, sparse, low-rank and containing noise data, which are the same interests to some researchers from statistics and computer science. Low-rank constraint of data is a common phenomenon, how to process data under constraint of low-rank becomes one of the focuses of the researchers in recent years. In this thesis, we propose some new researches about classification and feature analysis. More concretely, the main contributions are as follows:1. Analyzing and summarizing the related theory of low-rank constraint. We carry on detailed summary and classification for domestic and foreign development of low-rank constraint theory which mainly including low-rank matrix recovery, low-rank matrix completion and low-rank matrix representation. Their algorithms are also described in detail.2. Putting forward a new method for data classification on the basis of low-rank constraint. For the low-rank constraint of data is a widespread phenomenon, we propose a new classification method based on non-negative matrix factorization and harmonic function. At first, we expound the basic principles and specific properties of non-negative matrix factorization and harmonic function, then non-negative matrix factorization and harmonic function are merged together for data classification. We do some experiments based on some real datasets, and get satisfactory experimental results using our new method compared with the traditional classification methods.3. Proposing a new method for data feature analysis on the basis of low-rank constraint. From low-rank constraint properties, we put forward a new data feature selection method based on neighborhood preserving embedding and sparse regularization. The basic principles and specific properties of neighborhood preserving embedding and sparse regularization are analyzed in detail. We introduce L2,1 regularization to the theory of neighborhood preserving embedding for feature selection. In the fourth chapter, we do a lot of comparison experiments, compared with the traditional feature selection method, and the results verify the effectiveness of our method in some fields.