Research Of Semi-supervised Dimensionality Reduction Algorithms Based On Local Sparse Representation

With the rapid development of information technology, a large number of high-dimensional data hasbeen generated in many fields. How to discover knowledge from these high-dimensional data is one of thehottest research topics in the technological community. However, processing these data needs more storageand computational cost, which makes many algorithms inapplicable to real-world problems, such as patternrecognition and rule mining. Under this background, the research of dimensionality reduction of data hasattracted the attention of the researchers.Semi-supervised dimensionality reduction, as one of the dimensionality reduction algorithms has beenwidely used in many practical applications. Most of the algorithms are based on class labels, however,besides the class labels, there exists another form of supervision information for semi-superviseddimensionality reduction i. e, pairwise constraints. Pairwise constraints can be more easily obtained thanclass labels, it have been applied in many areas of machine learning. On the one hand, we focus onstudying semi-supervised dimension reduction algorithms with pairwise constraints and study thesignificance of constructing a well-structured graph in Semi-supervised dimensionality reductionalgorithms; on the other hand, inspired by the excellent characteristics of sparse representations, we imposethe notion of sparse representation to semi-supervised dimensionality reduction methods and propose anovel semi-supervised dimensionality reduction algorithm based on sparse representation. In summary, thekey contributions of the thesis are:(1) We comprehensively analyze the research background, the current research status ofsemi-supervised dimensionality reduction algorithms and the sparse representation theory. And then wesummarize the main idea about common semi-supervised dimensionality reduction algorithm.(2) We study Semi-Supervised Dimensionality Reduction method based on Sparse Representation(SpSSDR) firstly. Then by integrating the concept of nearest neighborhood graph, a novel semi-superviseddimensionality reduction algorithm called (LSpSSDR) is proposed. LSpSSDR can make use of both thelocal information of unlabeled data and the pairwise constraints information for dimensionality reduction.Experimental results show the method has good performances on several high-dimensional datasets. (3) For the shortcoming of LSpSSDR which susceptible to noise features, we proposed a method calledSparse Mixture Graph-based Semi-Supervised Dimensionality Reduction (SpMGSSDR) by combiningwith subspace learning. SpMGSSDR first constructs multiple local sparse graphs in multiple generatedrandom subspaces and integrates these local sparse graphs into a sparse mixture graph. Experimentalanalysis demonstrates that SpMGSSDR is robust to noisy features and parameter selection, so it can makeup the shortcoming of LSpSSDR, which susceptible to noise features.Finally, the work is summarized and the directions of future research are discussed.