Exploring The Use Of Low-rank Matrix Recovery In Dimensionality Reduction Of High-dimensional Data

In recent years, with the rapid development in computer and collecting equipment manufacturing technology, people’s demand for visual perception is higher and higher, and the dimensionality of data such as image and video data is also growing. In compressed sensing community, people tend to think these redundant data make analysis feasible, take intrinsic structure invisible. How to find an effectively way of representation by dimensionality reduction, and how to reveal intrinsic structure of the high-dimensional data has become a frontier topic in pattern recognition, artificial intelligence and data mining etc fields. Low-rank matrix recovery that can learn effective low-rank structure of data consist of robust principal component analysis, matrix completion and low rank representation. This paper researches on robust principal analysis and low rank representation theory, then incorporate these theory into the traditional method of image processing and pattern recognition, and major contributions are outlined as follows:1. A novel unsupervised feature selection base on low-rank representation Score for high-dimensional image feature selection is proposed. the algorithm construct two new low-rank representation models with ―cleanly‖ dictionary constraint and sparsity constraint respectively to learn an efficiency weight matrix which with the capacities of capturing the global structure information, identifying and expressing the data information of it, then introduce the weight matrix into the Laplacian Score.2. An efficiency feature extraction base on low rank representation linear preserving projections for high-dimensional image feature extraction is proposed. The algorithm use different low rank representation model to learn low rank characteristics of data, and preserve these properties during linear projection to achieve dimensionality reduction of high-dimensional data. Three different models were used to learn three different low rank properties of data. First the original low rank representation model is used; and second, in order to remove the previous low rank property-intensive, construct a weighted low rank representation model for learning weighted low rank property; and in the end, incorporate local properties form manifold learning into the original low rank model to learn a new low rank property of data.3. An improved moving object detection method based on low rank and sparse matrix decomposition and sparse representation for online moving object detection is presented. The method have important abilities that can get low dimensional feature space, and in this sub-space treat moving object detection as sparse signal recovery. When there is a video data, protection matrix protects it to low rank subspace, then the method is use sparse representation theory to get the moving object’s true position.