Local Information Preserving Projection And Its Application

Representation the high-dimensional data in a low-dimensional subspace is one of the fundamental problems in data analysis, pattern recognition, machine learning, and computer vision. With the rapid development of sensor and data collection techniques, the dimension of data is becoming higher and higher. So, how to efficiently represent the data has become an active research area and urgent problem to be solved. In the existing methods, the most classical one is PCA (Principal Component Analysis), which is an unsupervised feature extraction technique in the sense of minimization mean squared error. It efficiently preserves the global Euclidean distance, i.e. diversity information between data, but fails to the nonlinear data. In this dissertation the scheme of preserving the diversity of data is studied by using the graph theory and manifold learning technique. The main contributions and work are as follows.First, a novel method, namely Local Information Preserving Projection (LIPP), based on graph theory is proposed. LIPP defines an adjacency graph with a vertex set which are composed of the training data and an affinity matrix whose elements measure the diversity information between vertexes. A concise feature extraction criterion is then developed by maximizing the diversity scatter which is determined by adjacency graph. Compared to PCA, LIPP not only suits to linear data but also efficiently preserves the diversity information of non-linear data. Extensive experiments indicate the efficiency of the proposed method.Second, two-dimensional feature extraction method, namely two-Dimensional Local Information Preserving Projection (2DLIPP), is proposed by combining the two-dimensional feature extraction techniques and LIPP. As opposed to LIPP, 2DLIPP directly calculates the diversity scatter from the image matrices rather than image vectors, so it avoids transforming the image matrix into a vector, can well preserve the local spatial information among pixels of the image. Compared to 2DPCA, 2DLIPP not only suits to linear data but also efficiently preserves the local diversity information of non-linear data. Experiments on Yale, UMIST, AR and ORL face databases indicate the efficiency of 2DLIPP.