The Research And Application Of Metric Learning

The main task of distance metric learning is that learning the distance and similarity between data. And many basic tasks of machine leaning and pattern recognition are based on the distance metric of data, such as classification, clustering and recognition. So the distance metric learning has important value of research and application to solving the practical problems in the field of machine learning and computer vision. Distance metric learning can mainly divide into linear distance metric learning and nonlinear distance metric learning according to the learning samples is linear or nonlinear. Linear distance metric learning is for low dimensional linear space and nonlinear distance metric learning is suitable for high dimensional nonlinear space, it can maintain the low dimensional manifold embedded in the high dimensional nonlinear space, so it is called the manifold learning. Since most data of actual applications in the real world is high-dimensional and nonlinear, this dissertation mainly studies the manifold learning. Research of Riemannian manifold, global feature and local feature and weight distance metric is carried, and the proposed algorithms are applied to the face recognition and high dimension data visualization. The main contributions are as follows:1. In the aspect of theoretical knowledge, the basic idea and concrete steps of classical metric learning algorithms are introduced, and the advantages and disadvantages of each algorithm are given. Then get the analysis and comparisons of four classic algorithms through the experiments of high dimension data visualization.2. Recently the proposed Riemannian manifold learning is a nonlinear dimensionality reduction algorithm based on Riemannian normal coordinates. However, in practical applications, manifold learning algorithms cannot effectively eliminate the redundant information such as higher-order correlation in images. Therefore, in this dissertation, we present an algorithm for face recognition which is based on Log-Gabor wavelet and Riemannian manifold learning. Firstly, images are processed by the Log-Gabor to obtain high-dimension Log-Gabor image features, and then use the Riemannian manifold learning algorithm to reduce the dimensionality of the image features. Research shows that the integration of Log-Gabor wavelet and Riemannian manifold learning is in accord with the visual perception of humans. The proposed algorithm has better robustness to illumination and angle variation of the image. The experimental results on several standard databases indicate the effectiveness of the proposed algorithm.3. Manifold learning algorithms can be divided into global manifold learning and local manifold learning, and they keep global features and local features of manifolds respectively. However, experiments show that manifold learning algorithm based only on global or local feature information cannot maintain the real structure of manifold well which affects the results of manifold learning. Therefore, in the view of kernel, we present a multi-information manifold learning algorithm based on the kernel fusion of the ISOMAP and LTSA. The proposed algorithm can maintain the global and local features of manifolds synchronously, and the experimental results on several synthetic data and standard face databases indicate the effectiveness of the algorithm.4. Most manifold learning algorithms cannot handle the problem of the points samples distribution does not accord with the normal distribution and uneven density. We propose the CAM-LLE algorithm through using the CAM weight distance metric instead of the traditional Euclidean distance metric to improve the original neighbor selection method of LLE algorithm. The CAM weight distance metric gives the smaller weight to the points in the dense density part to reduce the redundancy information; and the larger weight to the sparse part to fully use the feature information. And the experimental results of high dimension data visualization indicate that the CAM weight distance metric is suitable for high dimensional space..