Some Research Problems in Metric Learning and Manifold Learning

In the past few years, metric learning, semi-supervised learning, and manifold learning methods have aroused a great deal of interest in the machine learning community. Many machine learning and pattern recognition algorithms rely on a distance metric. Instead of choosing the metric manually, a promising approach is to learn the metric from data automatically. Besides some early work on metric learning for classification, more and more efforts have been devoted in recent years to learning a distance metric for the semi-supervised learning setting. Semisupervised learning is a learning paradigm between the supervised and unsupervised learning extremes. Algorithms of this class usually solve the classification or clustering problems with the aid of additional background knowledge. While there has been a whole set of interesting ideas on how to learn from data with supervisory information, we focus our study on semisupervised learning in the metric learning context. Manifold learning mainly aims to automatically discover the low-dimensional nonlinear manifold in a high-dimensional data space and then embed the data points into a low-dimensional embedding space. Besides manifold learning for data representation, some researchers have explored the possibility of using manifold structure for supervised and unsupervised learning tasks. We have explored some possibilities for the solutions of several research problems in manifold learning under the unsupervised learning setting. To summarize, in this proposal, we will focus on several research problems in metric learning under the semi-supervised learning setting and manifold learning under the unsupervised learning setting. On one hand, we will report some primary work that has been done. On the other hand, we will propose some possible future research directions.