Extending generalized unsupervised manifold alignment

Xiaoyi Yin, Zhen Cui, Hong Chang, Bingpeng Ma, Shiguang Shan

Abstract: Building connections between different data sets is a fundamental task in machine learning and related application community. With proper manifold alignment, the correspondences between data sets will assist us with comprehensive study of data processes and analyses. Despite the several progresses in semi-supervised and unsupervised scenarios, potent manifold alignment methods in generalized and realistic circumstances remain in absence. Besides, theretofore unsupervised algorithms seldom prove themselves mathematically. In this paper, we devise an efficient method to properly solve the unsupervised manifold alignment problem and denominate it as extending generalized unsupervised manifold alignment (EGUMA) method. More specifically, an explicit relaxed integer programming method is adopted to solve the unsupervised manifold alignment problem, which reconciles three factors covering the updated local structure matching, the the feature comparability and geometric preservation. An additional effort is retained on extending the Frank Wolfe algorithm to tacking our optimization problem. Besides our previous endeavors we adopt a new strategy for neighborhood discovery in the manifolds. The main advantages over previous methods accommodate (1) simultaneous alignment and discovery of manifolds; (2) complete unsupervised learning structure without any prerequisite correspondence; (3) more concise local geometry for the embedding space; (4) efficient alternative optimization; (5) strict mathematical analysis on the convergence and efficiency issues. Experiments on real-world applications verify the high accuracy and efficiency of our proposed method.