THE HUFFMAN-LIKE ALIGNMENT IN MANIFOLD LEARNING

In manifold learning, the neighborhood is often called a patch of the manifold, and the corresponding open set is called the local coordinate of the patch. The so-called alignment is to align the local coordinates in the d-dimensional Euclidean space to get the global coordinate of the manifold. There are two kinds of alignment methods: global and progressive alignment methods. The global alignment methods align the local coordinates of the manifold all at one time by solving an eigenvalue problem. The progressive alignment methods often take the local coordinate of a patch as the basic local coordinate and then attach other local ordinates to the basic local coordinate patch-by-patch until the basic local coordinate evolves into the global coordinate of the manifold. In this paper, a new progressive alignment method is proposed, where only the local coordinates of the two patches with the largest intersection at the current stage of progressive alignment will be aligned into a larger local coordinate. It is inspired by the famous Huffman coding, where two random events with the smallest probabilities at the current phase will be merged into a random event with a larger probability. Therefore, the proposed method is a Huffman-like alignment method. The experiments on benchmark data show that the proposed method outperforms both the global alignment methods and the other progressive alignment methods and is more robust to the changes of data size. The experiments on real-world data show the feasibility of the proposed method.