Selecting the independent coordinates of manifolds with large aspect ratios

Yu-Chia Chen, Marina Meila

Abstract: Many manifold embedding algorithms fail apparently when the data manifold has a large aspect ratio (such as a long, thin strip). Here, we formulate success and failure in terms of finding a smooth embedding, showing also that the problem is pervasive and more complex than previously recognized. Then, we propose a bicriterial {\em Independent Eigencoordinate Selection (IES)} algorithm that selects smooth embeddings with few eigenvectors. The algorithm is grounded in theory, has low computational overhead, and is successful on synthetic and large real data.

Code Link: https://github.com/yuchaz/independent_coordinate_search

CMT Num: 635