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Selecting the independent coordinates of manifolds with large aspect ratios
Yu-Chia Chen · Marina Meila

Thu Dec 12 05:00 PM -- 07:00 PM (PST) @ East Exhibition Hall B + C #16
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. Mathematically, success is possible under very broad conditions, provided that embedding is done by carefully selected eigenfunctions of the Laplace-Beltrami operator $\Delta_\M$. Hence, we propose a bicriterial 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.

Author Information

Yu-Chia Chen (University of Washington)
Marina Meila (University of Washington)

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