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Nearly Isometric Embedding by Relaxation
James McQueen · Marina Meila · Dominique Perrault-Joncas

Mon Dec 05 09:00 AM -- 12:30 PM (PST) @ Area 5+6+7+8 #30

Many manifold learning algorithms aim to create embeddings with low or no distortion (i.e. isometric). If the data has intrinsic dimension d, it is often impossible to obtain an isometric embedding in d dimensions, but possible in s > d dimensions. Yet, most geometry preserving algorithms cannot do the latter. This paper proposes an embedding algorithm that overcomes this problem. The algorithm directly computes, for any data embedding Y, a distortion loss(Y), and iteratively updates Y in order to decrease it. The distortion measure we propose is based on the push-forward Riemannian metric associated with the coordinates Y. The experiments confirm the superiority of our algorithm in obtaining low distortion embeddings.

Author Information

James McQueen (University of Washington)
Marina Meila (University of Washington)
Dominique Perrault-Joncas (Google)

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