A circuit framework for robust manifold learning

Jens Nilsson

doi:10.1016/j.neucom.2006.12.021

2007-12-01

PRE

Jens Nilsson *

Фредрик Андерссон

DOI：10.1016/j.neucom.2006.12.021

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摘要

En 中文

Manifold learning and nonlinear dimensionality reduction addresses the problem of detecting possibly nonlinear structure in high-dimensional data and constructing lower-dimensional configurations representative of this structure. A popular example is the Isomap algorithm which uses local. information to approximate geodesic distances and adopts multidimensional scaling to produce lower-dimensional representations. Isomap is accurate on a global scale in contrast to many competing methods which approximate locally. However, a drawback of the Isomap algorithm is that it is topologically instable, that is, incorrectly chosen algorithm parameters or perturbations of data may drastically change the resulting configurations. We propose new methods for more robust approximation of the geodesic distances using a viewpoint of electric circuits. In this way, we achieve both the stability of local methods and the global approximation property of global methods, while compromising with local accuracy. This is demonstrated by a study of the performance of the proposed and competing methods on different data sets. (C) 2007 Elsevier B.V. All rights reserved.

Keyword:

manifold learning

Isomap

Laplacian Eigenmaps

topological instability

multidimensional scaling