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On the relation of slow feature analysis and Laplacian eigenmaps

Sprekeler, H (2011) On the relation of slow feature analysis and Laplacian eigenmaps. Neural Computation, 23. pp. 3287-3302. ISSN 0899-7667

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Abstract

The past decade has seen a rise of interest in Laplacian eigenmaps (LEMs) for nonlinear dimensionality reduction. LEMs have been used in spectral clustering, in semisupervised learning, and for providing efficient state representations for reinforcement learning. Here, we show that LEMs are closely related to slow feature analysis (SFA), a biologically inspired, unsupervised learning algorithm originally designed for learning invariant visual representations. We show that SFA can be interpreted as a function approximation of LEMs, where the topological neighborhoods required for LEMs are implicitly defined by the temporal structure of the data. Based on this relation, we propose a generalization of SFA to arbitrary neighborhood relations and demonstrate its applicability for spectral clustering. Finally, we review previous work with the goal of providing a unifying view on SFA and LEMs. © 2011 Massachusetts Institute of Technology.

Item Type: Article
Subjects: UNSPECIFIED
Divisions: Div F > Computational and Biological Learning
Depositing User: Cron Job
Date Deposited: 07 Mar 2014 11:25
Last Modified: 14 Dec 2014 20:45
DOI: 10.1162/NECO_a_00214