On the relation of slow feature analysis and Laplacian eigenmaps.

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.

journal_name

Neural Comput

journal_title

Neural computation

authors

Sprekeler H

doi

10.1162/NECO_a_00214

subject

Has Abstract

pub_date

2011-12-01 00:00:00

pages

3287-302

issue

12

eissn

0899-7667

issn

1530-888X

journal_volume

23

pub_type

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