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On the Relation of Slow Feature Analysis and Laplacian Eigenmaps

Henning Sprekeler
2011 Neural Computation  
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
more » ... 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.
doi:10.1162/neco_a_00214 pmid:21919780 fatcat:ypmqpsaatvgutozkvq275ctlny