title: 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.
authors.affiliation: Laboratory for Computational Neuroscience, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland  henning.sprekeler@epfl.ch.
authors.forename: Henning
authors.initials: H
authors.lastname: Sprekeler
mesh_terms: D000465:Algorithms; D000818:Animals; D001185:Artificial Intelligence; D006801:Humans; D016571:Neural Networks, Computer; D009434:Neural Pathways / Q000502:physiology; D009474:Neurons / Q000502:physiology; D010363:Pattern Recognition, Automated / Q000379:methods*; D010364:Pattern Recognition, Visual / Q000502:physiology; D013997:Time Factors; D014793:Visual Cortex / Q000502:physiology