NDLI: Local conditions for critical and principal manifolds

Content Provider	IEEE Xplore Digital Library
Author	Ozertem, U. Erdogmus, D.
Copyright Year	2008
Description	Author affiliation: CSEE Dept., Oregon Health & Sci. Univ., Portland, OR (Ozertem, U.; Erdogmus, D.)
Abstract	Principal manifolds are essential underlying structures that manifest canonical solutions for significant problems such as data de- noising and dimensionality reduction. The traditional definition of self-consistent manifolds rely on a least-squares construction error approach that utilizes semi-global expectations across hyperplanes orthogonal to the solution. This definition creates various practical difficulties for algorithmic solutions to identify such manifolds, besides the theoretical shortcoming that self-intersecting or nonsmooth manifolds are not acceptable in this framework. We present local conditions for critical and principal manifolds by introducing the concept of subspace local maxima. The conditions generalize the two conditions that characterize stationary points of a function to stationary surfaces. The proposed framework yields a unique set of principal points which can be partitioned into principal curves and manifolds of any intrinsic dimensionality. A subspace-constrained fixed-point algorithm is proposed to determine the principal graph.
Starting Page	1893
Ending Page	1896
File Size	503605
Page Count	4
File Format	PDF
ISBN	9781424414833
ISSN	15206149
DOI	10.1109/ICASSP.2008.4518004
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-03-31
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Noise reduction Principal component analysis Partitioning algorithms Unsupervised learning Feature extraction Lead Eigenvalues and eigenfunctions Surface reconstruction Subspace constraints Piecewise linear techniques denoising Principal curves unsupervised learning manifold learning dimensionality reduction feature extraction
Content Type	Text
Resource Type	Article

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