Connectivity of projected high dimensional data charts on one-dimensional curves

We propose a principal curve tracing algorithm, which uses the gradient and the Hessian of a given density estimate. Curve definition requires the local smoothness of data density and is based on the concept of subspace local maxima. Tracing of the curve is handled through the leading eigenvector wh...

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Published in:Signal processing Vol. 91; no. 10; pp. 2404 - 2409
Main Authors: Bas, E., Erdogmus, D.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.10.2011
Elsevier
Subjects:
Applied sciences
Connectivity analysis
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
Image processing
Information, signal and communications theory
Principal curves
Signal and communications theory
Signal processing
Signal, noise
Telecommunications and information theory
Topological skeleton
Connectivity analysis
Principal curves
Topological skeleton
Performance evaluation
Image processing
Eigenvector
Subspace method
Updating
Algorithm
Image segmentation
One dimensional model
Signal processing
Connectedness
Skeleton
ISSN:0165-1684, 1872-7557
Online Access:Get full text
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Abstract We propose a principal curve tracing algorithm, which uses the gradient and the Hessian of a given density estimate. Curve definition requires the local smoothness of data density and is based on the concept of subspace local maxima. Tracing of the curve is handled through the leading eigenvector where fixed step updates are used. We also propose an image segmentation algorithm based on the original idea and show the effectiveness of the proposed algorithm on a Brainbow dataset. Lastly, we showed a simple approach to define connectivity in complex topologies, by providing a tree representation for the bifurcating synthetic data.
AbstractList We propose a principal curve tracing algorithm, which uses the gradient and the Hessian of a given density estimate. Curve definition requires the local smoothness of data density and is based on the concept of subspace local maxima. Tracing of the curve is handled through the leading eigenvector where fixed step updates are used. We also propose an image segmentation algorithm based on the original idea and show the effectiveness of the proposed algorithm on a Brainbow dataset. Lastly, we showed a simple approach to define connectivity in complex topologies, by providing a tree representation for the bifurcating synthetic data.
Author Bas, E.
Erdogmus, D.
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Issue 10
Keywords Connectivity analysis
Principal curves
Topological skeleton
Performance evaluation
Image processing
Eigenvector
Subspace method
Updating
Algorithm
Image segmentation
One dimensional model
Signal processing
Connectedness
Skeleton
Language English
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SubjectTerms Applied sciences
Connectivity analysis
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
Image processing
Information, signal and communications theory
Principal curves
Signal and communications theory
Signal processing
Signal, noise
Telecommunications and information theory
Topological skeleton
Title Connectivity of projected high dimensional data charts on one-dimensional curves
URI https://dx.doi.org/10.1016/j.sigpro.2011.04.009
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