Nonlinear Projection with Curvilinear Distances: Isomap Versus Curvilinear Distance Analysis
Abstract
Dimension Reduction Techniques Are Widely Used for the Analysis and Visualization of Complex Sets of Data. This Paper Compares Two Recently Published Methods for Nonlinear Projection: Isomap and Curvilinear Distance Analysis (Cda). Contrarily to the Traditional Linear Pca, These Methods Work Like Multidimensional Scaling, by Reproducing in the Projection Space the Pairwise Distances Measured in the Data Space. However, They Differ from the Classical Linear Mds by the Metrics They Use and by the Way They Build the Mapping (Algebraic or Neural). While Isomap Relies Directly on the Traditional Mds, Cda is based on a Nonlinear Variant of Mds, Called Curvilinear Component Analysis (Cca). Although Isomap and Cda Share the Same Metric, the Comparison Highlights their Respective Strengths and Weaknesses. © 2004 Elsevier B.v. All Rights Reserved.
Recommended Citation
J. A. Lee et al., "Nonlinear Projection with Curvilinear Distances: Isomap Versus Curvilinear Distance Analysis," Neurocomputing, vol. 57, no. 1 thru 4, pp. 49 - 76, Elsevier, Mar 2004.
The definitive version is available at https://doi.org/10.1016/j.neucom.2004.01.007
Department(s)
Engineering Management and Systems Engineering
Keywords and Phrases
Curvilinear distance; Geodesic distance; Nonlinear dimensionality reduction; Nonlinear projection
International Standard Serial Number (ISSN)
0925-2312
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Elsevier, All rights reserved.
Publication Date
01 Mar 2004