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WIREs Data Mining Knowl Discov
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Distance‐preserving dimensionality reduction

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Abstract This paper presents an overview of basic concepts and principles that deal with the problem of mapping high‐dimensional data to low‐dimensional space such that distances between all or some pairs of data points are preserved. It introduces related techniques and systematizes today's methods into linear methods, methods using iterative optimization, methods preserving exact distances, methods using geodesic distances, and methods using alignments of local models. It discusses these methods by focusing on their basic ideas, by summarizing their common features and differences, and by comparing their strengths and weaknesses. This paper assumes no familiarity with dimensionality reduction. The main text should be readable by people with little technical background. Technical information of important algorithms is briefly presented in sidebars, the reading of which assumes basics in statistics and matrix computation. © 2011 John Wiley & Sons, Inc. WIREs Data Mining Knowl Discov 2011 1 369–380 DOI: 10.1002/widm.39 This article is categorized under: Technologies > Data Preprocessing Technologies > Machine Learning

Principal components of a Gaussian distribution.

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(a) Swiss‐roll data superimposed with neighborhoods; (b) two‐dimensional projection by alignment of local models.

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(a) A Swiss‐roll data set, (b) its 5‐NN neighborhood graph, and (c) its two‐dimensional projection.

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Three steps for dimensionality reduction using geodesic distances.

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Plots of the UN statistical data using (a) nearest neighbors; (b) two reference points.

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Technologies > Data Preprocessing
Technologies > Machine Learning

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