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Natural data structure extracted from neighborhood-similarity graphs


Lorimer, Tom; Kanders, Karlis; Stoop, Ruedi (2019). Natural data structure extracted from neighborhood-similarity graphs. Chaos, Solitons & Fractals, 119:326-331.

Abstract

‘Big’ high-dimensional data are commonly analyzed in low-dimensions, after performing a dimensionality reduction step that inherently distorts the data structure. For a similar analysis, clustering methods are also often used. These methods introduce a bias as well, either by starting from the assumption of a particular, often geometric, property of the clusters, or by using iterative schemes to enhance cluster contours, with consequences that are hard to control. The goal of data analysis should, however, be to encode and detect structural data features at all scales and densities simultaneously, without assuming a parametric form of data point distances, or modifying them. Here, we propose a novel approach that directly encodes data point neighborhood similarities as a sparse graph. Our non-iterative framework permits a transparent interpretation of data, without altering the original data dimension and metric. Several natural and synthetic data applications demonstrate the efficacy of our novel method.

Abstract

‘Big’ high-dimensional data are commonly analyzed in low-dimensions, after performing a dimensionality reduction step that inherently distorts the data structure. For a similar analysis, clustering methods are also often used. These methods introduce a bias as well, either by starting from the assumption of a particular, often geometric, property of the clusters, or by using iterative schemes to enhance cluster contours, with consequences that are hard to control. The goal of data analysis should, however, be to encode and detect structural data features at all scales and densities simultaneously, without assuming a parametric form of data point distances, or modifying them. Here, we propose a novel approach that directly encodes data point neighborhood similarities as a sparse graph. Our non-iterative framework permits a transparent interpretation of data, without altering the original data dimension and metric. Several natural and synthetic data applications demonstrate the efficacy of our novel method.

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Additional indexing

Item Type:Journal Article, not_refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Neuroinformatics
Dewey Decimal Classification:570 Life sciences; biology
Scopus Subject Areas:Physical Sciences > Statistical and Nonlinear Physics
Physical Sciences > General Mathematics
Physical Sciences > General Physics and Astronomy
Physical Sciences > Applied Mathematics
Uncontrolled Keywords:General Mathematics
Language:English
Date:1 February 2019
Deposited On:13 Feb 2020 09:26
Last Modified:29 Jul 2020 14:15
Publisher:Elsevier
ISSN:0960-0779
OA Status:Closed
Publisher DOI:https://doi.org/10.1016/j.chaos.2018.12.033

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