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A PROBABILISTIC ℓ1 METHOD FOR CLUSTERING HIGH-DIMENSIONAL DATA

Published online by Cambridge University Press:  05 April 2021

Tsvetan Asamov  and
Adi Ben-Israel Open the ORCID record for Adi Ben-Israel [Opens in a new window]
Tsvetan Asamov
Affiliation:
Department of Management Science & Information Systems, Rutgers Business School, 100 Rockafeller Road, Piscataway, NJ08854, USA E-mails: tsvetan.asamov@gmail.com; adi.benisrael@gmail.com
Adi Ben-Israel
Affiliation:
Department of Management Science & Information Systems, Rutgers Business School, 100 Rockafeller Road, Piscataway, NJ08854, USA E-mails: tsvetan.asamov@gmail.com; adi.benisrael@gmail.com
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Abstract

In general, the clustering problem is NP-hard, and global optimality cannot be established for non-trivial instances. For high-dimensional data, distance-based methods for clustering or classification face an additional difficulty, the unreliability of distances in very high-dimensional spaces. We propose a probabilistic, distance-based, iterative method for clustering data in very high-dimensional space, using the ℓ1-metric that is less sensitive to high dimensionality than the Euclidean distance. For K clusters in ℝn, the problem decomposes to K problems coupled by probabilities, and an iteration reduces to finding Kn weighted medians of points on a line. The complexity of the algorithm is linear in the dimension of the data space, and its performance was observed to improve significantly as the dimension increases.

Keywords

clusteringcontinuous locationhigh-dimensional dataℓ1-norm
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 2 , April 2022 , pp. 433 - 448
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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