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Braverman’s Spectrum and Matrix Diagonalization Versus iK-Means: A Unified Framework for Clustering

  • Boris MirkinEmail author
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11100)

Abstract

In this paper, I discuss current developments in cluster analysis to bring forth earlier developments by E. Braverman and his team. Specifically, I begin by recalling their Spectrum clustering method and Matrix diagonalization criterion. These two include a number of user-specified parameters such as the number of clusters and similarity threshold, which corresponds to the state of affairs as it was at early stages of data science developments; it remains so currently, too. Meanwhile, a data-recovery view of the Principal Component Analysis method admits a natural extension to clustering which embraces two of the most popular clustering methods, K-Means partitioning and Ward agglomerative clustering. To see that, one needs just adjusting the point of view and recognising an equivalent complementary criterion demanding the clusters to be simultaneously “large-sized” and “anomalous”. Moreover, this paradigm shows that the complementary criterion can be reformulated in terms of object-to-object similarities. This criterion appears to be equivalent to the heuristic Matrix diagonalization criterion by Dorofeyuk-Braverman. Moreover, a greedy one-by-one cluster extraction algorithm for this criterion appears to be a version of the Braverman’s Spectrum algorithm – but with automated adjustment of parameters. An illustrative example with mixed scale data completes the presentation.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Data Analysis and Machine IntelligenceNational Research University Higher School of EconomicsMoscowRussian Federation
  2. 2.Department of Computer ScienceBirkbeck University of LondonLondonUK

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