Unsupervised Initialization of Archetypal Analysis and Proportional Membership Fuzzy Clustering

  • Susana NascimentoEmail author
  • Nuno Madaleno
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11872)


This paper further investigates and compares a method for fuzzy clustering which retrieves pure individual types from data, known as the fuzzy clustering with proportional membership (FCPM), with the FurthestSum Archetypal Analysis algorithm (FS-AA). The Anomalous Pattern (AP) initialization algorithm, an algorithm that sequentially extracts clusters one by one in a manner similar to principal component analysis, is shown to outperform the FurthestSum not only by improving the convergence of FCPM and AA algorithms but also to be able to model the number of clusters to extract from data.

A study comparing nine information-theoretic validity indices and the soft ARI has shown that the soft Normalized Mutual Information max (\(NMI_{sM}\)) and the Adjusted Mutual Information (AMI) indices are more adequate to access the quality of FCPM and AA partitions than soft internal validity indices. The experimental study was conducted exploring a collection of 99 synthetic data sets generated from a proper data generator, the FCPM-DG, covering various dimensionalities as well as 18 benchmark data sets from machine learning.


Archetypal analysis Fuzzy clustering Number of clusters Information-Theoretic validity indices 



S.N. acknowledges the support by FCT/MCTES, NOVA LINCS (UID/CEC/04516/2019). The authors are thankful to the anonymous reviewers for their insightful and constructive comments that allowed to improve the paper.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Computer Science Department and NOVA LINCS, Faculdade de Ciências e TecnologiaUniversidade Nova de LisboaLisbonPortugal

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