Ideal type model and an associated method for relational fuzzy clustering

Susana Nascimento, Boris Mirkin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

The ideal type model by Mirkin and Satarov (1990) expresses data points as convex combinations of some 'ideal type' points. However, this model cannot prevent the ideal type points being far away from the observations and, in fact, requires that. Archetypal analysis by Cutler and Breiman (1994) and proportional membership fuzzy clustering by Nascimento et al. (2003) propose different ways of avoiding this entrapment. We propose one more way out - by assuming the ideal types being mutually orthogonal and transforming the model by multiplying it over its transpose. The obtained additive fuzzy clustering model for relational data is akin to that more recently analysed by Mirkin and Nascimento (2012) in a different context. The one-by-one clustering approach to the ideal type model is reformulated here as that naturally leading to a spectral clustering algorithm for finding fuzzy membership vectors. The algorithm is proven to be computationally valid and competitive against popular relational fuzzy clustering algorithms.

Original languageEnglish
Title of host publication2017 IEEE International Conference on Fuzzy Systems, FUZZ 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)978-1-5090-6034-4
DOIs
Publication statusPublished - 23 Aug 2017
Event2017 IEEE International Conference on Fuzzy Systems, FUZZ 2017 - Naples, Italy
Duration: 9 Jul 201712 Jul 2017

Conference

Conference2017 IEEE International Conference on Fuzzy Systems, FUZZ 2017
CountryItaly
CityNaples
Period9/07/1712/07/17

Fingerprint

Fuzzy clustering
Fuzzy Clustering
Clustering algorithms
Clustering Algorithm
Fuzzy Membership
Farthest Point
Spectral Clustering
Model
Transpose
Fuzzy Algorithm
Convex Combination
Express
Directly proportional
Clustering
Valid

Keywords

  • C-MEANS

Cite this

Nascimento, S., & Mirkin, B. (2017). Ideal type model and an associated method for relational fuzzy clustering. In 2017 IEEE International Conference on Fuzzy Systems, FUZZ 2017 [8015473] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/FUZZ-IEEE.2017.8015473
Nascimento, Susana ; Mirkin, Boris. / Ideal type model and an associated method for relational fuzzy clustering. 2017 IEEE International Conference on Fuzzy Systems, FUZZ 2017. Institute of Electrical and Electronics Engineers Inc., 2017.
@inproceedings{b07069332d5a44ebadde9cea5ed2a138,
title = "Ideal type model and an associated method for relational fuzzy clustering",
abstract = "The ideal type model by Mirkin and Satarov (1990) expresses data points as convex combinations of some 'ideal type' points. However, this model cannot prevent the ideal type points being far away from the observations and, in fact, requires that. Archetypal analysis by Cutler and Breiman (1994) and proportional membership fuzzy clustering by Nascimento et al. (2003) propose different ways of avoiding this entrapment. We propose one more way out - by assuming the ideal types being mutually orthogonal and transforming the model by multiplying it over its transpose. The obtained additive fuzzy clustering model for relational data is akin to that more recently analysed by Mirkin and Nascimento (2012) in a different context. The one-by-one clustering approach to the ideal type model is reformulated here as that naturally leading to a spectral clustering algorithm for finding fuzzy membership vectors. The algorithm is proven to be computationally valid and competitive against popular relational fuzzy clustering algorithms.",
keywords = "C-MEANS",
author = "Susana Nascimento and Boris Mirkin",
note = "sem pdf conforme despacho. NOVA LINCS - UID/CEC/04516/2013",
year = "2017",
month = "8",
day = "23",
doi = "10.1109/FUZZ-IEEE.2017.8015473",
language = "English",
booktitle = "2017 IEEE International Conference on Fuzzy Systems, FUZZ 2017",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
address = "United States",

}

Nascimento, S & Mirkin, B 2017, Ideal type model and an associated method for relational fuzzy clustering. in 2017 IEEE International Conference on Fuzzy Systems, FUZZ 2017., 8015473, Institute of Electrical and Electronics Engineers Inc., 2017 IEEE International Conference on Fuzzy Systems, FUZZ 2017, Naples, Italy, 9/07/17. https://doi.org/10.1109/FUZZ-IEEE.2017.8015473

Ideal type model and an associated method for relational fuzzy clustering. / Nascimento, Susana; Mirkin, Boris.

2017 IEEE International Conference on Fuzzy Systems, FUZZ 2017. Institute of Electrical and Electronics Engineers Inc., 2017. 8015473.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

TY - GEN

T1 - Ideal type model and an associated method for relational fuzzy clustering

AU - Nascimento, Susana

AU - Mirkin, Boris

N1 - sem pdf conforme despacho. NOVA LINCS - UID/CEC/04516/2013

PY - 2017/8/23

Y1 - 2017/8/23

N2 - The ideal type model by Mirkin and Satarov (1990) expresses data points as convex combinations of some 'ideal type' points. However, this model cannot prevent the ideal type points being far away from the observations and, in fact, requires that. Archetypal analysis by Cutler and Breiman (1994) and proportional membership fuzzy clustering by Nascimento et al. (2003) propose different ways of avoiding this entrapment. We propose one more way out - by assuming the ideal types being mutually orthogonal and transforming the model by multiplying it over its transpose. The obtained additive fuzzy clustering model for relational data is akin to that more recently analysed by Mirkin and Nascimento (2012) in a different context. The one-by-one clustering approach to the ideal type model is reformulated here as that naturally leading to a spectral clustering algorithm for finding fuzzy membership vectors. The algorithm is proven to be computationally valid and competitive against popular relational fuzzy clustering algorithms.

AB - The ideal type model by Mirkin and Satarov (1990) expresses data points as convex combinations of some 'ideal type' points. However, this model cannot prevent the ideal type points being far away from the observations and, in fact, requires that. Archetypal analysis by Cutler and Breiman (1994) and proportional membership fuzzy clustering by Nascimento et al. (2003) propose different ways of avoiding this entrapment. We propose one more way out - by assuming the ideal types being mutually orthogonal and transforming the model by multiplying it over its transpose. The obtained additive fuzzy clustering model for relational data is akin to that more recently analysed by Mirkin and Nascimento (2012) in a different context. The one-by-one clustering approach to the ideal type model is reformulated here as that naturally leading to a spectral clustering algorithm for finding fuzzy membership vectors. The algorithm is proven to be computationally valid and competitive against popular relational fuzzy clustering algorithms.

KW - C-MEANS

UR - http://www.scopus.com/inward/record.url?scp=85030180487&partnerID=8YFLogxK

U2 - 10.1109/FUZZ-IEEE.2017.8015473

DO - 10.1109/FUZZ-IEEE.2017.8015473

M3 - Conference contribution

BT - 2017 IEEE International Conference on Fuzzy Systems, FUZZ 2017

PB - Institute of Electrical and Electronics Engineers Inc.

ER -

Nascimento S, Mirkin B. Ideal type model and an associated method for relational fuzzy clustering. In 2017 IEEE International Conference on Fuzzy Systems, FUZZ 2017. Institute of Electrical and Electronics Engineers Inc. 2017. 8015473 https://doi.org/10.1109/FUZZ-IEEE.2017.8015473