Abstract
This paper presents two clustering algorithms based on α-divergence between memberships and variables that control cluster sizes: one is for spherical data and the other for categorical multivariate data. First, this paper shows that a conventional method for vectorial data can be interpreted as the regularization of another conventional method with α-divergence. Second, with this interpretation, a spherical clustering algorithm based on α-divergence is derived from an optimization problem built by regularizing a conventional method with α-divergence. Third, this paper connects the facts that the α-divergence is a generalization of Kullback-Leibler (KL)-divergence, and that three conventional co-clustering methods are based on KL-divergence. Based on these facts, a co-clustering algorithm based on α-divergence is derived from an optimization problem built by extending the KL-divergence in conventional methods to α-divergence. This paper also demonstrates some numerical examples for the proposed methods.
| Original language | English |
|---|---|
| Title of host publication | FUZZ-IEEE 2015 - IEEE International Conference on Fuzzy Systems |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Volume | 2015-November |
| ISBN (Electronic) | 9781467374286 |
| DOIs | |
| Publication status | Published - 2015 Nov 25 |
| Event | IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2015 - Istanbul, Turkey Duration: 2015 Aug 2 → 2015 Aug 5 |
Other
| Other | IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2015 |
|---|---|
| Country | Turkey |
| City | Istanbul |
| Period | 15/8/2 → 15/8/5 |
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Keywords
- Atmospheric measurements
- Clustering algorithms
- Clustering methods
- Entropy
- Machine learning algorithms
- Optimization
- Particle measurements
ASJC Scopus subject areas
- Software
- Theoretical Computer Science
- Artificial Intelligence
- Applied Mathematics
Cite this
Fuzzy clustering based on α-divergence for spherical data and for categorical multivariate data. / Kanzawa, Yuchi.
FUZZ-IEEE 2015 - IEEE International Conference on Fuzzy Systems. Vol. 2015-November Institute of Electrical and Electronics Engineers Inc., 2015. 7337853.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Fuzzy clustering based on α-divergence for spherical data and for categorical multivariate data
AU - Kanzawa, Yuchi
PY - 2015/11/25
Y1 - 2015/11/25
N2 - This paper presents two clustering algorithms based on α-divergence between memberships and variables that control cluster sizes: one is for spherical data and the other for categorical multivariate data. First, this paper shows that a conventional method for vectorial data can be interpreted as the regularization of another conventional method with α-divergence. Second, with this interpretation, a spherical clustering algorithm based on α-divergence is derived from an optimization problem built by regularizing a conventional method with α-divergence. Third, this paper connects the facts that the α-divergence is a generalization of Kullback-Leibler (KL)-divergence, and that three conventional co-clustering methods are based on KL-divergence. Based on these facts, a co-clustering algorithm based on α-divergence is derived from an optimization problem built by extending the KL-divergence in conventional methods to α-divergence. This paper also demonstrates some numerical examples for the proposed methods.
AB - This paper presents two clustering algorithms based on α-divergence between memberships and variables that control cluster sizes: one is for spherical data and the other for categorical multivariate data. First, this paper shows that a conventional method for vectorial data can be interpreted as the regularization of another conventional method with α-divergence. Second, with this interpretation, a spherical clustering algorithm based on α-divergence is derived from an optimization problem built by regularizing a conventional method with α-divergence. Third, this paper connects the facts that the α-divergence is a generalization of Kullback-Leibler (KL)-divergence, and that three conventional co-clustering methods are based on KL-divergence. Based on these facts, a co-clustering algorithm based on α-divergence is derived from an optimization problem built by extending the KL-divergence in conventional methods to α-divergence. This paper also demonstrates some numerical examples for the proposed methods.
KW - Atmospheric measurements
KW - Clustering algorithms
KW - Clustering methods
KW - Entropy
KW - Machine learning algorithms
KW - Optimization
KW - Particle measurements
UR - http://www.scopus.com/inward/record.url?scp=84975760671&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84975760671&partnerID=8YFLogxK
U2 - 10.1109/FUZZ-IEEE.2015.7337853
DO - 10.1109/FUZZ-IEEE.2015.7337853
M3 - Conference contribution
AN - SCOPUS:84975760671
VL - 2015-November
BT - FUZZ-IEEE 2015 - IEEE International Conference on Fuzzy Systems
PB - Institute of Electrical and Electronics Engineers Inc.
ER -