Direct Log-Density Gradient Estimation with Gaussian Mixture Models and Its Application to Clustering
Summary :
Estimation of the gradient of the logarithm of a probability density function is a versatile tool in statistical data analysis. A recent method for model-seeking clustering called the least-squares log-density gradient clustering (LSLDGC) [Sasaki et al., 2014] employs a sophisticated gradient estimator, which directly estimates the log-density gradients without going through density estimation. However, the typical implementation of LSLDGC is based on a spherical Gaussian function, which may not work well when the probability density function for data has highly correlated local structures. To cope with this problem, we propose a new gradient estimator for log-density gradients with Gaussian mixture models (GMMs). Covariance matrices in GMMs enable the new estimator to capture the highly correlated structures. Through the application of the new gradient estimator to mode-seeking clustering and hierarchical clustering, we experimentally demonstrate the usefulness of our clustering methods over existing methods.
- Publication
- IEICE TRANSACTIONS on Information Vol.E102-D No.6 pp.1154-1162
- Publication Date
- 2019/06/01
- Publicized
- 2019/03/22
- Online ISSN
- 1745-1361
- DOI
- 10.1587/transinf.2018EDP7354
- Type of Manuscript
- PAPER
- Category
- Artificial Intelligence, Data Mining
Authors
Qi ZHANG
Graduate University for Advanced Studies
Hiroaki SASAKI
Nara Institute of Science and Technology
Kazushi IKEDA
Nara Institute of Science and Technology
Keyword
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Qi ZHANG, Hiroaki SASAKI, Kazushi IKEDA, "Direct Log-Density Gradient Estimation with Gaussian Mixture Models and Its Application to Clustering" in IEICE TRANSACTIONS on Information,
vol. E102-D, no. 6, pp. 1154-1162, June 2019, doi: 10.1587/transinf.2018EDP7354.
Abstract: Estimation of the gradient of the logarithm of a probability density function is a versatile tool in statistical data analysis. A recent method for model-seeking clustering called the least-squares log-density gradient clustering (LSLDGC) [Sasaki et al., 2014] employs a sophisticated gradient estimator, which directly estimates the log-density gradients without going through density estimation. However, the typical implementation of LSLDGC is based on a spherical Gaussian function, which may not work well when the probability density function for data has highly correlated local structures. To cope with this problem, we propose a new gradient estimator for log-density gradients with Gaussian mixture models (GMMs). Covariance matrices in GMMs enable the new estimator to capture the highly correlated structures. Through the application of the new gradient estimator to mode-seeking clustering and hierarchical clustering, we experimentally demonstrate the usefulness of our clustering methods over existing methods.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2018EDP7354/_p
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@ARTICLE{e102-d_6_1154,
author={Qi ZHANG, Hiroaki SASAKI, Kazushi IKEDA, },
journal={IEICE TRANSACTIONS on Information},
title={Direct Log-Density Gradient Estimation with Gaussian Mixture Models and Its Application to Clustering},
year={2019},
volume={E102-D},
number={6},
pages={1154-1162},
abstract={Estimation of the gradient of the logarithm of a probability density function is a versatile tool in statistical data analysis. A recent method for model-seeking clustering called the least-squares log-density gradient clustering (LSLDGC) [Sasaki et al., 2014] employs a sophisticated gradient estimator, which directly estimates the log-density gradients without going through density estimation. However, the typical implementation of LSLDGC is based on a spherical Gaussian function, which may not work well when the probability density function for data has highly correlated local structures. To cope with this problem, we propose a new gradient estimator for log-density gradients with Gaussian mixture models (GMMs). Covariance matrices in GMMs enable the new estimator to capture the highly correlated structures. Through the application of the new gradient estimator to mode-seeking clustering and hierarchical clustering, we experimentally demonstrate the usefulness of our clustering methods over existing methods.},
keywords={},
doi={10.1587/transinf.2018EDP7354},
ISSN={1745-1361},
month={June},}
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TY - JOUR
TI - Direct Log-Density Gradient Estimation with Gaussian Mixture Models and Its Application to Clustering
T2 - IEICE TRANSACTIONS on Information
SP - 1154
EP - 1162
AU - Qi ZHANG
AU - Hiroaki SASAKI
AU - Kazushi IKEDA
PY - 2019
DO - 10.1587/transinf.2018EDP7354
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E102-D
IS - 6
JA - IEICE TRANSACTIONS on Information
Y1 - June 2019
AB - Estimation of the gradient of the logarithm of a probability density function is a versatile tool in statistical data analysis. A recent method for model-seeking clustering called the least-squares log-density gradient clustering (LSLDGC) [Sasaki et al., 2014] employs a sophisticated gradient estimator, which directly estimates the log-density gradients without going through density estimation. However, the typical implementation of LSLDGC is based on a spherical Gaussian function, which may not work well when the probability density function for data has highly correlated local structures. To cope with this problem, we propose a new gradient estimator for log-density gradients with Gaussian mixture models (GMMs). Covariance matrices in GMMs enable the new estimator to capture the highly correlated structures. Through the application of the new gradient estimator to mode-seeking clustering and hierarchical clustering, we experimentally demonstrate the usefulness of our clustering methods over existing methods.
ER -
English
