A flexible approach to high-dimensional clustering and classification using mixtures of finite mutually repulsive mixtures
Abstract
We propose a novel approach for clustering that is later extended to classification. Our methods are based on an underlying determinantal point process (DPP) that generates sparsity and separation of location parameters in a mixture of finite mixture models specification. A key aspect is the assumption of a DPP conditional on the number of groups and a prior on this number, which results in a dynamic mixture of repulsive mixtures. The proposed model also involves a sparse tensor decomposition of the covariance function used to define the DPP, which is coupled with a separate mixture model employed to handle the intra-cluster correlation structure. Further computational enhancement in the high-dimensional case comes from exploiting a mapping from Euclidean space to the space of (valid) correlation matrices. A suitable posterior simulation scheme involving a modified telescopic sampler is developed. The resulting approach is seen to perform satisfactorily in simulated and real data examples.
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BibTeX
@misc{murua2026flexible,
title = {{A flexible approach to high-dimensional clustering and classification using mixtures of finite mutually repulsive mixtures}},
author = {Alejandro Murua and Fernando Andrés Quintana},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37607},
eprint = {2610.37607},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37607},
}
RIS
TY - UNPB
TI - A flexible approach to high-dimensional clustering and classification using mixtures of finite mutually repulsive mixtures
AU - Alejandro Murua
AU - Fernando Andrés Quintana
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37607
UR - https://arxiv.org/abs/2610.37607
AB - We propose a novel approach for clustering that is later extended to classification. Our methods are based on an underlying determinantal point process (DPP) that generates sparsity and separation of location parameters in a mixture of finite mixture models specification. A key aspect is the assumption of a DPP conditional on the number of groups and a prior on this number, which results in a dynamic mixture of repulsive mixtures. The proposed model also involves a sparse tensor decomposition of the covariance function used to define the DPP, which is coupled with a separate mixture model employed to handle the intra-cluster correlation structure. Further computational enhancement in the high-dimensional case comes from exploiting a mapping from Euclidean space to the space of (valid) correlation matrices. A suitable posterior simulation scheme involving a modified telescopic sampler is developed. The resulting approach is seen to perform satisfactorily in simulated and real data examples.
ER -