Hierarchical mixtures of Gaussians for combined dimensionality reduction and clustering

• URL: http://arxiv.org/abs/2206.04841v1
• Date: Fri, 10 Jun 2022 02:03:18 GMT
• Title: Hierarchical mixtures of Gaussians for combined dimensionality reduction and clustering
• Authors: Sacha Sokoloski, Philipp Berens
• Abstract summary: We show how a family of such two-stage models can be combined into a single, hierarchical model that we call a hierarchical mixture of Gaussians (HMoG) An HMoG simultaneously captures both dimensionality-reduction and clustering, and its performance is quantified in closed-form by the likelihood function. We apply HMoGs to synthetic data and RNA sequencing data, and demonstrate how they exceed the limitations of two-stage models.
• Score: 5.819751855626331
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: To avoid the curse of dimensionality, a common approach to clustering high-dimensional data is to first project the data into a space of reduced dimension, and then cluster the projected data. Although effective, this two-stage approach prevents joint optimization of the dimensionality-reduction and clustering models, and obscures how well the complete model describes the data. Here, we show how a family of such two-stage models can be combined into a single, hierarchical model that we call a hierarchical mixture of Gaussians (HMoG). An HMoG simultaneously captures both dimensionality-reduction and clustering, and its performance is quantified in closed-form by the likelihood function. By formulating and extending existing models with exponential family theory, we show how to maximize the likelihood of HMoGs with expectation-maximization. We apply HMoGs to synthetic data and RNA sequencing data, and demonstrate how they exceed the limitations of two-stage models. Ultimately, HMoGs are a rigorous generalization of a common statistical framework, and provide researchers with a method to improve model performance when clustering high-dimensional data.

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