k -spaces: Mixtures of Gaussian latent variable models

Area of Science:

• Computational Biology
• Machine Learning
• Genomics

Background:

• Principal Component Analysis (PCA) and k-means clustering are distinct methods for dimension reduction and clustering.
• These methods can be viewed as special cases within a Gaussian latent variable model framework.

Purpose of the Study:

• To develop a unified probabilistic framework for simultaneous dimension reduction, clustering, and latent space learning.
• To introduce an efficient and interpretable algorithm, k-spaces, as an alternative to combined PCA and clustering methods.

Main Methods:

• Developed a probabilistic framework based on Gaussian latent variable models.
• Introduced the k-spaces algorithm for integrated analysis.
• Applied the method to diverse genomic datasets.

Main Results:

• Demonstrated that PCA and k-means are special cases of Gaussian latent variable models.
• Showcased the broad applicability of k-spaces in genomics.
• Successfully applied k-spaces for gene expression modeling in qHCR images, epigenomics inference, and single-cell RNA-sequencing data dimension reduction.

Conclusions:

• k-spaces provides an efficient and interpretable probabilistic approach for simultaneous dimension reduction and clustering.
• The unified framework offers a principled replacement for ad hoc combinations of existing methods.
• k-spaces shows significant potential across various genomic applications.