arXiv subjects

Lingsong Meng

Publications and source records attributed to Lingsong Meng.

3 recordsLinked to original sources

arXiv2025

K-Tensors: Clustering Positive Semi-Definite Matrices

This paper presents a new clustering algorithm for symmetric positive semi-definite (SPSD) matrices, called K-Tensors. The method identifies structured subsets of the SPSD cone characterized by common principal component (CPC) representations, where each subset corresponds to matrices sharing a common eigenstructure. Unlike conventional clustering approaches that rely on vectorization or transformations of SPSD matrices, thereby losing critical geometric and spectral information, K-Tensors introduces a divergence that respects the intrinsic geometry of SPSD matrices. This divergence preserves the shape and eigenstructure information and yields principal SPSD tensors, defined as a set of representative matrices that summarize the distribution of SPSD matrices. By exploring its theoretical properties, we show that the proposed clustering algorithm is self-consistent under mild distribution assumptions and converges to a local optimum. We demonstrate the use of the algorithm through an application to resting-state functional magnetic resonance imaging (rs-fMRI) data from the Human Connectome Project, where we cluster brain connectivity matrices to discover groups of subjects with shared connectivity structures.

cs.LG↗

arXiv2023

Outcome-guided Bayesian Clustering for Disease Subtype Discovery Using High-dimensional Transcriptomic Data

The discovery of disease subtypes is an essential step for developing precision medicine, and disease subtyping via omics data has become a popular approach. While promising, subtypes obtained from conventional approaches may not be necessarily associated with clinical outcomes. The collection of rich clinical data along with omics data has provided an unprecedented opportunity to facilitate the disease subtyping process and to discovery clinically meaningful disease subtypes. Thus, we developed an outcome-guided Bayesian clustering (GuidedBayesianClustering) method to fully integrate the clinical data and the high-dimensional omics data. A Gaussian mixed model framework was applied to perform sample clustering; a spike-and-slab prior was utilized to perform gene selection; a mixture model prior was employed to incorporate the guidance from a clinical outcome variable; and a decision framework was adopted to infer the false discovery rate of the selected genes. We deployed conjugate priors to facilitate efficient Gibbs sampling. Our proposed full Bayesian method is capable of simultaneously (i) obtaining sample clustering (disease subtype discovery); (ii) performing feature selection (select genes related to the disease subtype); and (iii) utilizing clinical outcome variable to guide the disease subtype discovery. The superior performance of the GuidedBayesianClustering was demonstrated through simulations and applications of breast cancer expression data.

stat.AP↗

arXiv2022

Outcome-guided Sparse K-means for Disease Subtype Discovery via Integrating Phenotypic Data with High-dimensional Transcriptomic Data

The discovery of disease subtypes is an essential step for developing precision medicine, and disease subtyping via omics data has become a popular approach. While promising, subtypes obtained from existing approaches are not necessarily associated with clinical outcomes. With the rich clinical data along with the omics data in modern epidemiology cohorts, it is urgent to develop an outcome-guided clustering algorithm to fully integrate the phenotypic data with the high-dimensional omics data. Hence, we extended a sparse K-means method to an outcome-guided sparse K-means (GuidedSparseKmeans) method. An unified objective function was proposed, which was comprised of (i) weighted K-means to perform sample clusterings; (ii) lasso regularizations to perform gene selection from the high-dimensional omics data; (iii) incorporation of a phenotypic variable from the clinical dataset to facilitate biologically meaningful clustering results. By iteratively optimizing the objective function, we will simultaneously obtain a phenotype-related sample clustering results and gene selection results. We demonstrated the superior performance of the GuidedSparseKmeans by comparing with existing clustering methods in simulations and applications of high-dimensional transcriptomic data of breast cancer and Alzheimer's disease. Our algorithm has been implemented into an R package, which is publicly available on GitHub (https://github.com/LingsongMeng/GuidedSparseKmeans).

q-bio.QM↗