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Research on cluster analysis for categorical data continues to develop, with new clustering algorithms being proposed. However, in this context, the determination of the number of clusters is rarely addressed. In this paper, we propose a…

The task of clustering a set of objects based on multiple sources of data arises in several modern applications. We propose an integrative statistical model that permits a separate clustering of the objects for each data source. These…

Spatial transcriptomics is a modern sequencing technology that allows the measurement of the activity of thousands of genes in a tissue sample and map where the activity is occurring. This technology has enabled the study of the so-called…

We propose two related unsupervised clustering algorithms which, for input, take data assumed to be sampled from a uniform distribution supported on a metric space $X$, and output a clustering of the data based on the selection of a…

This paper investigates the computational and statistical limits in clustering matrix-valued observations. We propose a low-rank mixture model (LrMM), adapted from the classical Gaussian mixture model (GMM) to treat matrix-valued…

Network theory has proven invaluable in unraveling complex protein interactions. Previous studies have employed statistical methods rooted in network theory, including the Gaussian graphical model, to infer networks among proteins,…

Deep learning methods are primarily proposed for supervised learning of images or text with limited applications to clustering problems. In contrast, tabular data with heterogeneous features pose unique challenges in representation…

The availability of large microarray data has led to a growing interest in biclustering methods in the past decade. Several algorithms have been proposed to identify subsets of genes and conditions according to different similarity measures…

In this paper, we solve a semi-supervised regression problem. Due to the lack of knowledge about the data structure and the presence of random noise, the considered data model is uncertain. We propose a method which combines graph Laplacian…

Characterizing patient somatic mutations through next-generation sequencing technologies opens up possibilities for refining cancer subtypes. However, catalogues of mutations reveal that only a small fraction of the genes are altered…

The estimation of covariance matrices of gene expressions has many applications in cancer systems biology. Many gene expression studies, however, are hampered by low sample size and it has therefore become popular to increase sample size by…

Mapper, a topological algorithm, is frequently used as an exploratory tool to build a graphical representation of data. This representation can help to gain a better understanding of the intrinsic shape of high-dimensional genomic data and…

Modern high-throughput sequencing technologies have enabled us to profile multiple molecular modalities from the same single cell, providing unprecedented opportunities to assay celluar heterogeneity from multiple biological layers.…

Recent experimental advances in biology allow researchers to obtain gene expression profiles at single-cell resolution over hundreds, or even thousands of cells at once. These single-cell measurements provide snapshots of the states of the…

The joint analysis of biomedical data in Alzheimer's Disease (AD) is important for better clinical diagnosis and to understand the relationship between biomarkers. However, jointly accounting for heterogeneous measures poses important…

Subspace clustering algorithms are used for understanding the cluster structure that explains the dataset well. These methods are extensively used for data-exploration tasks in various areas of Natural Sciences. However, most of these…

We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are…

This paper addresses the problem of clustering measurement vectors that are heteroscedastic in that they can have different covariance matrices. From the assumption that the measurement vectors within a given cluster are Gaussian…

High-throughput microarray and sequencing technology have been used to identify disease subtypes that could not be observed otherwise by using clinical variables alone. The classical unsupervised clustering strategy concerns primarily the…

Cancer diagnosis, prognosis, and therapeutic response predictions are based on morphological information from histology slides and molecular profiles from genomic data. However, most deep learning-based objective outcome prediction and…