Related papers: Genomics Data Analysis via Spectral Shape and Topo…
In this article, we study the question of the statistical convergence of the 1-dimensional Mapper to its continuous analogue, the Reeb graph. We show that the Mapper is an optimal estimator of the Reeb graph, which gives, as a byproduct, a…
We propose a curve-based Riemannian-geometric approach for general shape-based statistical analyses of tumors obtained from radiologic images. A key component of the framework is a suitable metric that (1) enables comparisons of tumor…
Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…
Autonomous individuals establish a structural complex system through pairwise connections and interactions. Notably, the evolution reflects the dynamic nature of each complex system since it recodes a series of temporal changes from the…
Cancer subtyping is crucial for understanding the nature of tumors and providing suitable therapy. However, existing labelling methods are medically controversial, and have driven the process of subtyping away from teaching signals.…
Important objectives in cancer research are the prediction of a patient's risk based on molecular measurements such as gene expression data and the identification of new prognostic biomarkers (e.g. genes). In clinical practice, this is…
We propose a novel computational framework leveraging hypergraph theory to analyse cancer stem cell markers (CSCMs) across multiple organs. Hypergraphs provide a robust representation of CSCM co-expression patterns, capturing their complex…
Single-cell RNA sequencing (scRNA-seq) enables dissecting cellular heterogeneity in tissues, resulting in numerous biological discoveries. Various computational methods have been devised to delineate cell types by clustering scRNA-seq data…
Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…
Gaussian graphical models represent the underlying graph structure of conditional dependence between random variables which can be determined using their partial correlation or precision matrix. In a high-dimensional setting, the precision…
Generative adversarial network (GAN) is widely used for generalized and robust learning on graph data. However, for non-Euclidean graph data, the existing GAN-based graph representation methods generate negative samples by random walk or…
Traditional feature engineering approaches for molecular sequence classification suffer from sparsity issues and computational complexity, while deep learning models often underperform on tabular biological data. This paper introduces a…
We consider the problem of estimating multiple related but distinct graphical models on the basis of a high-dimensional data set with observations that belong to distinct classes. A motivating example occurs in the analysis of gene…
Alterations in nuclear morphology are useful adjuncts and even diagnostic tools used by pathologists in the diagnosis and grading of many tumors, particularly malignant tumors. Large datasets such as TCGA and the Human Protein Atlas, in…
We present the extention and application of a new unsupervised statistical learning technique--the Partition Decoupling Method--to gene expression data. Because it has the ability to reveal non-linear and non-convex geometries present in…
Cancer detection is one of the key research topics in the medical field. Accurate detection of different cancer types is valuable in providing better treatment facilities and risk minimization for patients. This paper deals with the…
Many of today's most interesting questions involve understanding and interpreting complex relationships within graph-based structures. For instance, in materials science, predicting material properties often relies on analyzing the…
Subgraph isomorphism counting is known as #P-complete and requires exponential time to find the accurate solution. Utilizing representation learning has been shown as a promising direction to represent substructures and approximate the…
Mapper is an unsupervised machine learning algorithm generalising the notion of clustering to obtain a geometric description of a dataset. The procedure splits the data into possibly overlapping bins which are then clustered. The output of…
Dimensionality reduction (DR) is an important technique for data exploration and knowledge discovery. However, most of the main DR methods are either linear (e.g., PCA), do not provide an explicit mapping between the original data and its…