Unsupervised machine learning framework for discriminating major variants of concern during COVID-19

Due to the high mutation rate of the virus, the COVID-19 pandemic evolved rapidly. Certain variants of the virus, such as Delta and Omicron emerged with altered viral properties leading to severe transmission and death rates. These variants burdened the medical systems worldwide with a major impact to travel, productivity, and the world economy. Unsupervised machine learning methods have the ability to compress, characterize, and visualize unlabelled data. This paper presents a framework that utilizes unsupervised machine learning methods to discriminate and visualize the associations between major COVID-19 variants based on their genome sequences. These methods comprise a combination of selected dimensionality reduction and clustering techniques. The framework processes the RNA sequences by performing a k-mer analysis on the data and further visualises and compares the results using selected dimensionality reduction methods that include principal component analysis (PCA), t-distributed stochastic neighbour embedding (t-SNE), and uniform manifold approximation projection (UMAP). Our framework also employs agglomerative hierarchical clustering to visualize the mutational differences among major variants of concern and country-wise mutational differences for selected variants (Delta and Omicron) using dendrograms. We also provide country-wise mutational differences for selected variants via dendrograms. We find that the proposed framework can effectively distinguish between the major variants and has the potential to identify emerging variants in the future.

Principal Component Analysis and Related Methods for Investigating the Dynamics of Biological Macromolecules

Principal component analysis (PCA) is used to reduce the dimensionalities of high-dimensional datasets in a variety of research areas. For example, biological macromolecules, such as proteins, exhibit many degrees of freedom, allowing them to adopt intricate structures and exhibit complex functions by undergoing large conformational changes. Therefore, molecular simulations of and experiments on proteins generate a large number of structure variations in high-dimensional space. PCA and many PCA-related methods have been developed to extract key features from such structural data, and these approaches have been widely applied for over 30 years to elucidate macromolecular dynamics. This review mainly focuses on the methodological aspects of PCA and related methods and their applications for investigating protein dynamics.

Tukey's Depth for Object Data

We develop a novel exploratory tool for non-Euclidean object data based on data depth, extending celebrated Tukey's depth for Euclidean data. The proposed metric halfspace depth, applicable to data objects in a general metric space, assigns to data points depth values that characterize the centrality of these points with respect to the distribution and provides an interpretable center-outward ranking. Desirable theoretical properties that generalize standard depth properties postulated for Euclidean data are established for the metric halfspace depth. The depth median, defined as the deepest point, is shown to have high robustness as a location descriptor both in theory and in simulation. We propose an efficient algorithm to approximate the metric halfspace depth and illustrate its ability to adapt to the intrinsic data geometry. The metric halfspace depth was applied to an Alzheimer's disease study, revealing group differences in the brain connectivity, modeled as covariance matrices, for subjects in different stages of dementia. Based on phylogenetic trees of 7 pathogenic parasites, our proposed metric halfspace depth was also used to construct a meaningful consensus estimate of the evolutionary history and to identify potential outlier trees.