Orthogonal outlier detection and dimension estimation for improved MDS embedding of biological datasets

Abstract

Conventional dimensionality reduction methods like Multidimensional Scaling (MDS) are sensitive to the presence of orthogonal outliers, leading to significant defects in the embedding. We introduce a robust MDS method, based on the geometry and statistics of simplices formed by data points, that allows to detect orthogonal outliers and subsequently reduce dimensionality. We validate our methods using synthetic datasets, and further show how it can be applied to a variety of large real biological datasets, including cancer image cell data and human microbiome project data.

Using a Riemannian elastic metric for statistical analysis of tumor cell shape heterogeneity

“…The elastic metric has been the object of several theoretical and computational developments that primarily focused on curves (for a recent overview, see [4]), with applications to various kinds of biological shapes, including tumor images from MRI (but no cell shapes), plant leafs, or protein backbones [5,6,23]. More recent studies have applied the elastic metric to cell shapes [15,7,17,11] for classification [15,7], dimensionality reduction [11] and regression with metric learning [17]. To our knowledge, the present study is the first to perform a comparative statistical analysis of the elastic metric for tumor cells across different conditions.…”

“…More details about the experimental methods are available in [1]. We remove outliers from artefacts due to bad segmentation [11], and discretize the cell contour into 100 2D points. After processing, the DUNN cell lines contains 392 cells, including 203 cells in the control group, 96 cells treated by jasp and 93 cells treated by cytD.…”