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, called DeCOr-MDS (Detection and Correction of Orthogonal outliers using MDS), 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, human microbiome project data and single cell RNA sequencing data, to address the task of data cleaning and visualization.
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