Visualizing the Effects of a Changing Distance Using Continuous Embeddings

• Activity Number: 163
• Type: Topic Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Gina Gruenhage*+ and Simon Barthelme
• Companies: Artificial Intelligence Group, TU Berlin, BCCN Berlin and University of Geneva
• Keywords: dimensionality reduction ; multidimensional scaling ; statistical graphics ; MDS ; cMDS ; visualization

Abstract

Most statistics and machine learning methods, from clustering to classification, rely on a distance function to describe relationships between data points. For complex data it is often hard to avoid making arbitrary choices when defining a distance function. To compare images, one must choose a spatial scale. To compare signals, one must choose a temporal scale. The right scale is hard to pin down and it is preferable when results do not depend too tightly on the exact chosen value. Topological data analysis addresses this issue by focusing on the notion of neighborhood instead of that of distance. Here, we present a simpler solution. One can check how strongly distance relationships depend on a hyperparameter using dimensionality reduction. We formulate a variant of dynamical multidimensional scaling (MDS), which embeds data points as curves. The resulting algorithm provides a simple and efficient way of visualizing changes and invariances in distance patterns as a hyperparameter is varied. We apply it to challenging brain connectivity data sets. We also show how the algorithm can be used to visualize the effects of changing the relative weight of two groups of variables.