Bigeometric Organization of Deep Nets

TL;DR

This paper introduces a novel geometric organization method for high-dimensional datasets with missing data and irrelevant features, utilizing deep net representations to achieve a smooth, intrinsic low-dimensional structure.

Contribution

The paper presents a new algorithm that reorganizes high-dimensional data geometry using deep nets and local z-scoring, independent of deep net parameters, to better model functions of interest.

Findings

Generated an intrinsic low-dimensional organization of hospitals.

Achieved smoothness of the organization with respect to a quality function.

Demonstrated effectiveness on healthcare data from CMS.

Abstract

In this paper, we build an organization of high-dimensional datasets that cannot be cleanly embedded into a low-dimensional representation due to missing entries and a subset of the features being irrelevant to modeling functions of interest. Our algorithm begins by defining coarse neighborhoods of the points and defining an expected empirical function value on these neighborhoods. We then generate new non-linear features with deep net representations tuned to model the approximate function, and re-organize the geometry of the points with respect to the new representation. Finally, the points are locally z-scored to create an intrinsic geometric organization which is independent of the parameters of the deep net, a geometry designed to assure smoothness with respect to the empirical function. We examine this approach on data from the Center for Medicare and Medicaid Services Hospital Quality Initiative, and generate an intrinsic low-dimensional organization of the hospitals that is smooth with respect to an expert driven function of quality.