Geometry-aware Deep Transform

TL;DR

This paper introduces a geometry-aware deep transform that unifies classification and metric learning, enhancing robustness and performance on small datasets through a formal robustness analysis.

Contribution

It proposes a novel deep learning objective that combines classification and metric learning with a geometry-aware transform for improved small dataset performance.

Findings

Competitive performance on small datasets

Robustness analysis supports the framework

Effective on synthetic and real-world data

Abstract

Many recent efforts have been devoted to designing sophisticated deep learning structures, obtaining revolutionary results on benchmark datasets. The success of these deep learning methods mostly relies on an enormous volume of labeled training samples to learn a huge number of parameters in a network; therefore, understanding the generalization ability of a learned deep network cannot be overlooked, especially when restricted to a small training set, which is the case for many applications. In this paper, we propose a novel deep learning objective formulation that unifies both the classification and metric learning criteria. We then introduce a geometry-aware deep transform to enable a non-linear discriminative and robust feature transform, which shows competitive performance on small training sets for both synthetic and real-world data. We further support the proposed framework with a formal $(K,\epsilon)$-robustness analysis.