Learning from Few Samples: Transformation-Invariant SVMs with Composition and Locality at Multiple Scales

TL;DR

This paper introduces a novel approach to enhance support-vector machines (SVMs) by embedding invariances, local features, and multi-scale composition, inspired by CNNs, to improve learning with small sample sizes.

Contribution

It demonstrates that kernels based on maximum similarity over transformations are positive definite with high probability and effective for small sample learning, integrating CNN-like properties into SVMs.

Findings

SVMs with transformation-invariant kernels outperform deep neural networks on small datasets.

Positive definiteness of maximum similarity kernels holds with high probability in small sample regimes.

Incorporating local features and multi-scale composition improves SVM accuracy.

Abstract

Motivated by the problem of learning with small sample sizes, this paper shows how to incorporate into support-vector machines (SVMs) those properties that have made convolutional neural networks (CNNs) successful. Particularly important is the ability to incorporate domain knowledge of invariances, e.g., translational invariance of images. Kernels based on the \textit{maximum} similarity over a group of transformations are not generally positive definite. Perhaps it is for this reason that they have not been studied theoretically. We address this lacuna and show that positive definiteness indeed holds \textit{with high probability} for kernels based on the maximum similarity in the small training sample set regime of interest, and that they do yield the best results in that regime. We also show how additional properties such as their ability to incorporate local features at multiple spatial scales, e.g., as done in CNNs through max pooling, and to provide the benefits of composition through the architecture of multiple layers, can also be embedded into SVMs. We verify through experiments on widely available image sets that the resulting SVMs do provide superior accuracy in comparison to well-established deep neural network benchmarks for small sample sizes.