Learning from Few Samples: Transformation-Invariant SVMs with Composition and Locality at Multiple Scales
This addresses the challenge of limited data for machine learning practitioners, offering a theoretically grounded and effective alternative to deep learning in small-sample scenarios.
The paper tackled the problem of learning with small sample sizes by incorporating convolutional neural network properties like transformation invariance and multi-scale local features into support-vector machines, showing that the resulting SVMs achieve superior accuracy compared to deep neural network benchmarks in this regime.
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.