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Kernel Methods on Approximate Infinite-Dimensional Covariance Operators for Image Classification by Minh, Hà Quang; Biagio, Marco San; Bazzani, Loris; Murino, Vittorio is a scholarly article available to read on EtoBox.

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This paper presents a novel framework for visual object recognition using infinite-dimensional covariance operators of input features in the paradigm of kernel methods on infinite-dimensional Riemannian manifolds. Our formulation provides in particular a rich representation of image features by exploiting their non-linear correlations. Theoretically, we provide a finite-dimensional approximation of the Log-Hilbert-Schmidt (Log-HS) distance between covariance operators that is scalable to large datasets, while maintaining an effective discriminating capability. This allows us to efficiently approximate any continuous shift-invariant kernel defined using the Log-HS distance. At the same time, we prove that the Log-HS inner product between covariance operators is only approximable by its finite-dimensional counterpart in a very limited scenario. Consequently, kernels defined using the Log-HS inner product, such as polynomial kernels, are not scalable in the same way as shift-invariant kernels. Computationally, we apply the approximate Log-HS distance formulation to covariance operators of both handcrafted and convolutional features, exploiting both the expressiveness of these features

Author

Minh, Hà Quang; Biagio, Marco San; Bazzani, Loris; Murino, Vittorio

Published

2016

Language

EN