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Covariance and histogram image descriptors provide an effective way tocapture information about images. Both excel when used in combination withspecial purpose distance metrics. For covariance descriptors these metricsmeasure the distance along the non-Euclidean Riemannian manifold of symmetricpositive definite matrices. For histogram descriptors the Earth Mover'sdistance measures the optimal transport between two histograms. Although moreprecise, these distance metrics are very expensive to compute, making themimpractical in many applications, even for data sets of only a few thousandexamples. In this paper we present two methods to compress the size ofcovariance and histogram datasets with only marginal increases in test errorfor k-nearest neighbor classification. Specifically, we show that we can reducedata sets to 16% and in some cases as little as 2% of their original size,while approximately matching the test error of kNN classification on the fulltraining set. In fact, because the compressed set is learned in a supervisedfashion, it sometimes even outperforms the full data set, while requiring onlya fraction of the space and drastically reducing test-time computation.

Image Data Compression for Covariance and Histogram Descriptors