Similarity by Composition

Abstract

We propose a new approach for measuring similarity between two signals, which is applicable to many machine learning tasks, and to many signal types. We say that a signal S 1 is "similar" to a signal S 2 if it is "easy" to compose S 1 from few large contiguous chunks of S 2. Obviously, if we use small enough pieces, then any signal can be composed of any other. Therefore, the larger those pieces are, the more similar S 1 is to S 2. This induces a local similarity score at every point in the signal, based on the size of its supported surrounding region. These local scores can in turn be accumulated in a principled information-theoretic way into a global similarity score of the entire S 1 to S 2. "Similarity by Composition" can be applied between pairs of signals, between groups of signals, and also between different portions of the same signal. It can therefore be employed in a wide variety of machine learning problems (clustering, classification, retrieval, segmentation, attention, saliency, labelling, etc.), and can be applied to a wide range of signal types (images, video, audio, biological data, etc.) We show a few such examples.

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