Similarity by Composition

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3 Author(s)

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 S1 is “similar” to a signal S2 if it is “easy” to compose S1 from few large contiguous chunks of S2. 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 S1 is to S2. 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 S1 to S2. “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.