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This paper introduces kdiff, a novel kernel-based measure for estimatingdistances between instances of time series, random fields and other forms ofstructured data. This measure is based on the idea of matching distributionsthat only overlap over a portion of their region of support. Our proposedmeasure is inspired by MPdist which has been previously proposed for suchdatasets and is constructed using Euclidean metrics, whereas kdiff isconstructed using non-linear kernel distances. Also, kdiff accounts for bothself and cross similarities across the instances and is defined using a lowerquantile of the distance distribution. Comparing the cross similarity to selfsimilarity allows for measures of similarity that are more robust to noise andpartial occlusions of the relevant signals. Our proposed measure kdiff is amore general form of the well known kernel-based Maximum Mean Discrepancy (MMD)distance estimated over the embeddings. Some theoretical results are providedfor separability conditions using kdiff as a distance measure for clusteringand classification problems where the embedding distributions can be modeled astwo component mixtures. Applications are demonstrated for clustering ofsynthetic and real-life time series and image data, and the performance ofkdiff is compared to competing distance measures for clustering.

Kernel distance measures for time series, random fields and other structured data