  This paper introduces kdiff, a novel kernel-based measure for estimating
distances between instances of time series, random fields and other forms of
structured data. This measure is based on the idea of matching distributions
that only overlap over a portion of their region of support. Our proposed
measure is inspired by MPdist which has been previously proposed for such
datasets and is constructed using Euclidean metrics, whereas kdiff is
constructed using non-linear kernel distances. Also, kdiff accounts for both
self and cross similarities across the instances and is defined using a lower
quantile of the distance distribution. Comparing the cross similarity to self
similarity allows for measures of similarity that are more robust to noise and
partial occlusions of the relevant signals. Our proposed measure kdiff is a
more general form of the well known kernel-based Maximum Mean Discrepancy (MMD)
distance estimated over the embeddings. Some theoretical results are provided
for separability conditions using kdiff as a distance measure for clustering
and classification problems where the embedding distributions can be modeled as
two component mixtures. Applications are demonstrated for clustering of
synthetic and real-life time series and image data, and the performance of
kdiff is compared to competing distance measures for clustering.
