A multi-scale smoothing kernel for measuring time-series similarity

In this paper a kernel for time-series data is introduced so that it can be used for any data mining task that relies on a similarity or distance metric. The main idea of our kernel is that it should recognize as highly similar time-series that are essentially the same but may be slightly perturbed from each other: for example, if one series is shifted with respect to the other or if it slightly misaligned. Namely, our kernel tries to focus on the shape of the time-series and ignores small perturbations such as misalignments or shifts. First, a recursive formulation of the kernel directly based on its definition is proposed. Then it is shown how to efficiently compute the kernel using an equivalent matrix-based formulation. To validate the proposed kernel three experiments have been carried out. As an initial step, several synthetic datasets have been generated from UCR time-series repository and the KDD challenge of 2007 with the purpose of validating the kernel-derived distance over shifted time-series. Also, the kernel has been applied to the original UCR time-series to analyze its potential in time-series classification in conjunction with Support Vector Machines. Finally, two real-world applications related to ozone concentration in atmosphere and electricity demand have been considered.