A Kernel for Time Series Based on Global Alignments

Abstract

We propose in this paper a new family of kernels to handle times series, notably speech data, within the framework of kernel methods which includes popular algorithms such as the Support Vector Machine. These kernels elaborate on the well known Dynamic Time Warping (DTW) family of distances by considering the same set of elementary operations, namely substitutions and repetitions of tokens, to map a sequence onto another. Associating to each of these operations a given score, DTW algorithms use dynamic programming techniques to compute an optimal sequence of operations with high overall score. In this paper we consider instead the score spanned by all possible alignments, take a smoothed version of their maximum and derive a kernel out of this formulation. We prove that this kernel is positive de nite under favorable conditions and show how it can be tuned effectively for practical applications as we report encouraging results on a speech recognition task.

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

“…In the second experiment, the proposed kernel has been applied to the original UCR time-series [20] to analyze its potential in time-series classification using an SVM. In this case, the proposed kernel shows a remarkable performance when comparing with a kernel based on DTW [10] and a linear kernel. Finally, two realworld applications related to ozone concentration in atmosphere and electricity demand have been considered to show the performance of the MUSS kernel over very specific datasets.…”

“…Thus, the matrix can be precomputed just once when computing the pair-wise kernel of a whole dataset providing a reduction of the computing time. Most of kernels for time series proposed in the literature can not be represented by a matrix, which is not depending on the values of the time series [6,10,34]. Moreover, the structure of the Z = {z ij } 1≤i,j≤N matrix can be obtained by unwrapping Eq.…”

“…In [10] a new kernel based on the DTW distance is defined by global alignments (GA-DTW). In particular, the kernel is defined as the sum of the exponential function of the distances for all possible alignments.…”

Domain-Adaptive Discriminative One-Shot Learning of Gestures

“…Furthermore, it is unlikely to be robust as a similarity measure as it only uses the cost of the minimum alignment. In this work we use a recently proposed positive definite kernel, the Global Alignment (GA) kernel [12,13]. In addition to being positive definite, it has the interesting property of considering all possible alignment distances instead of only the minimum (as in DTW).…”

Learning Pedestrian Trajectories with Kernels

“…We first cluster trajectories using Kernel K-means equipped a DTW kernel [4] to effectively compare paths of different length. Then we learn a function which allows to estimate the instantaneous velocity of a target given its current position and the cluster membership.…”