  This paper presents an efficient approach for subsequence search in data
streams. The problem consists in identifying coherent repetitions of a given
reference time-series, eventually multi-variate, within a longer data stream.
Dynamic Time Warping (DTW) is the metric most widely used to implement pattern
query, but its computational complexity is a well-known issue. In this paper we
present an approach aimed at learning a kernel able to approximate DTW to be
used for efficiently analyse streaming data collected from wearable sensors,
reducing the burden of computation. Contrary to kernel, DTW allows for
comparing time series with different length. Thus, to use a kernel, a feature
embedding is used to represent a time-series as a fixed length vector. Each
vector component is the DTW between the given time-series and a set of 'basis'
series, usually randomly chosen. The vector size is the number of basis series
used for the feature embedding. Searching for the portion of the data stream
minimizing the DTW with the reference subsequence leads to a global
optimization problem. The proposed approach has been validated on a benchmark
dataset related to the identification of users depending on their walking
activity. A comparison with a traditional DTW implementation is also provided.
