This paper presents an efficient approach for subsequence search in data streams. The problem consists of identifying coherent repetitions of a given reference time-series, also in the multivariate case, within a longer data stream. The most widely adopted metric to address this problem is Dynamic Time Warping (DTW), but its computational complexity is a well-known issue. In this paper, we present an approach aimed at learning a kernel approximating DTW for efficiently analyzing streaming data collected from wearable sensors, while reducing the burden of DTW computation. Contrary to kernel, DTW allows for comparing two time-series with different length. To enable the use of kernel for comparing two time-series with different length, a feature embedding is required in order to obtain a fixed length vector representation. Each vector component is the DTW between the given time-series and a set of "basis" series, randomly chosen. The approach has been validated on two benchmark datasets and on a real-life application for supporting self-rehabilitation in elderly subjects has been addressed. A comparison with traditional DTW implementations and other state-of-the-art algorithms is provided: results show a slight decrease in accuracy, which is counterbalanced by a significant reduction in computational costs
