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Efficient subsequence matching with lcs

Advances in sensors and wireless network technologies have produced many sensor network applications. In a typical setting, a large number of different types of sensors are deployed over a wide area. The sensor streams generated from individual sensors are then combined in a server node, naturally forming a multivariable time series, and then saved in a storage system. Searching and mining interesting patterns from this multivariable time series dataset is a key challenge in time series analysis. In this paper, we will propose an efficient subsequence matching method in a single channel time series and extend the method to multivariable time series data. We propose a novel subsequence matching framework using a non-Euclidean measure, in particular, LCS, and a new index query scheme. The purpose of the subsequence matching is to find a query sequence in a long range of data sequences. Due to the abundance of applications, many solutions have been proposed. Virtually all previous solutions have used the Euclidean distance as the basis for measuring distance between sequences. Recent studies, however, suggest that the Euclidean distance often fails to produce proper results due to the irregularity in the data, which is not so uncommon in our problem domain. Addressing this problem, some non-Euclidean measures, such as Dynamic Time Warping (DTW) and Longest Common Subsequence (LCS) have been proposed. However, most of the previous work in this direction focused on the whole sequence matching problem where query and data sequences are of the same length. 
The proposed framework is based on the Dual Match framework where data sequences are divided into a series of disjoint equi-length subsequences which are then indexed in an R-tree. We introduced a new way to compute the similarity bound in the index matching framework using LCS. The proposed query matching scheme that is named as multiple window sliding scheme, reduces many false alarms encountered in the previous approaches. We also developed an algorithm to skip expensive LCS computations by observing the warping paths. 
We applied our subsequence matching framework to multivariable time series data. Multivariable stream data is ubiquitous today. Advances in sensors and wireless network technologies enable many sensor network applications, such as object tracking, surveillance, object guarding, structural integrity monitoring of large constructions, to name a few. We extended the proposed subsequence matching technique for a single channel time series to multivariable time series data. Our experimental results on 48 datasets in a single channel and 14 in a multivariable time series suggest that our approach greatly enhances the subsequence matching performance in various metrics.