Nowadays, many applications, like the Internet of Things and Industrial Internet, collect data points from sensors continuously to form long time series. Finding the correlation between time series is a fundamental task for many time series mining problems. However, it is meaningless to directly measure the global correlation between two long time series due to concept shift or noise data. To tackle this challenge, in this paper, we formulate the novel problem of finding maximal significant linear representation. The major idea is that, given two time series and a quality constraint, we want to find the longest gapped time interval on which a time series can be linearly represented by the other within the quality constraint requirement. We develop both exact and approximate algorithms (with approximation quality guarantees), which exploit a novel representation of the linear correlation between time series on subsequences, and transform the problem into a geometric search. Moreover, we propose an online approach to find this correlation in each sliding window incrementally for the streaming data. We present a systematic empirical study to verify the efficiency and effectiveness of our approaches.

In some applications on time series data, finding linear correlation between time series is important. However, it is meaningless to measure the global correlation between two long time series. Moreover, more often than not, two time series may be correlated in various segments. To tackle the challenges in measuring linear correlation between two long time series, in this paper, we formulate the novel problem of finding maximal significant linear representation. The major idea is that, given two time series and a quality constraint, we want to find the longest gapped time interval on which a time series can be linearly represented by the other within the quality constraint requirement. We develop a point-based approach, which exploits a novel representation of linear correlation between time series on segments, and transforms the problem into geometric search. We present a systematic empirical study to verify its efficiency and effectiveness.

Similarity search on time series is an essential operation in many applications. In the state-of-the-art methods, such as the R-tree based methods, SAX and iSAX, time series are by default divided into equi-length segments globally, that is, all time series are segmented in the same way. Those methods then focus on how to approximate or symbolize the segments and construct indexes. In this paper, we make an important observation: global segmentation of all time series may incur unnecessary cost in space and time for indexing time series. We develop DSTree, a data adaptive and dynamic segmentation index on time series. In addition to savings in space and time, our new index can provide tight upper and lower bounds on distances between time series. An extensive empirical study shows that our new index DSTree supports time series similarity search effectively and efficiently.