Subsequence Matching In Time-series Databases Research Articles

Embedding-based subsequence matching in time-series databases

We propose an embedding-based framework for subsequence matching in time-series databases that improves the efficiency of processing subsequence matching queries under the Dynamic Time Warping (DTW) distance measure. This framework partially reduces subsequence matching to vector matching, using an embedding that maps each query sequence to a vector and each database time series into a sequence of vectors. The database embedding is computed offline, as a preprocessing step. At runtime, given a query object, an embedding of that object is computed online. Relatively few areas of interest are efficiently identified in the database sequences by comparing the embedding of the query with the database vectors. Those areas of interest are then fully explored using the exact DTW-based subsequence matching algorithm. We apply the proposed framework to define two specific methods. The first method focuses on time-series subsequence matching under unconstrained Dynamic Time Warping. The second method targets subsequence matching under constrained Dynamic Time Warping (cDTW), where warping paths are not allowed to stray too much off the diagonal. In our experiments, good trade-offs between retrieval accuracy and retrieval efficiency are obtained for both methods, and the results are competitive with respect to current state-of-the-art methods.

Linear Detrending Subsequence Matching in Time-Series Databases

Each time-series has its own linear trend, the directionality of a timeseries, and removing the linear trend is crucial to get the more intuitive matching results. Supporting the linear detrending in subsequence matching is a challenging problem due to a huge number of possible subsequences. In this paper we define this problem the linear detrending subsequence matching and propose its efficient index-based solution. To this end, we first present a notion of LD-windows (LD means linear detrending), which is obtained as follows: we eliminate the linear trend from a subsequence rather than each window itself and obtain LD-windows by dividing the subsequence into windows. Using the LD-windows we then present a lower bounding theorem for the index-based matching solution and formally prove its correctness. Based on the lower bounding theorem, we next propose the index building and subsequence matching algorithms for linear detrending subsequence matching.We finally show the superiority of our index-based solution through extensive experiments.

Using multiple indexes for efficient subsequence matching in time-series databases

A time- series database is a set of data sequences, each of which is a list of changing values of an object in a given period of time. Subsequence matching is an operation that searches for such data subsequences whose changing patterns are similar to a query sequence in a time-series database. This paper addresses a performance issue of time-series subsequence matching. First, we quantitatively examine the performance degradation caused by the window size effect, and then show that the performance of subsequence matching with a single index is not satisfactory in real applications. We claim that index interpolation is a fairly effective tool to solve this problem. Index interpolation performs subsequence matching by selecting the most appropriate one from multiple indexes built on windows of their distinct sizes. For index interpolation, we need to decide the sizes of windows for multiple indexes to be built. In this paper, we solve the problem of selecting optimal window sizes from the perspective of physical database design. Given a set of pairs 〈 length, frequency〉 of query sequences to be performed in a target application and a set of window sizes for building multiple indexes, we devise a formula that estimates the overall cost of all the subsequence matchings performed in a target application. By using this formula, we propose an algorithm that determines the optimal window sizes for maximizing the performance of entire subsequence matchings. We formally prove the optimality as well as the effectiveness of the algorithm. Finally, we show the superiority of our approach by performing extensive experiments with a real-life stock data set and a large volume of synthetic data sets.

Performance bottleneck of subsequence matching in time-series databases: Observation, solution, and performance evaluation

Subsequence matching is an operation that finds subsequences whose changing patterns are similar to a given query sequence from time-series databases. This paper identifies a performance bottleneck in subsequence matching, and then proposes an effective method that substantially improves the performance of entire subsequence matching by resolving the performance bottleneck. First, we analyze the disk access and CPU processing times required during the index searching and post-processing steps of subsequence matching through preliminary experiments. Based on these results, we show that the post-processing step is a main performance bottleneck in subsequence matching. Then, we argue that the optimization of the post-processing step is a crucial issue overlooked in previous approaches. In order to resolve the performance bottleneck, we propose a simple yet highly effective method for expediting the post-processing step. By rearranging the order of candidate subsequences to be compared with a query sequence, our method completely eliminates the redundancies of disk accesses and CPU processing that occur in the post-processing step. Our method is fairly efficient, and does not incur any false dismissal. We quantitatively demonstrate the superiority of our method through extensive experimentation. The results show that our method produces a significantly faster post-processing step; When using a data set of real-world stock sequences, our method was 43.36–96.75 times faster than previous methods, and when using data sets of large numbers of synthetic sequences, our method was 12.48–26.95 times faster than previous methods. Also, the results show that our method reduces the weight of the post-processing step over entire subsequence matching from more than 97% to less than 67%. This implies that our method successfully resolves the performance bottleneck in subsequence matching. As a result, our method provides excellent performance in entire subsequence matching. Compared with previous methods, our method is 16.17–32.64 times faster when using a data set of real-world stock sequences and 8.64–14.29 times faster when using data sets of large numbers of synthetic sequences.

이원성 기반 시계열 서브시퀀스 매칭의 인덱스 검색을 위한 최적의 기법

In this paper, we address efficient processing of subsequence matching in time-series databases. We first point out the performance problems occurring in the index searching of a prior method for subsequence matching. Then, we propose a new method that resolves these problems. Our method starts with viewing the index searching of subsequence matching from a new angle, thereby regarding it as a kind of a spatial-join called a window-join. For speeding up the window-join, our method builds an R＊-tree in main memory for f query sequence at starting of sub-sequence matching. Our method also includes a novel algorithm for joining effectively one R＊-tree in disk, which is for data sequences, and another R＊-tree in main memory, which is for a query sequence. This algorithm accesses each R＊-tree page built on data sequences exactly cure without incurring any index-level false alarms. Therefore, in terms of the number of disk accesses, the proposed algorithm proves to be optimal. Also, performance evaluation through extensive experiments shows the superiority of our method quantitatively.

Fast subsequence matching in time-series databases

We present an efficient indexing method to locate 1-dimensional subsequences within a collection of sequences, such that the subsequences match a given (query) pattern within a specified tolerance. The idea is to map each data sequences into a small set of multidimensional rectangles in feature space. Then, these rectangles can be readily indexed using traditional spatial access methods, like the R*-tree [9]. In more detail, we use a sliding window over the data sequence and extract its features; the result is a trail in feature space. We propose an efficient and effective algorithm to divide such trails into sub-trails, which are subsequently represented by their Minimum Bounding Rectangles (MBRs). We also examine queries of varying lengths, and we show how to handle each case efficiently. We implemented our method and carried out experiments on synthetic and real data (stock price movements). We compared the method to sequential scanning, which is the only obvious competitor. The results were excellent: our method accelerated the search time from 3 times up to 100 times.