Similarity-Based Queries for Time Series Data

2006

Indexing Time Series Data is an interesting problem that has attracted much interest in the research community for the last decade. Traditional indexing methods organize the data space using different metrics. For time series, however, there are some cases when a metric is not suited for properly assessing the similarity between sequences. For instance, to detect similarities between sequences that are locally out of phase Dynamic Time Warping (DTW) must be used. DTW is not a metric as it does not satisfy the triangular inequality. Therefore, traditional spatial access methods cannot be used without introducing false dismissals. In such cases, alternative methods for organizing and searching time series data must be proposed. In this paper we propose the use of quantization to generate small and homogeneous representations of time series. We compute upper-and lower-bounds on the DTW distance to a query sequence using this quantized representation to filter-out sequences that cannot be a best match for the query. In the proposed approach, efficient search is achieved by organizing the quantized representation of data in a linear array that can be efficiently read from disk. The computational cost of processing the query is shadowed by the IO cost required to scan the file containing the linear array and it does affect the total query cost.

IEEE Internet Computing, 2010

the similarity search problem is one of the main problems in time series data mining. Traditionally, this problem has been tackled by sequentially comparing the given query against all the time series in the database and returning the time series that are within a predetermined threshold of that query. But the large size and the high dimensionality of time series databases that are in use nowadays make that scenario inefficient. There are many representation techniques that aim at reducing the dimensionality of time series so that the search can be handled faster at a lower-dimensional space level. In this paper we propose a new method which is based on using multiple reduced spaces that correspond to certain segments' lengths. The new method also uses fast-and-dirty filters which speed up the similarity search process. For each space an approximating function is used to represent the time series at that space. The distances between the time series and those approximating functions are calculated and stored at indexing time. At query time, the designed filters use these pre-computed distances to exclude the time series which are not answers to the query, making the least number of distance computations and return a candidate response set. The representation level is increased gradually to higher levels with stronger exclusion power. The cardinality of the candidate response set gets smaller as we move from one level to another. A post-processing scanning on this response set is performed to filter out any false alarms and return the final response set. We present experimentations that compare our method with sequential scanning on different datasets, using different threshold values and different approximating functions. The experiments show that our new method is faster than sequential scanning by an order of magnitude.

Journal of Information Science, 2006

This paper discusses the way of processing time-series subsequence matching under time warping. Time warping enables sequences to be found with similar patterns even when they are of different lengths. The prefix-querying method is the first index-based approach that efficiently performs time-series subsequence matching under time warping without false dismissals. This method employs the L distance metric as a base distance function so as to allow users to issue queries conveniently. In this paper, we extend the prefix-querying method for absorbing L1, which is the most widely used as a base distance function in time-series subsequence matching under time warping, instead of L. We formally prove that the prefix-querying method with the L1 distance metric does not incur any false dismissals in the subsequence matching. To show its superiority, we conduct performance evaluation via a variety of experiments. The results reveal that our method achieves significant performance improvemen...

abstract.cs.washington.edu

We propose an indexing and searching scheme for multi-dimensional time series. To avoid the curse of dimensionality we introduce a novel method for structured dimensionality reduction which allows our system to store separate database tables for user-specified sets of dimensions. To find similar matches for a query, we run separate queries on nonintersecting subsets of dimensions of the full query, and then join on the ids of those results to find all candidate matches to the query; then, with fewer candidates, we can apply more costly similarity measures to find the best matches to the query. While checking each table sequentially may take longer than just using one table to index the full time series, the whole system will be faster using a parallelized process. Our system also allows for users to query on a partial set of dimensions efficiently.

Proceedings of the …, 2008

The last decade has witnessed a tremendous growths of in-terests in applications that deal with querying and min-ing of time series data. Numerous representation methods for dimensionality reduction and similarity measures geared towards time series have been ...

Lecture Notes in Computer Science, 2007

Similarity search in time series databases usually deals with comparing entire time series objects or subsequence search. In this paper, we formalize the notion of interval-focused similarity queries which take a set of intervals specifying relevant time frames as additional parameter and compare the time series objects only within this user-defined time focus. We propose an original method to efficiently support intervalfocused distance range and k-nearest neighbor queries implementing a filter/refinement architecture. In our broad experimental evaluation we show the superiority of our novel approach compared to existing approaches on several real-world data sets.

Journal of Systems and Software, 2006

The shape-based retrieval is defined as the operation that searches for the (sub)sequences whose shapes are similar to that of a query sequence regardless of their actual element values. In this paper, we propose a similarity model suitable for shape-based retrieval and present an indexing method for supporting the similarity model. The proposed similarity model enables to retrieve similar shapes accurately by providing the combination of multiple shape-preserving transformations such as normalization, moving average, and time warping. Our indexing method stores every distinct subsequence concisely into the disk-based suffix tree for efficient and adaptive query processing. We allow the user to dynamically choose a similarity model suitable for a given application. More specifically, we allow the user to determine the parameter p of the distance function L p when submitting a query. The result of extensive experiments revealed that our approach not only successfully finds the subsequences whose shapes are similar to a query shape but also significantly outperforms the sequential scan method.

Information Systems, 2004

This paper discusses the effective processing of similarity search that supports time warping in large sequence databases. Time warping enables sequences with similar patterns to be found even when they are of different lengths. Prior methods for processing similarity search that supports time warping failed to employ multi-dimensional indexes without false dismissal since the time warping distance does not satisfy the triangular inequality. They have to scan the entire database, thus suffering from serious performance degradation in large databases. Another method that hires the suffix tree, which does not assume any distance function, also shows poor performance due to the large tree size. In this paper, we propose a novel method for similarity search that supports time warping. Our primary goal is to enhance the search performance in large databases without permitting any false dismissal. To attain this goal, we have devised a new distance function, D twÀlb ; which consistently underestimates the time warping distance and satisfies the triangular inequality. D twÀlb uses a 4-tuple feature vector that is extracted from each sequence and is invariant to time warping. For the efficient processing of similarity search, we employ a multi-dimensional index that uses the 4-tuple feature vector as indexing attributes, and D twÀlb as a distance function. We prove that our method does not incur false dismissal. To verify the superiority of our method, we have performed extensive experiments. The results reveal that our method achieves a significant improvement in speed up to 43 times faster with a data set containing real-world S&P 500 stock data sequences, and up to 720 times with data sets containing a very large volume of synthetic data sequences. The performance gain increases: (1) as the number of data sequences increases, (2) the average length of data sequences increases, and (3) as the tolerance in a query decreases. Considering the characteristics of real databases, these tendencies imply that our approach is suitable for practical applications.

International Journal of Data Warehousing and Mining (IJDWM), 2006

Sequences constitute a large portion of data stored in databases. Data mining applications require the ability to process similarity queries over a large amount of time series data. The query processing performance is an important factor that needs to be taken into consideration. This article proposes a similarity retrieval algorithm for time series. The proposed approach utilizes wavelet transformation in order to reduce the dimensionality of the time series. The transformed series are indexed using X-Trees, which is a spatial ...

22nd International Conference on Data Engineering (ICDE'06), 2006

Similarity search in time series data is an active area of research. In this paper, we introduce the novel concept of threshold-similarity queries in time series databases which report those time series exceeding a user-defined query threshold at similar time frames compared to the query time series. In addition, we present a new data structure to support threshold similarity queries efficiently. The performance of our solution is demonstrated by an extensive experimental evaluation.