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...es constant-value segments to approximate sequences. While many dimensionality reduction techniques have been proposed (e.g. DFT [20, 10], Discrete Wavelet Transform [24] and Karhunen-Loeve Transform =-=[9]-=-), APCA gives especially high approximation quality. Recent applications require DTW for calculating the similarity of sequences [13, 21, 19, 12]. To reduce the matching cost, many sequence-matching t...

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...lculate the distance between sequences whose lengths and/or sampling rates are different. Furthermore, it can be sensitive to outliers [2]. Recent applications have adopted Dynamic Time Warping (DTW) =-=[5, 22]-=- to overcome these problems [13, 21, 19, 12]. DTW is a transformation that allows sequences to be stretched along the time axis to minimize the distance between the sequences. The distance of DTW is c...

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...at of [14]. Thus, we show the results of a performance evaluation that compared FTW with the best existing method proposed in [27]. [27]’s method is denoted by LB PAA. For LB PAA, we used the R*-tree =-=[3]-=-, and each sequence was indexed according to 16 reduced dimensions as shown in [27]. We evaluated the search performance mainly 0 50 100 150 200 250 300 350 400 25000 50000 75000 100000sW al l C lo ck...

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...andomly, feature data are visited sequentially in query processing. A sequential scan of feature data should significantly boost performance because of the sequential nature of their I/O requests. In =-=[23]-=-, Weber et al. indicate two speed-up factors for the phenomenon: a practical factor of 10 and a conservative one of 5. Thus, we used these speed-up factors, SF , in our experimental evaluations. The n...

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... high enough performance for high-dimensional data because of the dimensionality curse problem [4, 23]. Their work focus on whole sequence matching. This was generalized to allow subsequence matching =-=[8, 18]-=-. Keogh et al. presented an indexing method by using the Adaptive Piecewise Constant Approximation (APCA) [15]. APCA is a dimensionality reduction technique for sequence matching based on the Euclidea...

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...he results of the experiments, which clearly show the effectiveness of FTW. Section 5 is a brief conclusion. 2. RELATED WORK Agrawal et al. first proposed an approach for similarity sequence matching =-=[1]-=-. Their method extracts feature vectors from sequences, and indexes them using R*-trees. Only a small number of features are extracted, since most multidimensional index structures cannot provide high...

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...lidean distance. This technique uses constant-value segments to approximate sequences. While many dimensionality reduction techniques have been proposed (e.g. DFT [20, 10], Discrete Wavelet Transform =-=[24]-=- and Karhunen-Loeve Transform [9]), APCA gives especially high approximation quality. Recent applications require DTW for calculating the similarity of sequences [13, 21, 19, 12]. To reduce the matchi...

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...ven data sequences of different lengths and/or data sequences with lengths different from that of the query sequence. 4. Support for any, as well as for no restriction on warping scope: The method in =-=[14]-=- is fast, because it cleverly exploits global constraints [22] that appear in dynamic programming (See Figure 2). We would like to have a method that can exploit the restrictions on the warping scope,...

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...ment over the one of [14]. The search methods of [14] and [27] compute the envelope of the query sequence from the scope of warping paths; they then derive the PAA (Piecewise Aggregate Approximation) =-=[16, 25]-=- of the envelope (See Figures 3 and 4). The lower bounding distance between each data sequence and the query sequence is defined as the Euclidean distance between the PAA of the envelope and the MBR (...

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...ces whose lengths and/or sampling rates are different. Furthermore, it can be sensitive to outliers [2]. Recent applications have adopted Dynamic Time Warping (DTW) [5, 22] to overcome these problems =-=[13, 21, 19, 12]-=-. DTW is a transformation that allows sequences to be stretched along the time axis to minimize the distance between the sequences. The distance of DTW is calculated by dynamic programming (See Figure...

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...n treats sequence elements independently, it cannot be used to calculate the distance between sequences whose lengths and/or sampling rates are different. Furthermore, it can be sensitive to outliers =-=[2]-=-. Recent applications have adopted Dynamic Time Warping (DTW) [5, 22] to overcome these problems [13, 21, 19, 12]. DTW is a transformation that allows sequences to be stretched along the time axis to ...

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...ion, which varies its accuracy during the course of query processing. Although this method is efficient, it does not guarantee no false dismissals. Yi et al. proposed a lower bounding measure for DTW =-=[26]-=-. The distance from a query sequence to each data sequence is evaluated by using a lower bounding measure, after which a candidate set is constructed. The current data sequence for each candidate is v...

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...nly a small number of features are extracted, since most multidimensional index structures cannot provide high enough performance for high-dimensional data because of the dimensionality curse problem =-=[4, 23]-=-. Their work focus on whole sequence matching. This was generalized to allow subsequence matching [8, 18]. Keogh et al. presented an indexing method by using the Adaptive Piecewise Constant Approximat...

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...ment over the one of [14]. The search methods of [14] and [27] compute the envelope of the query sequence from the scope of warping paths; they then derive the PAA (Piecewise Aggregate Approximation) =-=[16, 25]-=- of the envelope (See Figures 3 and 4). The lower bounding distance between each data sequence and the query sequence is defined as the Euclidean distance between the PAA of the envelope and the MBR (...

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...lculate the distance between sequences whose lengths and/or sampling rates are different. Furthermore, it can be sensitive to outliers [2]. Recent applications have adopted Dynamic Time Warping (DTW) =-=[5, 22]-=- to overcome these problems [13, 21, 19, 12]. DTW is a transformation that allows sequences to be stretched along the time axis to minimize the distance between the sequences. The distance of DTW is c...

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...lobal constraints that appear in dynamic programming. Global constraints (e.g. the Sakoe-Chiba Band and the Itakura Parallelogram [22]) limit the scope of the warping path. Zhu et al.’s search method =-=[27]-=- is also based on global constraints and represents an improvement over the one of [14]. The search methods of [14] and [27] compute the envelope of the query sequence from the scope of warping paths;...

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...wer bounding measure also employs elements in the data sequence that are smaller than the minimum of the query sequence. Kim et al. introduced a lower bounding measure employing 4-dimensional vectors =-=[17]-=- that represent the first, last, minimum, and maximum sequence elements. The vectors can be readily indexed using any spatial access method. The lower bounding measures proposed in [26] and [17] guara...

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...per bounds that totally enclose the sequence. sequence retrieval speed against precision. They must visit all data sequences of length N , and the time complexity is still basically O(N2). Chu et al. =-=[6]-=- proposed a search method based on distance approximation, which varies its accuracy during the course of query processing. Although this method is efficient, it does not guarantee no false dismissals...

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...tc−1 < tc < N That is, PAc is the coarsest, while P A 1 is the most accurate. Various algorithms have been proposed to find the optimal representation of approximate segments of each sequences (e.g., =-=[7]-=-). We will use equal-sized segments to approximate sequences for simplicity although segments of different time intervals would be acceptable to FTW. Since we operate on equal-sized segments, the time...

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... high enough performance for high-dimensional data because of the dimensionality curse problem [4, 23]. Their work focus on whole sequence matching. This was generalized to allow subsequence matching =-=[8, 18]-=-. Keogh et al. presented an indexing method by using the Adaptive Piecewise Constant Approximation (APCA) [15]. APCA is a dimensionality reduction technique for sequence matching based on the Euclidea...

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...ces whose lengths and/or sampling rates are different. Furthermore, it can be sensitive to outliers [2]. Recent applications have adopted Dynamic Time Warping (DTW) [5, 22] to overcome these problems =-=[13, 21, 19, 12]-=-. DTW is a transformation that allows sequences to be stretched along the time axis to minimize the distance between the sequences. The distance of DTW is calculated by dynamic programming (See Figure...

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...ces whose lengths and/or sampling rates are different. Furthermore, it can be sensitive to outliers [2]. Recent applications have adopted Dynamic Time Warping (DTW) [5, 22] to overcome these problems =-=[13, 21, 19, 12]-=-. DTW is a transformation that allows sequences to be stretched along the time axis to minimize the distance between the sequences. The distance of DTW is calculated by dynamic programming (See Figure...

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...ature: Temperature measurements, from 55 sensors in buildings of Carnegie Mellon University. Each sensor gives one value every 30 seconds. 2. FinTime: This is the financial time-series benchmark from =-=[11]-=-. We used historical stock market data for 100,000 securities. 3. RandomWalk: We generated 100,000 sequences by using random-walk models [25]: pi = pi−1 + xi where the p1 of each sequence is uniformly...

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...ces whose lengths and/or sampling rates are different. Furthermore, it can be sensitive to outliers [2]. Recent applications have adopted Dynamic Time Warping (DTW) [5, 22] to overcome these problems =-=[13, 21, 19, 12]-=-. DTW is a transformation that allows sequences to be stretched along the time axis to minimize the distance between the sequences. The distance of DTW is calculated by dynamic programming (See Figure...