Abstract:The dynamic time warping (DTW) is a popular similarity measure between time series. The DTW fails to satisfy the triangle inequality and its computation requires quadratic time. Hence, to find closest neighbors quickly, we use bounding techniques. We can avoid most DTW computations with an inexpensive lower bound (LB_Keogh). We compare LB_Keogh with a tighter lower bound (LB_Improved). We find that LB_Improved-based search is faster. As an example, our approach is 2-3 times faster over random-walk and shape ti… Show more
“…We also used a synthetic corpus of sequences of several dimensions (1, 5, 10, 20 and 60). We generated 1000 sequences (for each number of dimensions) with a random walk (for each dimension of the sequence) defined by x i = x i−1 + N (0, 1) and x 1 = 0 as in [19].…”
Section: Methodsmentioning
confidence: 99%
“…since it is possible to find counterexamples where DTW does not satisfy it [14,19] (thus, CDTW is not a metric either). The correction of algorithms such as AESA (Figure 3) depends on having a metric distance and then it has to satisfy this property.…”
Section: Improving the Heuristic With The Intrinsic Dimensionalitymentioning
confidence: 99%
“…In [15], in 15 millions of triplets there were no cases where the triangular inequality was violated. In [19], the authors made experiments with synthetic time series (sequences of one dimension) of three types: white-noise, random-walk and cylinder-bell-funnel. The most problematic was random-walk where 20% of triplets violated the triangular inequality.…”
Section: Improving the Heuristic With The Intrinsic Dimensionalitymentioning
confidence: 99%
“…We performed an experiment similar to the one in [19], with random-walk sequences, but varying the number of dimensions (in [19] this experiment was done for just one dimension). We generated 1000 sequences for each number of dimensions, then we checked 1000000000 triplets.…”
Section: Intrinsic Dimensionality and Triangular Inequalitymentioning
Abstract. Cyclic Dynamic Time Warping (CDTW) is a good dissimilarity of shape descriptors of high dimensionality based on contours, but it is computationally expensive. For this reason, to perform recognition tasks, a method to reduce the number of comparisons and avoid an exhaustive search is convenient. The Approximate and Eliminate Search Algorithm (AESA) is a relevant indexing method because of its drastic reduction of comparisons, however, this algorithm requires a metric distance and that is not the case of CDTW. In this paper, we introduce a heuristic based on the intrinsic dimensionality that allows to use CDTW and AESA together in classification and retrieval tasks over these shape descriptors. Experimental results show that, for descriptors of high dimensionality, our proposal is optimal in practice and significantly outperforms an exhaustive search, which is the only alternative for them and CDTW in these tasks.
“…We also used a synthetic corpus of sequences of several dimensions (1, 5, 10, 20 and 60). We generated 1000 sequences (for each number of dimensions) with a random walk (for each dimension of the sequence) defined by x i = x i−1 + N (0, 1) and x 1 = 0 as in [19].…”
Section: Methodsmentioning
confidence: 99%
“…since it is possible to find counterexamples where DTW does not satisfy it [14,19] (thus, CDTW is not a metric either). The correction of algorithms such as AESA (Figure 3) depends on having a metric distance and then it has to satisfy this property.…”
Section: Improving the Heuristic With The Intrinsic Dimensionalitymentioning
confidence: 99%
“…In [15], in 15 millions of triplets there were no cases where the triangular inequality was violated. In [19], the authors made experiments with synthetic time series (sequences of one dimension) of three types: white-noise, random-walk and cylinder-bell-funnel. The most problematic was random-walk where 20% of triplets violated the triangular inequality.…”
Section: Improving the Heuristic With The Intrinsic Dimensionalitymentioning
confidence: 99%
“…We performed an experiment similar to the one in [19], with random-walk sequences, but varying the number of dimensions (in [19] this experiment was done for just one dimension). We generated 1000 sequences for each number of dimensions, then we checked 1000000000 triplets.…”
Section: Intrinsic Dimensionality and Triangular Inequalitymentioning
Abstract. Cyclic Dynamic Time Warping (CDTW) is a good dissimilarity of shape descriptors of high dimensionality based on contours, but it is computationally expensive. For this reason, to perform recognition tasks, a method to reduce the number of comparisons and avoid an exhaustive search is convenient. The Approximate and Eliminate Search Algorithm (AESA) is a relevant indexing method because of its drastic reduction of comparisons, however, this algorithm requires a metric distance and that is not the case of CDTW. In this paper, we introduce a heuristic based on the intrinsic dimensionality that allows to use CDTW and AESA together in classification and retrieval tasks over these shape descriptors. Experimental results show that, for descriptors of high dimensionality, our proposal is optimal in practice and significantly outperforms an exhaustive search, which is the only alternative for them and CDTW in these tasks.
“…There are a number of ways to speed up the Dynamic Time Warping procedure, however, they either do not guarantee the finding of the optimal solution [6,[11][12][13][14], or the performance improvement is provided only in cases, when comparing close or sparse signals [15,16]. But such situations are rare in the analysis of electroencephalograms.…”
Automatic analysis of electroencephalograms (EEGs) is one of the promising areas of research, which results can be used, in particular, to build systems of mental control of objects. The Dynamic Time Warping procedure (DTW) is used in this work for comparing signals representing EEG. An important feature of the problem we are considering is the need for multiple comparison of signals at the stage of machine learning, which requires enormous computational costs. We propose a parallel algorithm that was implemented in C++ using the MPI technology and tested using the resources of the supercomputer complex of Moscow State University "Lomonosov". The results of its testing on real data showed that the proposed method allows achieving an almost linear speedup and reducing the total calculation time from 29 days to 3.5 hours using 128 processes, which opens the possibility of improving the quality of automatic analysis of electroencephalograms.
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