Mitigating the influence of the curse of dimensionality on time series similarity measures
01 Aug 2015-Journal of Computer Applications in Technology (Inderscience Publishers (IEL))-Vol. 52, Iss: 1, pp 94-105
TL;DR: This paper investigates the application of three dimensionality reduction techniques random projection, downsampling and averaging on time series similarity search and shows that a high similarity matching accuracy can still be achieved after the reduction onto lower dimensions.
Abstract: Time series are ubiquitous application domains that generate data including GPS, stock market, and ECG. Researchers concentrate on mining time series data to extract important knowledge and insights. Time series similarity search is a data mining technique that is widely used to compare time series data using similarity measurements, such as dynamic timewarping and Euclidean distance. The large number of sequences dimensions makes the mining process costly. Therefore, we need to extract fewer representative points, hence making the mining process manageable. In this paper, we investigate the application of three dimensionality reduction techniques random projection, downsampling and averaging on time series similarity search. Our study has been conducted based on very exhaustive experiments. Results show the performance of the reduction techniques on two similarity measures. Simulation shows that a high similarity matching accuracy can still be achieved after the reduction onto lower dimensions.
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References
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NEC1
TL;DR: This paper reports on an optimum dynamic progxamming (DP) based time-normalization algorithm for spoken word recognition, in which the warping function slope is restricted so as to improve discrimination between words in different categories.
Abstract: This paper reports on an optimum dynamic progxamming (DP) based time-normalization algorithm for spoken word recognition. First, a general principle of time-normalization is given using time-warping function. Then, two time-normalized distance definitions, called symmetric and asymmetric forms, are derived from the principle. These two forms are compared with each other through theoretical discussions and experimental studies. The symmetric form algorithm superiority is established. A new technique, called slope constraint, is successfully introduced, in which the warping function slope is restricted so as to improve discrimination between words in different categories. The effective slope constraint characteristic is qualitatively analyzed, and the optimum slope constraint condition is determined through experiments. The optimized algorithm is then extensively subjected to experimental comparison with various DP-algorithms, previously applied to spoken word recognition by different research groups. The experiment shows that the present algorithm gives no more than about two-thirds errors, even compared to the best conventional algorithm.
5,906 citations
"Mitigating the influence of the cur..." refers background or methods in this paper
...…. , sm (10) Q = q1, q2, q3, . . . , qj , . . . , qn (11) DTW is a time series association algorithm that was originally built for speech recognition Sakoe and Chiba (1990) to relate two sequences of feature vectors (two time series) by warping the time axis repetitively until an optimal match…...
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...DTW, on the other hand, non-linearly aligns any two sequences with arbitrary lengths (Sakoe and Chiba, 1990)....
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...Every warping path must satisfy the following constraints (Keogh and Ratanamahatana, 2005; Salvador and Chan, 2004; Sakoe and Chiba, 1990)....
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Journal Article•
2,789 citations
"Mitigating the influence of the cur..." refers background or methods in this paper
...In this paper, to reduce the dimensions of a set of n sequences in Rd (where d is a very large number), the RP technique proposed by Johnson and Lindenstrauss (1982) is used....
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...Lemma 3 (Johnson and Lindenstrauss, 1982): Given 0 ϵ 1 and an integer n, let k be a positive integer such that k ≥ k0 = O( lognϵ2 )....
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...Lemma 3 (Johnson and Lindenstrauss, 1982): Given 0 < ε < 1 and an integer n, let k be a positive integer such that k ≥ k0 = O( logn ε2 )....
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IBM1
TL;DR: An indexing method for time sequences for processing similarity queries using R * -trees to index the sequences and efficiently answer similarity queries and provides experimental results which show that the method is superior to search based on sequential scanning.
Abstract: We propose an indexing method for time sequences for processing similarity queries. We use the Discrete Fourier Transform (DFT) to map time sequences to the frequency domain, the crucial observation being that, for most sequences of practical interest, only the first few frequencies are strong. Another important observation is Parseval's theorem, which specifies that the Fourier transform preserves the Euclidean distance in the time or frequency domain. Having thus mapped sequences to a lower-dimensionality space by using only the first few Fourier coefficients, we use R * -trees to index the sequences and efficiently answer similarity queries. We provide experimental results which show that our method is superior to search based on sequential scanning. Our experiments show that a few coefficients (1–3) are adequate to provide good performance. The performance gain of our method increases with the number and length of sequences.
2,082 citations
TL;DR: This work introduces a novel technique for the exact indexing of Dynamic time warping and proves its vast superiority over all competing approaches in the largest and most comprehensive set of time series indexing experiments ever undertaken.
Abstract: The problem of indexing time series has attracted much interest. Most algorithms used to index time series utilize the Euclidean distance or some variation thereof. However, it has been forcefully shown that the Euclidean distance is a very brittle distance measure. Dynamic time warping (DTW) is a much more robust distance measure for time series, allowing similar shapes to match even if they are out of phase in the time axis. Because of this flexibility, DTW is widely used in science, medicine, industry and finance. Unfortunately, however, DTW does not obey the triangular inequality and thus has resisted attempts at exact indexing. Instead, many researchers have introduced approximate indexing techniques or abandoned the idea of indexing and concentrated on speeding up sequential searches. In this work, we introduce a novel technique for the exact indexing of DTW. We prove that our method guarantees no false dismissals and we demonstrate its vast superiority over all competing approaches in the largest and most comprehensive set of time series indexing experiments ever undertaken.
1,925 citations
TL;DR: Two constructions of k-dimensional Euclidean embeddings with the property that all elements of the projection matrix belong in {-1, 0, +1 } are given.
1,517 citations
"Mitigating the influence of the cur..." refers background in this paper
...Theorem 2 (Achlioptas, 2003): Let P be an arbitrary set of n points (sequences)in Rd, represented as an n× d matrix A....
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...More information is also available in Achlioptas (2003)....
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