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Locally Adaptive Dimensionality Reduction for Indexing Large Time Series Databases
 In proceedings of ACM SIGMOD Conference on Management of Data
, 2002
"... Similarity search in large time series databases has attracted much research interest recently. It is a difficult problem because of the typically high dimensionality of the data.. The most promising solutions' involve performing dimensionality reduction on the data, then indexing the reduced data w ..."
Abstract

Cited by 235 (28 self)
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Similarity search in large time series databases has attracted much research interest recently. It is a difficult problem because of the typically high dimensionality of the data.. The most promising solutions' involve performing dimensionality reduction on the data, then indexing the reduced data with a multidimensional index structure. Many dimensionality reduction techniques have been proposed, including Singular Value Decomposition (SVD), the Discrete Fourier transform (DFT), and the Discrete Wavelet Transform (DWT). In this work we introduce a new dimensionality reduction technique which we call Adaptive Piecewise Constant Approximation (APCA). While previous techniques (e.g., SVD, DFT and DWT) choose a common representation for all the items in the database that minimizes the global reconstruction error, APCA approximates each time series by a set of constant value segments' of varying lengths' such that their individual reconstruction errors' are minimal. We show how APCA can be indexed using a multidimensional index structure. We propose two distance measures in the indexed space that exploit the high fidelity of APCA for fast searching: a lower bounding Euclidean distance approximation, and a nonlower bounding, but very tight Euclidean distance approximation and show how they can support fast exact searchin& and even faster approximate searching on the same index structure. We theoretically and empirically compare APCA to all the other techniques and demonstrate its' superiority.
Exact Indexing of Dynamic Time Warping
, 2002
"... The problem of indexing time series has attracted much research interest in the database community. Most algorithms used to index time series utilize the Euclidean distance or some variation thereof. However is has been forcefully shown that the Euclidean distance is a very brittle distance me ..."
Abstract

Cited by 234 (30 self)
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The problem of indexing time series has attracted much research interest in the database community. Most algorithms used to index time series utilize the Euclidean distance or some variation thereof. However is 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.
Making Timeseries Classification More Accurate Using Learned Constraints
 In proc. of SDM Intâ€™l Conf
, 2004
"... It has long been known that Dynamic Time Warping (DTW) is superior to Euclidean distance for classification and clustering of time series. However, until lately, most research has utilized Euclidean distance because it is more efficiently calculated. A recently introduced technique that greatly miti ..."
Abstract

Cited by 62 (20 self)
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It has long been known that Dynamic Time Warping (DTW) is superior to Euclidean distance for classification and clustering of time series. However, until lately, most research has utilized Euclidean distance because it is more efficiently calculated. A recently introduced technique that greatly mitigates DTWs demanding CPU time has sparked a flurry of research activity. However, the technique and its many extensions still only allow DTW to be applied to moderately large datasets. In addition, almost all of the research on DTW has focused exclusively on speeding up its calculation; there has been little work done on improving its accuracy. In this work, we target the accuracy aspect of DTW performance and introduce a new framework that learns arbitrary constraints on the warping path of the DTW calculation. Apart from improving the accuracy of classification, our technique as a side effect speeds up DTW by a wide margin as well. We show the utility of our approach on datasets from diverse domains and demonstrate significant gains in accuracy and efficiency.
EnsembleIndex: A New Approach to Indexing Large Databases
 In Proceedings of the 7th ACM SIGKDD International Conference on Knowledge Discovery
, 2001
"... The problem of similarity search (querybycontent) has attracted much research interest. It is a difficult problem because of the inherently high dimensionality of the data. The most promising solutions involve performing dimensionality reduction on the data, then indexing the reduced data with a m ..."
Abstract
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The problem of similarity search (querybycontent) has attracted much research interest. It is a difficult problem because of the inherently high dimensionality of the data. The most promising solutions involve performing dimensionality reduction on the data, then indexing the reduced data with a multidimensional index structure. Many dimensionality reduction techniques have been proposed, including Singular Value Decomposition (SVD), the Discrete Fourier Transform (DFT), the Discrete Wavelet Transform (DWT) and Piecewise Polynomial Approximation. In this work, we introduce a novel framework for using ensembles of two or more representations for more efficient indexing. The basic idea is that instead of committing to a single representation for an entire dataset, different representations are chosen for indexing different parts of the database. The representations are chosen based upon a local view of the database. For example, sections of the data that can achieve a high fidelity representation with wavelets are indexed as wavelets, but highly spectral sections of the data are indexed using the Fourier transform. At query time, it is necessary to search several small heterogeneous indices, rather than one large homogeneous index. As we will theoretically and empirically demonstrate this results in much faster query response times.