Efficient and robust feature extraction and pattern matching of time series by a lattice structure

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Abstract
The efficiency of searching scaling-invariant and shifting-invariant shapes in a set of massive time series data can be improved if searching is performed on an approximated sequence which involves less data but contains all the significant features. However, commonly used smoothing techniques, such as moving averages and best-fitting polylines, usually miss important peaks and troughs and deform the time series. In addition, these techniques are not robust, as they often requires users to supply a set of smoothing parameters which has direct effect on the resultant approximation pattern. To address these problems, an algorithm to construct a lattice structure as an underlying framework for pattern matching is proposed in this paper. As inputs, the algorithm takes a time series and users' requirements of level of detail. The algorithm then identifies all the important peaks and troughs (known as controlm points) in the time series and classifies the points into appropriate layers of the lattice structure. The control points in each layer of the structure form an approximation pattern an yet preserve the overall shape of the original series with approximation error lies within certain bound. The lower the layer, the more precise the approximation pattern is. Putting in another way, the algorithm takes different levels of data smoothing into account. Also, the lattice structure can be indexed to further improve the performance of pattern matching.

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