On-line Elastic Similarity Measures for time series

The way similarity is measured among time series is of paramount importance in many data mining and machine learning tasks. For instance, Elastic Similarity Measures are widely used to determine whether two time series are similar to each other. Indeed, in off-line time series mining, these measures have been shown to be very effective due to their ability to handle time distortions and mitigate their effect on the resulting distance. In the on-line setting, where available data increase continuously over time and not necessary in a stationary manner, stream mining approaches are required to be fast with limited memory consumption and capable of adapting to different stationary intervals. In this sense, the computational complexity of Elastic Similarity Measures and their lack of flexibility to accommodate different stationary intervals, make these similarity measures incompatible with the requirements mentioned. To overcome these issues, this paper adapts the family of Elastic Similarity Measures – which includes Dynamic Time Warping, Edit Distance, Edit Distance for Real Sequences and Edit Distance with Real Penalty – to the on-line setting. The proposed adaptation is based on two main ideas: a forgetting mechanism and the incremental computation. The former makes the similarity consistent with streaming time series characteristics by giving more importance to recent observations, whereas the latter reduces the computational complexity by avoiding unnecessary computations. In order to assess the behavior of the proposed similarity measure in on-line settings, two different experiments have been carried out. The first aims at showing the efficiency of the proposed adaptation, to do so we calculate and compare the computation time for the elastic measures and their on-line adaptation. By analyzing the results drawn from a distance-based streaming machine learning model, the second experiment intends to show the effect of the forgetting mechanism on the resulting similarity value. The experimentation shows, for the aforementioned Elastic Similarity Measures, that the proposed adaptation meets the memory, computational complexity and flexibility constraints imposed by streaming data

Comparative study of conventional time series matching techniques for word spotting

International audienceIn word spotting literature, many approaches are considering word images as temporal signals that could be matched with classical Dynamic Time Warping algorithm. Consequently, DTW has been widely used as a on the shelf tool. However there exists many other improved versions of DTW, along with other robust sequence matching techniques. Very few of them have been studied extensively in the context of word spotting whereas it was done on other application domains such as speech processing. The motivation of this paper is to investigate such area in order to extract significant and useful information for users of such techniques. More precisely, this paper is presenting a comparative study of classical Dynamic Time Warping (DTW) technique and many of its improved modifications, as well as other sequence matching techniques in the context of word spotting, considering both theoretical properties as well as experimental ones. The experimental study is performed on historical documents, both handwritten and printed, at word or line segmentation level and with a limited or extended set of queries. The comparative analysis is showing that classical DTW remains a good choice when there is no segmentation problems for word extraction. Its constrained version (e.g. Itakura Parallelogram) seems better on handwritten data, as well as Hilbert transform also shows promising performances on handwritten and printed datasets. In case of printed data and low level features (pixels’ column based), the aggregation of features (e.g. Piecewise-DTW) seems also very important. Finally, when there are important word segmentation errors or when we are considering line segmentation level, Continuous Dynamic Programming (CDP) seems to be the best choice