Similar Sub-Sequences Search over Multi-Dimensional Time Series Data

When Euclidean distance between time series changes greatly with the compared time series moving slightly along the time-axis, a dynamic time warping distance is suggested as a more robust distance than Euclidean distance. Dynamic time warping distance is widely used as similarity measure in the domain of similar sub-sequences search over time series data. The similarity search in the single dimension may not get enough similar sub-sequences as the results to do further analysis and support the decision making. In this paper the problem is extended to the multi-dimensional scenario by introducing a data cube model which is well-studied in the multi-dimensional data analysis domain. Based on the data cube model the authors define the similar sub-sequences in multi-dimensional time series data and propose a nave algorithm to get more useful search results with extra valuable information. However, the efficiency of the nave algorithm is very poor which limits its application. So the efficiency of the nave algorithm is improved by studying the correlation of the cells among the neighboring levels in the data cube on the basis of keeping the accuracy of the search results. Extensive experiments based on the real network security dataset demonstrate the effectiveness of the proposed methods.