Abstract
Many applications generate and/or consume multi-variate temporal data, and experts often lack the means to adequately and systematically search for and interpret multi-variate observations. In this article, we first observe that multi-variate time series often carry localized multi-variate temporal features that are robust against noise. We then argue that these multi-variate temporal features can be extracted by simultaneously considering, at multiple scales, temporal characteristics of the time series along with external knowledge , including variate relationships that are known a priori. Relying on these observations, we develop data models and algorithms to detect robust multi-variate temporal (RMT) features that can be indexed for efficient and accurate retrieval and can be used for supporting data exploration and analysis tasks. Experiments confirm that the proposed RMT algorithm is highly effective and efficient in identifying robust multi-scale temporal features of multi-variate time series.
Highlights
Many applications, such as motion recognition [34], generate temporal data and, in many of these applications, (a) the resulting time-series data are multi-variate, (b) relevant processes underlying these time series are of different scales [17, 29, 48], and (c) the variates are dependent on each other in various ways [40].Analysis and exploration of time series often start with extraction of patterns and features that describe salient properties of the data
Noting that uni-variate time series often carry localized temporal features that can be used for efficient search and analysis, in our earlier work [4] we developed an sDTW algorithm for extracting salient local features of uni-variate time series and showed that these can help align similar time series more efficiently and effectively
In our preliminary work [51], we had shown that the diagonal scale-space-based robust multi-variate temporal (RMT) features (Section 5.1) are more effective in partial time-series search and classification tasks than alternative techniques, including Singular-Value Decomposition (SVD), where we created a single fingerprint for each multi-variate time series using the SVD transformation, and DTW, where distances were computed directly using dynamic time warping [9]
Summary
Many applications, such as motion recognition [34], generate temporal data and, in many of these applications, (a) the resulting time-series data are multi-variate, (b) relevant processes underlying these time series are of different scales [17, 29, 48], and (c) the variates (i.e., observation parameters) are dependent on each other in various ways [40].Analysis and exploration of time series (as well as other types of data) often start with extraction of patterns and features that describe salient properties of the data. Correlations, transfer functions, variate clusters, and spectral properties [47], Singular-Value Decomposition (SVD) and similar eigen-decompositions can be used for extracting global fingerprints of multi-variate time-series data [27]. The analogous analysis operation on a tensor, which can be used to represent temporal evolution of multi-modal data, is known as tensor decomposition [23]. Both matrix and tensor decomposition operations, as well as other techniques, such as probabilistic techniques (such as Dynamic Topic Modeling, DTM [3]) and AutoRegressive Integrated MovingAverage– (ARIMA) based analyses (which separate a time series into autoregressive, movingaverage, and integrative components for modeling and forecasting [33]) are expensive
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