Identify Significant Phenomenon-Specific Variables for Multivariate Time Series

Multivariate time series (MTS) are collected for different variables in studying scientific phenomena or monitoring system health where each time series records the values of one variable for a time period. Among the different variables, it is common that only a few variables contribute significantly to a specific phenomenon. Furthermore, the variables contributing significantly to different phenomena are often different. We denote the different variables that contribute to the occurrences of different phenomena as <italic>Phenomenon-specific Variables (PVs)</italic>. In this paper, we formulate a <italic>novel problem</italic> of identifying significant PVs from MTS datasets. To analyze MTS data, feature extraction techniques have been extensively studied. However, most of them identify important <italic>global</italic> features for one dataset and do not utilize the temporal order of time series. To solve the newly introduced problem, we propose a solution framework, <italic>CNN<inline-formula><tex-math notation="LaTeX">$_{mts}$</tex-math><alternatives><mml:math><mml:msub><mml:mrow/><mml:mrow><mml:mi>m</mml:mi><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:math><inline-graphic xlink:href="hao-ieq1-2934464.gif"/></alternatives></inline-formula>-X</italic>, which is a new variant of the Convolutional Neural Networks (<italic>CNN</italic>) and can embed other feature extraction techniques (as <italic>X</italic>). Furthermore, we design a <italic>CNN<inline-formula><tex-math notation="LaTeX">$_{mts}$</tex-math><alternatives><mml:math><mml:msub><mml:mrow/><mml:mrow><mml:mi>m</mml:mi><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:math><inline-graphic xlink:href="hao-ieq2-2934464.gif"/></alternatives></inline-formula>-LR</italic> method that implements a new feature identification approach (<italic>LR</italic>) as <italic>X</italic> in the <italic>CNN<inline-formula><tex-math notation="LaTeX">$_{mts}$</tex-math><alternatives><mml:math><mml:msub><mml:mrow/><mml:mrow><mml:mi>m</mml:mi><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:math><inline-graphic xlink:href="hao-ieq3-2934464.gif"/></alternatives></inline-formula>-X</italic> framework. The <italic>LR</italic> method leverages both Linear Discriminant Analysis (<italic>LDA</italic>) and Random Forest (<italic>RF</italic>). Our extensive experiments on five real datasets show that the <italic>CNN<inline-formula><tex-math notation="LaTeX">$_{mts}$</tex-math><alternatives><mml:math><mml:msub><mml:mrow/><mml:mrow><mml:mi>m</mml:mi><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:math><inline-graphic xlink:href="hao-ieq4-2934464.gif"/></alternatives></inline-formula>-LR</italic> method has exhibited much better performance than several other baseline methods. Using 30 percent of the PVs discovered from the <italic>CNN<inline-formula><tex-math notation="LaTeX">$_{mts}$</tex-math><alternatives><mml:math><mml:msub><mml:mrow/><mml:mrow><mml:mi>m</mml:mi><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:math><inline-graphic xlink:href="hao-ieq5-2934464.gif"/></alternatives></inline-formula>-LR</italic>, classifications can achieve better or similar performance than using all the variables.