In this era of big data, multivariate time-series (MTS) data are prevalent in diverse domains and often high dimensional. However, there have been limited studies of building a capable classifier with MTS via classical machine learning methods that can deal with the double curse of dimensionality due to high variable dimension and long time series (large sample size). In this thesis, we propose two approaches to address this problem for multiclass classification with high dimensional MTS.
Both approaches leverage the dynamics of an MTS captured by non-parametric modeling of its spectral density function. In the first approach, we introduce the reduced-rank spectral classifier (RRSC), which utilizes low-rank estimation and some new discrimination functions. We illustrate the efficacy of the RRSC with both simulations and real applications. For binary classification, we establish the consistency of the RRSC and provide an asymptotic formula for the misclassification error rates, under some regularity conditions. The second approach concerns the development of the random projection ensemble classifier for time series (RPECTS). This method first applies dimension reduction in the time domain via projecting the time-series variables into some low dimensional space, followed by measuring the disparity via some novel base classifier between the data and the candidate generating processes in the projected space.
We assess the classification performance of our new approaches by simulations and compare them with some existing methods using real applications. Finally, we elaborate two R packages that implement the aforementioned methods.