The decomposition of a time series signal into components is an age old problem, with many different approaches proposed, including traditional filtering and smoothing, seasonal-trend decomposition, Fourier and other decompositions, PCA and newer variants such as nonnegative matrix factorization, various statistical methods, and many heuristic methods. In this monograph, the well-studied problem of decomposing a vector time series signal into components with different characteristics, such as smooth, periodic, nonnegative, or sparse are covered. A general framework in which the components...