Graph Spectral Embedding for Parsimonious Transmission of Multivariate Time Series

We propose a graph spectral representation of time series data that 1) is parsimoniously encoded to user-demanded resolution; 2) is unsupervised and performant in data-constrained scenarios; 3) captures event and event-transition structure within the time series; and 4) has near-linear computational complexity in both signal length and ambient dimension. This representation, which we call Laplacian Events Signal Segmentation (LESS), can be computed on time series of arbitrary dimension and originating from sensors of arbitrary type. Hence, time series originating from sensors of heterogeneous type can be compressed to levels demanded by constrained-communication environments, before being fused at a common center. Temporal dynamics of the data is summarized without explicit partitioning or probabilistic modeling. As a proof-of-principle, we apply this technique on high dimensional wavelet coefficients computed from the Free Spoken Digit Dataset to generate a memory efficient representation that is interpretable. Due to its unsupervised and non-parametric nature, LESS representations remain performant in the digit classification task despite the absence of labels and limited data.