Interpretable Compression of Multivariate Time Series via Geometric Volume Compression

We present a framework that is both interpretable and parameter efficient for the compression of multivariate time series (MTS) based on the Geometric Path Features (GPF). The core contribution is a two stage pipeline with (i) a novel channel selection technique ranking channels based on their average distance to all others where here we use a Shape Based Distance (SBD), which keeps only the most geometrically distinct channels and (ii) which is a grouped k-volume compression scheme collapsing the selected channels into a smaller subset of series with each capturing the signed or unsigned geometric volume swept by the group of channels over time. Path signatures are computed on these compressed series in order to retrieve compact feature vectors. On a 963-channel traffic dataset, our full pipeline compresses to 60 channels while achieving 81.2% accuracy which is 98.8% of the full signature baseline accuracy while notably using 64 × fewer features. On a 61channel medical sensing benchmark, the bivariate compressed variant outperforms the baseline (72.2% vs. 70.7%) with 61 × fewer features. Empirically, the k-volume compression is robust to channel selection strategy where random selection matches SBD in accuracy which confirms that the grouped geometric compression itself is the key contribution.