SiBBlInGS: Similarity-driven Building-Block Inference using Graphs across States

Interpretable methods for extracting meaningful building blocks (BBs) underlying multi-dimensional time series are vital for discovering valuable insights in complex systems. Existing techniques, however, encounter limitations that restrict their applicability to real-world systems, like reliance on orthogonality assumptions, inadequate incorporation of inter- and intra-state variability, and incapability to handle sessions of varying duration. Here, we present a framework for Similarity-driven Building Block Inference using Graphs across States (SiBBlInGS). SiBBlInGS employs a graph-based dictionary learning approach for BB discovery, simultaneously considers both inter- and intra-state relationships in the data, can extract non-orthogonal components, and allows for variations in session counts and duration across states. Additionally, SiBBlInGS allows for cross-state variations in BB structure and per-trial temporal variability, can identify state-specific vs state-invariant BBs, and offers both supervised and data-driven approaches for controlling the level of BB similarity between states. We demonstrate SiBBlInGS on synthetic and real-world data to highlight its ability to provide insights into the underlying mechanisms of complex phenomena and its applicability to data in various fields.