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

Data in many scientific domains are often collected under multiple distinct states (e.g., different clinical interventions), wherein latent processes (e.g., internal biological factors) can create complex variability between individual trials both within single states and between states. A promising approach for addressing this complexity is uncovering fundamental representational units within the data, i.e., functional Building Blocks (BBs), that can adjust their temporal activity and component structure across trials to capture the diverse spectrum of cross-trial variability. However, existing methods for understanding such multi-dimensional data often rely on tensor factorization under assumptions that may not align with the characteristics of real-world data, and struggle to accommodate trials of different durations, missing samples, and varied sampling rates. Here, we present a framework for Similarity-driven Building Block Inference using Graphs across States (SiBBlInGS). SiBBlInGS employs a robust graph-based dictionary learning approach for BB discovery that considers shared temporal activity, inter- and intra-state relationships, non-orthogonal components, and variations in session counts and duration across states, while remaining resilient to noise, random initializations, and missing samples. Additionally, it enables the identification of state-specific vs. state-invariant BBs and allows for cross-state controlled variations in BB structure and per-trial temporal variability. We demonstrate SiBBlInGS on synthetic and several real-world examples to highlight its ability to provide insights into the underlying mechanisms of complex phenomena across fields.