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Data in many scientific domains are often collected under multiple distinctstates (e.g., different clinical interventions), wherein latent processes(e.g., internal biological factors) can create complex variability betweenindividual trials both within single states and between states. A promisingapproach for addressing this complexity is uncovering fundamentalrepresentational units within the data, i.e., functional Building Blocks (BBs),that can adjust their temporal activity and component structure across trialsto capture the diverse spectrum of cross-trial variability. However, existingmethods for understanding such multi-dimensional data often rely on tensorfactorization under assumptions that may not align with the characteristics ofreal-world data, and struggle to accommodate trials of different durations,missing samples, and varied sampling rates. Here, we present a framework forSimilarity-driven Building Block Inference using Graphs across States(SiBBlInGS). SiBBlInGS employs a robust graph-based dictionary learningapproach for BB discovery that considers shared temporal activity, inter- andintra-state relationships, non-orthogonal components, and variations in sessioncounts and duration across states, while remaining resilient to noise, randominitializations, and missing samples. Additionally, it enables theidentification of state-specific vs. state-invariant BBs and allows forcross-state controlled variations in BB structure and per-trial temporalvariability. We demonstrate SiBBlInGS on synthetic and several real-worldexamples to highlight its ability to provide insights into the underlyingmechanisms of complex phenomena across fields.

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