SCHENO: Measuring Schema vs. Noise in Graphs

Real-world data is typically a noisy manifestation of a core pattern (schema), and the purpose of data mining algorithms is to uncover that pattern, thereby splitting (i.e. decomposing) the data into schema and noise. We introduce SCHENO, a principled evaluation metric for the goodness of a schema-noise decomposition of a graph. SCHENO captures how schematic the schema is, how noisy the noise is, and how well the combination of the two represent the original graph data. We visually demonstrate what this metric prioritizes in small graphs, then show that if SCHENO is used as the fitness function for a simple optimization strategy, we can uncover a wide variety of patterns. Finally, we evaluate several well-known graph mining algorithms with this metric; we find that although they produce patterns, those patterns are not always the best representation of the input data.