Given an irregular dense tensor, how can we efficiently analyze it? An irregular tensor is a collection of matrices whose columns have the same size and rows have different sizes from each other. PARAFAC2 decomposition is a fundamental tool to deal with an irregular tensor in applications including phenotype discovery and trend analysis. Although several PARAFAC2 decomposition methods exist, their efficiency is limited for irregular dense tensors due to the expensive computations involved with the tensor.In this paper, we propose DPAR2, a fast and scalable PARAFAC2 decomposition method for irregular dense tensors. DPAR2 achieves high efficiency by effectively compressing each slice matrix of a given irregular tensor, careful reordering of computations with the compression results, and exploiting the irregularity of the tensor. Extensive experiments show that DPAR2 is up to 6.0× faster than competitors on real-world irregular tensors while achieving comparable accuracy. In addition, DPAR2 is scalable with respect to the tensor size and target rank.

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What are the key structures existing in a large real-world MMORPG (Massively Multiplayer Online Role-Playing Game) graph? How can we compactly summarize an MMORPG graph with hierarchical node labels, considering consistent substructures at different levels of hierarchy? Recent MMORPGs generate complex interactions between entities inducing a heterogeneous graph where each entity has hierarchical labels. Succinctly summarizing a heterogeneous MMORPG graph is crucial to better understand its structure; however it is a challenging task since it needs to handle complex interactions and hierarchical labels efficiently. Although there exist few methods to summarize a large-scale graph, they do not deal with heterogeneous graphs with hierarchical node labels.We propose GSHL, a novel method that summarizes a heterogeneous graph with hierarchical labels. We formulate the encoding cost of hierarchical labels using MDL (Minimum Description Length). GSHL exploits the formulation to identify and segment subgraphs, and discovers compact and consistent structures in the graph. Experiments on a large real-world MMORPG graph with multi-million edges show that GSHL is a useful and scalable tool for summarizing the graph, finding important and interesting structures in the graph, and finding similar users.