913 research outputs found
Graph Summarization
The continuous and rapid growth of highly interconnected datasets, which are
both voluminous and complex, calls for the development of adequate processing
and analytical techniques. One method for condensing and simplifying such
datasets is graph summarization. It denotes a series of application-specific
algorithms designed to transform graphs into more compact representations while
preserving structural patterns, query answers, or specific property
distributions. As this problem is common to several areas studying graph
topologies, different approaches, such as clustering, compression, sampling, or
influence detection, have been proposed, primarily based on statistical and
optimization methods. The focus of our chapter is to pinpoint the main graph
summarization methods, but especially to focus on the most recent approaches
and novel research trends on this topic, not yet covered by previous surveys.Comment: To appear in the Encyclopedia of Big Data Technologie
Bayesian Methods in Tensor Analysis
Tensors, also known as multidimensional arrays, are useful data structures in
machine learning and statistics. In recent years, Bayesian methods have emerged
as a popular direction for analyzing tensor-valued data since they provide a
convenient way to introduce sparsity into the model and conduct uncertainty
quantification. In this article, we provide an overview of frequentist and
Bayesian methods for solving tensor completion and regression problems, with a
focus on Bayesian methods. We review common Bayesian tensor approaches
including model formulation, prior assignment, posterior computation, and
theoretical properties. We also discuss potential future directions in this
field.Comment: 32 pages, 8 figures, 2 table
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