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Kings In The Direct Product Of Digraphs, Morgan Norge
Kings In The Direct Product Of Digraphs, Morgan Norge
Theses and Dissertations
A k-king in a digraph D is a vertex that can reach every other vertex in D by a directed path of length at most k. A king is a vertex that is a k-king for some k. We will look at kings in the direct product of digraphs and characterize a relationship between kings in the product and kings in the factors. This is a continuation of a project in which a similar characterization is found for the cartesian product of digraphs, the strong product of digraphs, and the lexicographic product of digraphs.
Optimization Methods For Learning Graph-Structured Sparse Models, Baojian Zhou
Optimization Methods For Learning Graph-Structured Sparse Models, Baojian Zhou
Legacy Theses & Dissertations (2009 - 2024)
Learning graph-structured sparse models has recently received significant attention thanks to their broad applicability to many important real-world problems. However, such models, of more effective and stronger interpretability compared with their counterparts, are difficult to learn due to optimization challenges. This thesis presents optimization algorithms for learning graph-structured sparse models under three different problem settings. Firstly, under the batch learning setting, we develop methods that can be applied to different objective functions that enjoy linear convergence guarantees up to constant errors. They can effectively optimize the statistical score functions in the task of subgraph detection; Secondly, under stochastic learning setting, …