2015/05/28 by Mark Sh. Levin, Levin, Mark Sh.
Computer Science · #90B50 #90B51 #90C27 #90C59 #Advanced Clustering Algorithms Research #Artificial Intelligence (cs.AI) #Data Management and Algorithms #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #G.1.6 #G.2.1 #G.2.3 #H.3.3 #I.2.8 #I.5.3 #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1505.07872
openalex publication_date 2015/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper describes clustering problems from the combinatorial viewpoint. A brief systemic survey is presented including the following: (i) basic clustering problems (e.g., classification, clustering, sorting, clustering with an order over cluster), (ii) basic approaches to assessment of objects and object proximities (i.e., scales, comparison, aggregation issues), (iii) basic approaches to evaluation of local quality characteristics for clusters and total quality characteristics for clustering solutions, (iv) clustering as multicriteria optimization problem, (v) generalized modular clustering framework, (vi) basic clustering models/methods (e.g., hierarchical clustering, k-means clustering, minimum spanning tree based clustering, clustering as assignment, detection of clisue/quasi-clique based clustering, correlation clustering, network communities based clustering), Special attention is targeted to formulation of clustering as multicriteria optimization models. Combinatorial optimization models are used as auxiliary problems (e.g., assignment, partitioning, knapsack problem, multiple choice problem, morphological clique problem, searching for consensus/median for structures). Numerical examples illustrate problem formulations, solving methods, and applications. The material can be used as follows: (a) a research survey, (b) a fundamental for designing the structure/architecture of composite modular clustering software, (c) a bibliography reference collection, and (d) a tutorial.