Visualizing data as objects by DC (difference of convex) optimization

• 成果类型: Article
• 署名作者: Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero
• 署名单位: University of Sevilla; Copenhagen Business School
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-017-1156-1
• 发表日期: 2018
• 页码: 119-140
• 关键词: sensor network localization; Principal Component Analysis; programming relaxation; approximate formulas; neighborhood search; weber problem; big data; distances; location; CHALLENGES

摘要

In this paper we address the problem of visualizing in a bounded region a set of individuals, which has attached a dissimilarity measure and a statistical value, as convex objects. This problem, which extends the standard Multidimensional Scaling Analysis, is written as a global optimization problem whose objective is the difference of two convex functions (DC). Suitable DC decompositions allow us to use the Difference of Convex Algorithm (DCA) in a very efficient way. Our algorithmic approach is used to visualize two real-world datasets.