New Developments in Sparse Factor Analysis

2017 Fiscal Year Final Research Report

• Project/Area Number: 26330039
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Statistical science
• Research Institution: Osaka University
• Principal Investigator: Adachi Kohei 大阪大学, 人間科学研究科, 教授 (60299055)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 多変量解析 / 因子分析 / 主成分分析 / スパース推定 / カーディナリティ制約 / 行列分解 / スパーセスト推定 / 因子モデル選択

Outline of Final Research Achievements

Factor analysis (FA) is a statistical procedure for finding the factors that can cause the phenomena observed as data. For example, when the phenomena observed are scores of tests, their factors are abilities. Sparse FA refers to the modified FA which purposes to computationally identify the pairs of phenomena to the related factors. The existing approach for this purpose is to dissociate the phenomena from the factors with their magnitudes of the relationships to the phenomena below a threshold. A difficulty in this approach is in the necessity of selecting the threshold among infinite continuous real values. For dealing with this difficulty, a sparse FA procedure was developed whose solution can be obtained once the number of unrelated pairs of phenomena to factors. As that number can be selected among restricted discrete integers, the best solution can be chosen among the ones for all pairs.

Free Research Field

統計科学