Theories and Methodologies for High-Dimensional Data Analysis

2014 Fiscal Year Final Research Report

• Project/Area Number: 22300094
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Statistical science
• Research Institution: University of Tsukuba
• Principal Investigator: AOSHIMA Makoto 筑波大学, 数理物質系, 教授 (90246679)
• Co-Investigator(Kenkyū-buntansha): YATA Kazuyoshi 筑波大学, 数理物質系, 助教 (90585803) ; SATO-ILIC Mika 筑波大学, システム情報系, 教授 (60269214) ; AKAHIRA Masafumi 筑波大学, 名誉教授 (70017424) ; KOIKE Ken-ichi 筑波大学, 数理物質系, 准教授 (90260471) ; OHYAUCHI Nao 筑波大学, 数理物質系, 助教 (40375374)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 高次元データ解析 / 多変量解析 / 主成分分析 / 判別分析 / クラスター分析 / ノイズ掃き出し法 / クロスデータ行列法 / マイクロアレイデータ

Outline of Final Research Achievements

We created two high-dimensional PCAs which we called the noise-reduction methodology and cross-data-matrix methodology. We proposed a new model, the power spiked model, for eigenvalues and gave consistent estimators of the eigenvalues, eigenvectors and PC scores. We did pioneering work on band-width confidence regions, two-sample problems, classification, variable selection, regression, pathway analysis and so on. We created the extended cross-data-matrix methodology which gives an unbiased estimator at low cost and applied it to the test of correlations. We considered multiclass discriminant analysis and showed that the distance-based classifier, geometric classifier and feature selection by DQDA are superior to sparse regularized classifiers. We proved their misclassification rates go to zero in high-dimension, non-sparse settings. Our work can be applied to many fields, such as medicine and big data, and has much lower computational costs with higher accuracy than existing methods.

Free Research Field

統計科学