Statistical theory of unsupervised learning with a focus on clustering methods

2015 Fiscal Year Final Research Report

• Project/Area Number: 26880031
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Statistical science
• Research Institution: National Institute of Information and Communications Technology
• Principal Investigator: Terada Yoshikazu 国立研究開発法人情報通信研究機構, 脳情報通信融合研究センター 脳情報通信融合研究室, 研究員 (10738793)
• Project Period (FY): 2014-08-29 – 2016-03-31
• Keywords: 関数データ解析 / 高次元データ解析 / fMRIデータ解析

Outline of Final Research Achievements

In this research, I studied unsupervised classification and binary classification from only positive and unlabeled functional data (PU classification for functional data). Some important properties of the functional data clustering method proposed by Chiou and Li (2007) were derived, and a simple classification algorithm for functional PU learning problem was developed. Moreover, I proved that the distance vector clustering works well under several important high-dimension low-sample size settings. In addition, the simple voxelwise statistical inference for the underlying hemodynamic response function based on the difference-based estimator was developed. Under mild regularity conditions, it was shown that the proposed test statistics based on the difference-based HRF estimator follow chi-squared distributions under null hypotheses for several important hypotheses.

Free Research Field

教師なし学習の統計理論，fMRIデータ解析