担当区分：筆頭著者,　責任著者   掲載種別：研究論文（学術雑誌）   出版者・発行元：Springer Science and Business Media {LLC}  

DOI： 10.1007/s11634-022-00506-6

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Springer Science and Business Media {LLC}  

DOI： 10.1007/s41237-020-00112-w

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担当区分：筆頭著者,　責任著者   掲載種別：研究論文（学術雑誌）  

© 2019, © 2019 Taylor & Francis Group, LLC. Factor rotation is usually performed for a p-variables ×-factors loading matrix so that the resulting rotated matrix has a simple structure. This simple structure was originally defined by Thurstone (1947) by specifying how zero elements are arranged in the loading matrix. In this article, we propose a new rotation technique, which is directly based on Thurstone’s definition. It can give a p-variables × r -factors target matrix of zero and nonzero elements, which stands for the properties to be possessed by the rotated loading matrix. However, it is unknown how the rows of the target matrix are associated with those of the loading matrix. In the proposed procedure, a loading matrix is rotated simultaneously with a permutation of the rows of the target matrix, so that the rotated loading matrix is optimally matched to the permuted target matrix in a least squares sense. Its novel feature is the use of permutation, thus we call the technique Permutimin. Its algorithm is presented, with Thurstone’s definition of simple structure modified so as to specify the target matrix uniquely. Permutimin is illustrated with real data examples. Finally, we discuss the relationships between Permutimin and Procrustes rotation.

DOI： 10.1080/00273171.2019.1598331

Scopus

PubMed

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記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：Springer Science and Business Media Deutschland GmbH  

Multivariate regression is known as a multivariate extension of multiple regression, which explain/predict the variations in multiple dependent variables by multiple independent variables. Recently, various procedures for Sparse Multivariate Regression (SMR) have been proposed, in which a sparse regression coefficient matrix (having a number of zero elements) is obtained aiming to facilitate its interpretation. The procedures for SMR can be classified into the following two types
penalized and cardinality-constrained procedures. In them, the resulting number of zeros in the regression coefficient matrix is controlled/constrained by a prespecified penalty parameter or cardinality value. In this research, we propose another approach for SMR, referred to as Layered Multivariate Regression (LMR). In LMR, the regression coefficient matrix is assumed to be a sum of several sparse matrices, which is called layer. Therefore, the sparseness of the resulting coefficient matrix is controlled by how many layers are used. In LMR, k-th layer can be viewed as the coefficient matrix in the regression of a partial residual (i.e., the residual for all but k-th layer) on independent variables, and thus the variance explained by LMR gets closer to that for the unconstrained regression as the number of layers increases. We present an alternating least squares algorithm for LMR and a procedure for determining how many layers should be used. LMR is assessed in a simulation study and illustrated with a real data example. As an application of LMR, procedures for sparse estimation in some multivariate analysis techniques (e.g., principal component analysis) are also presented.

DOI： 10.1007/978-981-15-3311-2_25

Scopus

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）  

© 2019, The Classification Society. k-means clustering is a well-known procedure for classifying multivariate observations. The resulting centroid matrix of clusters by variables is noted for interpreting which variables characterize clusters. However, between-clusters differences are not always clearly captured in the centroid matrix. We address this problem by proposing a new procedure for obtaining a centroid matrix, so that it has a number of exactly zero elements. This allows easy interpretation of the matrix, as we may focus on only the nonzero centroids. The development of an iterative algorithm for the constrained minimization is described. A cardinality selection procedure for identifying the optimal cardinality is presented, as well as a modified version of the proposed procedure, in which some restrictions are imposed on the positions of nonzero elements. The behaviors of our proposed procedure were evaluated in simulation studies and are illustrated with three real data examples, which demonstrate that the performances of the procedure is promising.

DOI： 10.1007/s00357-019-09324-6

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担当区分：筆頭著者,　責任著者   掲載種別：研究論文（国際会議プロシーディングス）  

© Springer International Publishing AG, part of Springer Nature 2018. k-means clustering is one of the popular procedures for multivariate analysis in which observations are classified into a reduced number of clusters. The resulting centroid matrix is refereed to capture variables which characterize clusters, but between-clusters contrasts in the centroid matrix are not always clear and thus difficult to interpret. In this research, we address the problem in interpretation and propose a new procedure of k-means clustering which produces a sparse and thus interpretable centroid matrix. The proposed procedure is called SPARK. In SPARK, the sparseness of the centroid matrix is constrained and therefore it contains a number of exact zero elements. Because of this, the contrasts between-clusters are highlighted and it allows us to interpret clusters easier in comparison with the standard k-means clustering. A sparsity selection procedure for determining the optimal sparsity of the centroid with reduced computational load is also proposed. Behaviors of the proposed procedure are evaluated by two real data examples, and the results indicate that SPARK performs well for dealing with real world problems.

DOI： 10.1007/978-3-319-77249-3_34

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担当区分：筆頭著者,　責任著者   掲載種別：研究論文（学術雑誌）  

© 2014, Springer-Verlag Berlin Heidelberg. Biplot is a technique for obtaining a low-dimensional configuration of the data matrix in which both the objects and the variables of the data matrix are jointly represented as points and vectors, respectively. However, biplots with a large number of objects and variables remain difficult to interpret. Therefore, in this research, we propose a new biplot procedure that allows us to interpret a large data matrix. In particular, the objects and variables are classified into a small number of clusters by using fuzzy $$c$$c-means clustering and the resulting clusters are simultaneously biplotted in lower-dimensional space. This procedure allows us to understand the configurations easily and to grasp the fuzzy memberships of the objects and variables to the clusters. A simulation study and real data example are also provided to demonstrate the effectiveness of the proposed procedure.

DOI： 10.1007/s11634-014-0184-4

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担当区分：筆頭著者,　責任著者   記述言語：日本語   出版者・発行元：日本行動計量学会  

In this paper, we propose a new formulation of canonical correlation analysis, which is equivalent to the existing one. Under the new formulation, two canonical structure matrices have freedom of orthogonal rotation. We thus propose an orthogonal rotation method for rotating two structure matrices individually to simple structures. This method is different from the one derived from the existing formulation which only allows the simultaneous rotation of two structure matrices. It is illustrated that our proposed method facilitates the interpretation of solutions of canonical correlation analysis in a real data example.

DOI： 10.2333/jbhmk.39.1

CiNii Books

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担当区分：筆頭著者,　責任著者   記述言語：日本語   出版者・発行元：日本分類学会  

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会議種別：ポスター発表  

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会議種別：口頭発表（招待・特別）  

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記述言語：日本語   会議種別：口頭発表（一般）  

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記述言語：日本語   会議種別：口頭発表（一般）  

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記述言語：日本語   会議種別：口頭発表（一般）  

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記述言語：日本語   会議種別：口頭発表（一般）  

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記述言語：日本語   会議種別：口頭発表（一般）  

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記述言語：英語   会議種別：口頭発表（一般）  

国名：チリ共和国  

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記述言語：日本語   会議種別：口頭発表（一般）  

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記述言語：英語   会議種別：口頭発表（一般）  

国名：アメリカ合衆国  

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国名：日本国  

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記述言語：英語   会議種別：口頭発表（一般）  

国名：スイス連邦  

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記述言語：日本語   会議種別：口頭発表（一般）  

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記述言語：日本語   会議種別：口頭発表（一般）  

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記述言語：英語   会議種別：口頭発表（一般）  

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記述言語：日本語   会議種別：口頭発表（一般）  

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記述言語：日本語   会議種別：口頭発表（一般）  

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記述言語：日本語   会議種別：口頭発表（一般）  

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記述言語：日本語   会議種別：口頭発表（一般）  

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記述言語：日本語   会議種別：口頭発表（一般）  

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