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◇テーマ 次元縮約とクラスタリング
◇日 時 2015年7月25日（土） 午後（15:00〜17：00）を予定
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コーディネーター：森 裕一（岡山理科大学）
質的データの分析や分類手法について造詣が深く，計量心理学や計算機統計学の分野で多くの業績をもたれているオランダ，Erasmus University RotterdamのMichel van de Velden 氏が来日される機会を利用して，次元縮約とクラスタリングに関する研究会をもちます。
研究会では，テーマに関連する発表と，van de Velden氏からは，最近の研究である質的データの分類を同時推定により行う方法とその周辺についてお話しいただきます。
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| 15:00 |
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開会あいさつと講師紹介
森 裕一（岡山理科大学）
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| 15:05 |
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講演1：DROC: An
outcome-guided clustering using a component-based approach
山本倫生（京都大学臨床研究総合センター／医学研究科医学統計生物情報学）
Abstract：
Cluster analysis, in which objects with various features are
partitioned into several unpredetermined homogeneous groups
(clusters), is one of the major exploratory multivariate analyses.
Practically, the cluster analysis is followed by considering the
meaning of the obtained clusters. Then, researchers hope that the
clusters are related to some outcomes that they are interested in.
For example, in the study of medical genetics, the cluster
structure given by genome data is expected to be related to the
degree of clinical disease. Also, in marketing research, the
clusters are expected to relate to consumer behavior. However, it
is often difficult to find the meaningful clusters since cluster
analysis is essentially an unsupervised classification technique,
that is, the cluster structure is estimated without referring to
the interested outcomes. Thus, in this study, we propose a new
clustering technique called DROC which can provide a partitioning
related to some outcome variables. The clusters estimated from the
method would be easy to understand since the result can be
interpreted from the outcome information. In the method, the aim
is attained by a simple transformation of exploratory variables
using outcome variables. Also, a property of the proposed method
as a dimension reduction technique is discussed. Furthermore, we
study a modification of the proposed method to deal with
moderately high-dimensional data.
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| 15:35 |
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講演2：Cluster
Correspondence Analysis
Michel van de Velden (Econometric Institute, Erasmus
University Rotterdam)
Abstract：
A new method is proposed that combines dimension reduction and
cluster analysis for categorical data. The new method
simultaneously assigns individuals to clusters and optimalscaling
values to categories in such a way that a single between variance
objective is achieved. In a uni ed framework, a brief review of
alternative methods is provided and performanceof the methods is
appraised by means of a simulation study. The results of the joint
dimension reduction and clustering methods are compared with the
so-called tandem approach; asequential analysis of dimension
reduction followed by cluster analysis. The tandem approach is
conjectured to perform worse when variables are added that are
unrelated to the clusterstructure. Our simulation study con rms
this conjecture. Moreover, the results of the simulation study
indicate that the new method outperforms alternative joint
dimension reductionand clustering methods in most scenarios.
(joint work with Alfonso Iodice D'Enza and Francesco Palumbo)
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| 16:20 |
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休憩 |
| 16:40 |
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講演3：Least-squares
Bilinear Clustering of Three-way Data
Michel van de Velden (Econometric Institute, Erasmus
University Rotterdam)
Abstract：
A least-squares bilinear clustering framework for modelling
three-way data, where each observationconsists of an ordinary
two-way matrix, is introduced. The method combines bilinear
decompositionsof the two-way matrices into overall means, row
margins, column margins and row-columninteractions with clustering
along the third way. Di erent clusterings are defined for each
part ofthe decomposition, so that up to four di erent
classifications are defined jointly. The computationalburden is
greatly reduced by the orthogonality of the bilinear model, such
that the joint clusteringproblem reduces to separate ones which
can be handled independently. Three of these sub-problemsare
specific cases of k-means clustering; a special algorithm is
formulated for the row-column interactions,which are displayed in
clusterwise biplots. The method is illustrated via two
empiricalexamples and interpreting the interaction biplots are
discussed.
(joint work with Pieter Schoonees and Patrick
Groenen)
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| 17:25 |
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総合討論 |
| 18:00 |
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閉 会
黒田 正博（岡山理科大学）
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懇親会に参加の方は次のフォームで，
黒田 正博（岡山理科大学） <kuroda(atmark)soci.ous.ac.jp>
までメールでお申し込みください（前日までにお願いします）。
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◇共 催 日本行動計量学会岡山地域部会（第56回研究会）
岡山統計研究会（第156回）
■ 連絡先
森 裕一（社会情報学科 第61回研究会世話人）
E-mail:
mori
岡山理科大学 総合情報学部 社会情報学科
〒700-0005 岡山市北区理大町1-1
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