非線形混合効果モデルに基づく関数データクラスタリング

摘要

We consider the problem of clustering functional data using nonlinear mixed effects models along with the technique of basis expansions. With the help of fixed and random effects functions, the nonlinear mixed effects model makes it easy to handle unbalanced or sparse data which are highly occurred in the longitudinal study. We assume different numbers of basis functions for fixed and random effects functions. Unknown parameters included in the model are estimated by the maximum likelihood method along with the EM algorithm, and then the numbers of basis functions included in the model are selected by model selection criteria. We then apply hierarchical and non-hierarchical clustering methods to the predicted coefficients of the random effect terms of functional data in order io highlight the features of each subject. The hierarchical clustering such as the Ward's method proceeds in successive steps from smaller to larger clusters, which can be directly observed visually. In contrast, the non-hieraxchiGal clustering such as the self-organizing maps consists of progressively refining the data partitions to obtain a given number of clusters. In functional cluster analysis, we can remove the measurement errors of observed data and therefore we can capture the functional structure behind the data. We report the results of application of the proposed method to some real data sets such as environmental data and weather data.%非線形混合効果モデルを用いた，経時測定データに対するクラスタリング手法について考察する.本論文では，基底関数展開に基づく非線形混合効果モデルを適用することで，経時観測データを平均効果関数および個体ごとの変動を表したランダム効果関数を用いて関数データとして表現する.次に，ランダム効果関数集合に対して，自己組織化マップゃウォード法等の手法を適用してクラスタリングを行う.提案した手法を，微小粒子状物質データ，気象データおよび台風経路データへ適用し，有効性を検証する.