This paper considers a situation where multiple explanatory variables and multiple objective variables are observed from several populations. When observed data with multiple explanatory variables together with a single objective variable is available from the uncertain number of populations, a clusterwise regression analysis has been proposed to obtain an efficient regression model. In this paper, we propose a clusterwise multivariate kernel ridge regression analysis to analyze nonlinear data including both multiple explanatory variables and multiple objective variables from several populations. In addition, through a numerical experiment and a case study, we show that the performance of the clusterwise multivariate kernel ridge regression analysis is superior to those of traditional k-means cluster analysis and kernel k-means cluster analysis.
Katsuyuki Abe introduced the notion of Tsunami Magnitude (denoted by Mt) for scaling the earthquakes which cause tsunami, measuring the tide-wave-heights, and published a dataset of Mt of tsunamis caused by the earthquakes in the sea around Japan (2006). The dataset includes historical Mt, which extends the original definition and calculated from old documents, monuments and digs. In this paper, we fit the generalized Pareto distribution to the Mt dataset and calculate return periods and other statistics to show the rarity of 2011/03/11 tsunami at the Pacific Ocean coast of Tohoku district.The point is to consider the effect of lost or neglected records in the historical data, as well as the considerable amount of missing data in the measurement of tidal level in the beginning of modern data, and to propose a new model.If the Mt of 03/11 tsunami is included in the dataset, the estimate of parameters change largely, showing the information of big Mt's.