Functional Clustering Approach for Analysis of Concentration

In this research, we study characteristics of concentration variation with functional data analysis. Functional data analysis, which combines traditional data analysis with the characteristics of functions, is suitable to analyze changing trend of observed data with the utility of derivatives. We applied functional clustering analysis to milk dataset, which contains milk concentration, sum of rain, average speed of wind, and average temperature, to reveal the relationship between milk concentration and other variables. We get eight dendrograms in functional clustering analysis. Cophenetic correlation coefficient is used to measure the similarities among the dendrograms. Multidimensional scaling is used to visualize the dissimilarities of the dendrograms clearly. As a result, we find that the trend of milk concentration has relation to those of sum of rain and of average speed of wind.