Research On Functional Data Clustering Based On Directional Multiple Hypothesis Testing And Information Entropy

The development and application of big data make the research of functional data important.Cluster analysis is often used as an initial step in data exploration to provide some explanation for the user.When the data belong to infinite dimensional space,it brings some difficulty to clustering,and also affects the effect of clustering.In recent years,functional clustering analysis has been developed to a certain extent.Therefore,it is very important to use the clustering algorithm of data information according to the characteristics of functional data sets.This paper proposes a new clustering method for functional data,which can better adapt to the characteristics of data and achieve better clustering effect.In the first chapter,the research status of functional cluster analysis is introduced,and the main work and innovation points of this paper are briefly summarized.In the second chapter,the theoretical basis of multiple hypothesis testing of directional false discovery rate and information entropy is firstly presented,and then a new statistic of parallelism is proposed to describe the morphological differences of functional curves.On the basis of the above,the author gives a new formula to calculate the proximity degree,and finally improves the agglomerative hierarchical clustering algorithm.In the third chapter,the clustering method in this paper is applied to four different types of functional data sets,and the clustering results are analyzed and compared with other existing methods,which proves the effectiveness and superiority of the improved agglomerative hierarchical clustering algorithm.