The Study Of Functional K-means Clustering Method Based On The Band Depth

With the rapid development of modern data collection and storage technology,the method of data collection and the form of data acquired by researchers are undergoing great changes.The sample data collected in many fields are presented in the form of functional images themselves.The sample data in some fields,although they do not appear in the form of the functional image,also make the collected observation data show the functional characteristics as time changes.The generating process of functional data is a function process.Functional data analysis takes functional data as the research object,and its basic idea is to regard the observed data as a whole.As the demand for public bicycles varies with time,for example,the continuous changes in the daily demand data and the formation of peaks and valleys,it can be considered as functional data.Based on the limitations of existing functional clustering methods,in order to solve the problem that outliers affect the selection of k-means clustering centers,a weight based on the band depth of functional data is added to the process of computing clustering centers,and the calculation method of clustering centers is improved.A k-means clustering method which can effectively reduce the impact of outliers on functional data is proposed.In order to verify the effectiveness of this method,this paper firstly compares the effect of the new method with that of the traditional clustering method by random simulation of several groups of functional data with different kinds of outliers.Secondly,according to the characteristics of public bicycle demand data,the demand data is regarded as functional data,so the functional data analysis method is introduced into the research field of public bicycle demand.In the empirical analysis,taking the borrowing record data of Capital Bikeshare bicycle system as an example,combined with weather data and holiday arrangement data,the fluctuation law and distribution of bicycle demand are analyzed by functional k-means clustering method based on band depth,and the effect of the original prediction model is improved,which provides a decision support for the arrangement of vehicles in public bicycle system.