关键词: 函数型数据分析, 聚类, 非负矩阵分解, 交替迭代方法

Abstract: Functional clustering algorithm involves two basic elements:projecting and clustering.Generally speaking,the optimal projection results may not effectively retain category information,thus affecting the subsequent clustering effect.In this paper,the elements and operating process of functional clustering are reviewed,a functional clustering algorithm is proposed by virtue of the clustering characteristics of non-negative matrix factorization,and a one-step implementation framework of“clustering while projecting”is constructed.Meanwhile,the alternative and interative algorithm is used to update the solution,and the computational complexity of our proposed algorithm is discussed.The test results of random simulation data and speech recognition data show that our functional clustering algorithm is helpful to improve the clustering effect.A case study on the hourly concentration of nitrogen dioxide (NO2) in Beijing shows that our algorithm can distinguish the types of air quality monitoring stations and fully identify the spatial pattern of station layout,which has good application value.

Key words: Functional Data Analysis, Clustering, Non-negative Matrix Factorization, Alternative and Iterative Algorithm