Functional Clustering Via Shrinkage Hypothesis Testing K-means

A functional clustering method,shrinkage hypothesis testing K-means for functional data(THSKM)is proposed in this thesis.The B-spline method is adopted to smooth functional data due to its feature of continuum infinite dimensionality.Then two test statistics are used to test parallelism and equality of means respectively.These two statistics will be set as the distance of the K-means algorithm to classify which cluster each curve belongs to.That is,we first apply test statistics to determine the clusters of each curve in every clustering iteration step of K-means,and the we use James-Stein type estimator to shrink the centroids of clusters toward the overall mean of all data,and these two steps are repeated until convergence.Since there's no inverse covariance function and inverse covariance of functional data is singular,we compute inverse covariance by graphical lasso to construct a James-Stein type estimator.In the end,simulation and real data examples show that our method is more competitive than others.