A Validity Measure for Fuzzy Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Cluster Dissection and Analysis Theory FORTRAN Programs Examples
The Cluster Dissection and Analysis Theory FORTRAN Programs Examples
Pattern Recognition with Fuzzy Objective Function Algorithms
Pattern Recognition with Fuzzy Objective Function Algorithms
Crisp and fuzzy k-means clustering algorithms for multivariate functional data
Computational Statistics
Upper and lower values for the level of fuzziness in FCM
Information Sciences: an International Journal
Fuzzy clusterwise linear regression analysis with symmetrical fuzzy output variable
Computational Statistics & Data Analysis
The fuzzy approach to statistical analysis
Computational Statistics & Data Analysis
A class of fuzzy clusterwise regression models
Information Sciences: an International Journal
Fuzzy clustering of time series in the frequency domain
Information Sciences: an International Journal
Switching regression models and fuzzy clustering
IEEE Transactions on Fuzzy Systems
On cluster validity for the fuzzy c-means model
IEEE Transactions on Fuzzy Systems
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We propose a functional extension of fuzzy clusterwise regression, which estimates fuzzy memberships of clusters and regression coefficient functions for each cluster simultaneously. The proposed method permits dependent and/or predictor variables to be functional, varying over time, space, and other continua. The fuzzy memberships and clusterwise regression coefficient functions are estimated by minimizing an objective function that adopts a basis function expansion approach to approximating functional data. An alternating least squares algorithm is developed to minimize the objective function. We conduct simulation studies to demonstrate the superior performance of the proposed method compared to its non-functional counterpart and to examine the performance of various cluster validity measures for selecting the optimal number of clusters. We apply the proposed method to real datasets to illustrate the empirical usefulness of the proposed method.