Semi-supervised Clustering Method for Non-negative Functional Data

Abstract

Functional clustering analysis is an important tool for exploring functional data. Most of the existing functional clustering methods are essentially unsupervised learning and do not take into account the label information of data. To resolve the issues of unsupervised characteristics of existing functional clustering methods and the non-negative characteristics of functional data, a semi-supervised non-negative functional clustering method (SSNFC) is proposed, focusing on processing clustering of non-negative functional data with a little label information. Firstly, the label information is integrated into the functional clustering by introducing the constrained non-negative matrix factorization (CNMF) technique, and a one-step model is constructed, which fuses the curve fitting, non-negative constraint and functional clustering into one objective function. Secondly, an iterative updating algorithm is con-ducted, and its local convergence and time complexity are discussed. Finally, the experimental results on simulation data, Growth data and TIMIT (Texas Instruments and Massachusetts Institute of Technology) speech data indicate that SSNFC is helpful for improving clustering performance compared with other unsupervised functional clustering methods.

Keywords

• functional data;
• clustering analysis;
• semi-supervised learning;
• constrained non-negative matrix factorization