Some Studies On Multivariate Function Clustering Method Based On Multi-view Learning

With the development of the Internet and the popularization of the smart terminals,the functional data with continuous characteristics have emerged in the domain of the social life and scientific research.The functional clustering analysis is an important tool to explore functional data.At present,there are a few studies on multivariate functional data clustering methods.Most of the studies have been carried out by “fitting”each variable to the data to build a model.This method is not conducive to fully mining the common and complementary information among variables.In the field of machine learning,multi-view learning can aggregate information from different sources to obtain more comprehendsive analysis results than unilateral description.Inspired by this,the paper carries out study on the clustering method for multivariate functional data under the framework of multi-view learning.This paper studies on the clustering methods for multivariate functional data in different situations.The general framework of multivariate functional clustering method based on multi-view learning is proposed.The paper further discusses clustering methods for the case of data with label information,the case of missing data and the case of functional data with high volatility.The specific work is as follows:(1)The general framework of multivariate functional clustering based on multi-view learning is proposed for multivariate functional data.Based on the clustering characteristics of NMF,the one-step model is constructed to unify the generation of multivariate functional data and the extraction of clustering features from each perspective.The iterative updating algorithm of the model is given,the convergence of the algorithm is proved,and the time complexity of the algorithm is discussed.The simulation results show that this method is conducive to fully mining the common and complementary information among variables which is helpful to improve the clustering performance.The clustering results on Beijing air quality monitoring stations show that the advantages of the multi-view learning in terms of clustering accuracy and information extraction.(2)The semi-supervised multi-view functional clustering method is proposed for multivariate functional data with a little label information,which can improve the clustering performance by making use of the label information of data.The label information is integrated into the functional clustering by introducing the constrained nonnegative matrix factorization,and the one-step model is constructed,which fuses the curve fitting and the functional clustering into one objective function.The iterative updating algorithm of the model is given,the convergence of the algorithm is proved,and the time complexity of the algorithm is discussed.The simulation experimental results show that the more label information in the data,the better on the clustering effect.The clustering analysis of ECG data is taken as an example to illustrate the practical value of this method.(3)The multi-view functional clustering method for multivariate functional data with missing data is proposed,which can deal with the clustering problem of incomplete datasets.By integrating the idea of functional matrix filling,NMF and multi-view clustering,the one-step model of filling and clustering is proposed.Considering that missing elements of samples can be reconstructed from their neighbors,and samples of the same class will naturally form a neighbor data relationship,the alternative iteration updating algorithm is given,the convergence of the algorithm is proved,and the time complexity of the algorithm is discussed.The simulation experimental results show that this method can solve the clustering for functional data with the random missing,the strip missing and the block missing effectively.The clustering results on the data of hourly concentration of air pollutants in Beijing show that the method can also deal with large-scale data missing.(4)The self-weighting multi-view functional clustering method based on mode decomposition is proposed for data with high volatility under the idea of decomposition-clustering.The data is decomposed into different modal functions using the variational modal technique,and then each modality is regarded as a different view for clustering.A self-weighted multi-view functional clustering model is proposed which considering that the modal function belongs to functional data essentially.The contribution of each to the clustering results is different,and learning the weight automatically can avoid the hyper-parameters in the model,so as to reduce the influence of the clustering performance by weighting subjectively.The iterative updating algorithm of the model is given,the convergence of the algorithm is proved,and the time complexity of the algorithm is discussed.The simulation experimental results show that the proposed method can effectively learn the weights of each mode,which is helpful to improve the clustering performance,and it is applied to the field of the quantitative investment,which provides a theoretical basis for stock selection.