Quantum Clustering Algorithm Based On Manifold Distance And Its Applications

Clustering is an unsupervised classification method which aims at dividing data into several homogeneous groups or clusters according to their similarities,so that data points within the same group are similar to each other while data points across different groups are dissimilar.Then clustering can effectively discover the inherent structure information in data and pave the way for further data analyses.Firstly we design a fusion algorithm of quantum clustering and study its performance on data sets with heterogeneous manifold structure.Secondly,we propose a quantum evolution clustering algorithm based on manifold distance and study its performance on data sets with heterogeneous manifold structure and data sets with cross manifold structure.Finally,an unsupervised feature selection algorithm based on quantum clustering is proposed to solve the feature selection problem by reducing the redundancy between features.The main contents of this paper are as follows:1.In order to give full play to the advantages of spectral clustering algorithm and quantum clustering algorithm,a fusion algorithm of spectral clustering and quantum clustering based on manifold distance kernel(MFD-NJW-QC)is proposed in this paper,and the clustering performance of the MFD-NJW-QC algorithm on data sets with different topologies is tested by experiments.The results show that the MFD-NJW-QC algorithm can significantly improve the clustering performance,especially for those datasets with manifold structure,uneven cluster size and uneven density distribution.2.A quantum evolutionary clustering algorithm based on manifold distance is designed.The average mainfold distance between the neighbors of the data point and each cluster center is calculated and every data point is divided into the cluster with the lowest average -nearest neighbor distance.The optimal solution of cluster center of each generation is selected by taking the sum of all the intraclass distance as the evaluation index.The optimal class centers are obtained by the quantum evolution algorithm iteratively,and then the class label is allocated by a well-determined class label.By introducing the average -nearest neighbor distance as the basis for class division,the designed quantum evolutionary clustering algorithm based on manifold distance also has good clustering effect on these data sets with unbalanced size and density,as well as on these data sets with cross manifold structure.3.In order to reduce the redundancy between features of data sets,an unsupervised feature selection algorithm based on quantum clustering is proposed.The distance between the two features was defined according to similarity measure between features,and a fusion algorithm of spectral clustering and quantum clustering is used to perform clustering analysis on the feature vectors.An optimized non-redundant feature subset is selected and a new data set is constructed through this feature subset to achieve the purpose of dimension reduction.LSTM neural network is used to classify the new data set.Experiments on UCI real data sets show that the unsupervised feature selection algorithm based on quantum clustering not only reduces the size of data set and time of feature selection,but also improves the classification accuracy of LSTM neural network.