Research On Quantum Feature Selection And Principal Component Analysis Algorithms

In the context of big data,the classification and clustering of massive data is an important step in machine learning.However,the big data that can be used for training has richer data features,and redundant feature data will greatly increase the complexity of calculation.In the classic field,computing resources and storage capacity have become urgent problems to be solved.The superposition characteristics of quantum and parallel computing capabilities can solve this problem well.Therefore,finding feasible and efficient algorithms for classification and clustering problems in the quantum field is a work of great theoretical value and research significance.With the help of very important data preprocessing algorithms in quantum machine learning(ie,quantum feature selection and principal component analysis algorithms),this paper can solve the problems of difficult extraction of massive feature data and high computational complexity,which is of great significance for improving computational efficiency and saving resource consumption.This paper separately studies the quantum feature selection algorithm for multi-classification problems and the quantum principal component analysis algorithm for clustering problems.The main research contents of this paper are as follows:(1)The computational complexity of the classic multi-classification feature selection algorithm will increase significantly with the size of the sample and the number of features,and the storage capacity,and computing power of classic computers are limited.In order to reduce the complexity of the algorithm and improve the efficiency of the algorithm,a quantum feature selection algorithm for multi-classification problems is proposed.The weight vectors of the sample points are updated by calculating the similarity of the samples,and selects appropriate features according to the threshold.In the process of finding the nearest neighbor k samples,Grover-Long algorithm is used to speed up the entire search process twice.By comparing three related algorithms,this paper conducted specific research and analysis,which proved that this algorithm has obvious advantages in the similarity calculation complexity,the complexity of finding the nearest neighbor,and the resource consumption.Finally,the implementation of related quantum experiments is completed on the Regetti quantum cloud platform to verify the feasibility of this algorithm.(2)The classic clustering problem is susceptible to abnormal points in the selection of cluster centers,and as the number of samples and the number of clusters increase,more computing resources are required for distance calculation.In order to improve the efficiency of the algorithm and reduce resource consumption,a new quantum principal component analysis algorithm for clustering problems is proposed.This algorithm performs singular value decomposition on the original data set matrix and compresses it,and the principal components are extracted.Then the singular values of the principal components are updated and restored,and k minimum values are selected as the cluster center of this sample set from the potential energy function of the new data subset.At the same time,an optimized minimum search algorithm is used to improve the search process,which uses a dynamic strategy to reduce the number of iterations of the algorithm.After comparing four related algorithms,this paper conducted specific research and analysis,which proved that this algorithm has reduced the time complexity of cluster center selection,time complexity of the search and resource consumption.Finally,related quantum experiments are completed with the help of Cirq toolkit to verify the feasibility of the algorithm.