Quantum Representation And Fusion Methods Of Feature Data

Serious redundancy and inconsistency inevitably exist in big data which are produced inthe informatization, intelligentization and automatization process of digitizing our planet andhuman activities, and they present serious challenges to effective management and integrationof big data because of the difficulty in processing data and the hidden cost in consumingresources. The purpose of feature fusion is to improve the completeness and conciseness ofthe given source feature data by eliminating the redundant and inconsistent data. Where,inconsistency denotes that the same data entities do not have the same or similar basicfeatures, and completeness means that any target data source is not leaved by the users andconciseness means that the target data sources do not have duplicate representations andcontradictions. The already developed feature fusion methods are based on classical datarepresentation and are still inadequate in effectively and efficiently eliminating the duplicatefeature data.The quantum algorithms on factorization and search proposed by Shor and Grover andthe appearance of quantum computer provide a new way to efficiently solve the problem ofthe fusion of duplicate data. This thesis represents the feature data with quantum state,quantum phase, and quantum bit (qubit) based density matrix, etc., which are different to theclassical real representation, and studies the methods of feature data cleaning, or featurecleaning, and feature data fusion, or feature fusion, based on quantum representation and theclassical based and quantum inspired feature fusion methods based on the collision andreaction mechanism from the perspective of cross disciplines of theoretical physics andcomputer science, which mainly includes:(1) The tasks of the feature cleaning methods based on von Neumann entropy are todetect the low quality samples based on the computing results of entropy contribution degreeand additional entropy according to the von Neumann theory and transform them with unitaryoperators in order to improve the data quality, i.e., completeness and conciseness, of the givensource feature data.(2) The tasks of the feature fusion method based on quantum representation are totransform the classical real representations of the feature sample elements into the quantumphase representations, detect and fuse the duplicate feature samples through discretization andquantum measurement in order to improve the completeness and conscience of the givensource feature data, and make a comparison in fusion performances with the classical featurefusion methods. (3) The tasks of the feature fusion methods based on Shannon entropy and von Neumannentropy are to compute the feature samples’ entropies and the mutual entropies betweensamples according to the theories of Shannon entropy and von Neumann entropy, detect theduplicate samples based on the principle of maximum mutual entropy, and fuse the duplicatesamples according to the weight of sample probability for the Shannon entropy based onfeature fusion method while quantum operations for the von Neumann entropy based featurefusion method.(4) The tasks of the feature fusion method based on the collision and reaction mechanismof data fusion are to establish the collision and reaction mechanism of data fusion which aimsto expand the difference between duplicate data and non duplicate data according to thecharacters of data fusion, and propose more simple and effective duplicate detection andfeature fusion methods based on this mechanism, which include classical based method andquantum inspired method.(5) The tasks of feature fusion architecture based on von Neumann entropy are tocombine the feature cleaning, duplicate detection and feature fusion into feature fusionarchitecture. Based on the same duplicate detection and feature fusion models, the fusion tothe cleaned feature data can better improve the completeness and conciseness of the givensource feature data than the one to the raw feature data.The experimental results show that the feature cleaning methods based on quantumrepresentation can improve the quality of source feature data preferably, and the featurefusion methods based on quantum representation can better improve the completeness andconciseness of the given source feature data compared to the classical feature fusion methods.Theoretically, according to the effect of quantum parallelism, the time efficiencies of thequantum algorithms of the feature fusion methods based on quantum representation and thecollision and reaction mechanism of data fusion are far more than the ones of thecorresponding classical algorithms. Therefore, the achievement of this thesis is invalueable toquantum algorithms of data fusion and big data processing in theory and application.