Dynamic Belief Entropy And Its Applications In Evidence Theory

Pattern recognition refers to the automatic recognition of patterns and laws in data,which has been widely used in many fields.However,pattern recognition models suffer from uncertain information in practical applications.If the mechanism of uncertainty processing and management is lacking,the accuracy and stability of the model will decrease.Therefore,the study of uncertainty measurement has important theoretical and engineering significance for pattern recognition.D-S evidence theory is an extension of probability theory,which can provide a theoretical basis for uncertain information processing,and has been applied in many areas such as pattern recognition,data fusion,and reliability analysis.As a generalization of Shannon entropy,belief entropy is able to measure the uncertainty in D-S evidence theory.In recent years,belief entropy has made great progress both theoretically and practically,but it also faces some issues and defects,especially “the weighting problem of discord and non-specificity in belief entropy”,which reduces the effectiveness of belief entropy in uncertainty measurement.To solve the above problem,this thesis proposes the concept of dynamic belief entropy.Compared with traditional belief entropy,the innovation of dynamic belief entropy is that it introduces the idea of dynamic weight,so that it can flexibly adjust the weight according to different scenarios,thereby improving the performance of uncertainty measurement.Based on the dynamic belief entropy,this thesis designs the corresponding evidential classification and evidential clustering algorithms respectively.Their innovation points lie in the consideration of dynamic mechanisms such as dynamic belief entropy,dynamic parameter,and hyper-parameter,which can dynamically evaluate the statistical characteristics of different problems,thus improving the effectiveness and stability of the algorithms.The main research contents of this thesis are as follows:(1)Basic theory and properties: To deal with the weighting problem in belief entropy,this thesis extends belief entropy based on the idea of dynamic weight,and proposes dynamic belief entropy.This thesis proves the maximum dynamic belief entropy and its distribution conditions.The relationships between dynamic belief entropy and other uncertainty measurements are analyzed.The properties of dynamic belief entropy are explored,such as monotonicity,additivity,and probability consistency.Experimental results illustrate the effectiveness of dynamic belief entropy,dynamic parameter,and normalization coefficient.(2)Application in evidential classification: Aiming at the problem that the traditional evidential classification algorithm cannot flexibly adjust the fusion strategy,resulting in the decline of classification accuracy,this thesis proposes a new evidential classification algorithm based on dynamic belief entropy.This algorithm can flexibly adjust the uncertainty measurement and evidence fusion strategy according to the statistical characteristics of different classification scenarios,thereby improving the classification performance of the algorithm.The effectiveness of the algorithm is evaluated and verified by several experiments.(3)Application in evidential clustering: To solve the local optimal problem of evidential clustering algorithm,this thesis proposes the dynamic belief entropy-based evidential C-means clustering algorithm.This algorithm utilizes the maximum entropy principle and dynamic belief entropy to unbiasedly estimate the basic belief assignment,so as to reduce the influence of poor initial centroids and solve the local optimal problem.Experimental results show that the algorithm has good clustering performance and stability.