Digital Pattern Recognition And Its Applications Based On Information Theory

Supported (No. 40074001) by the National Natural Science Foundation of China project "Information Pattern Rcognition Theory and Its Application in Earth Science", Concentrated on information theory, and combined with statistical theory, system theory, fuzzy mathematics theory and pattern recognition theory, the Digital Pattern Recognition (DPR) theory is studied systematically, which is included mainly four parts as follows.Firstly, on the basis of the known pattern measure theory, the Information Pattern Measure (IPM) is studied systematically. The basic concepts of the Symmetric Cross Entropy (SCE), Incidence Informarion Coefficient (EC) and Discrete Contents (DC) and so on are proposed based on information theory, and on the basis of the concepts, the some measures of Cross Distance Measure (CDM), Incidence Information Measure (EM), Information Distance Measure (IDM) and Information Coefficient Measure (ICM) are set up. All of these theories and methods expand research fields of information pattern similarity measure, and consist of important parts of DPR.Secondly, we discuss symtematically some methods of Information Feature Compression (IFC) based on dispersion matrix criterion, probability distance criterion, scatter criterion, information entropy criterion and so on, and study their algorithm respectively; According to the idea of information entropy, the new concepts of the 2nd representation entropy and geometry entropy are proposed and proved that the value of the 2nd representation entropy and geometry entropy by DKLT is mixmum. DKLT makes information content concentrate on the components transformed relatively and provides good base for IFC. On the basis of Principal Components Analysis (PCA) algorithm and according to the concept of Shannon information function, we define Possibility Information Function (PIF) of eigenvalue firstly, and propose Information Rate (IR) and Accumulated Information Rate (AIR), which is used to measure the information compression degree, and establish a new PCA feature compression algorithm based on information theory. We apply Partial Least Squares (PLS) regression to IFC field and propose IFC algorithm based on PLS firstly. It is a soft modeling and robust statistical analysis method for measurement data, which has more advantages than PCA, such as simplicity and robustness,clearly qualitative explanation. It is powerful for multicollinearity, particularly when the number of predictor variables is large and the sample size is small. Meanwhile the information of data matrix X is compressed while considering maximum correlation with objctive matrix Y. these make the algorithm here be more practical.At last, based on IPM and IFC theories, two information cluster algorithms based on ICM and EICM are set up and applied them to classification of land quality; According to information entropy theory, a new concept of Objective Entropy Weight (OEW) is proposed, and given the construction method of OEW. A new DPR algorithm Based on OEW is set up. The simulation results show that the model proposed here is efficient and reasonable; According to cross entropy theory, a new concept of SCEC is prposed, and a novel IFC algorithm is set up; On the basis of analysis of modeling method of PLS, regarded response variate as 0-1 variates, a novel DPR algorithm based on PLS is set up in this paper. It has moreadvantages than Fisher discriminant analysis and Bayes discriminant analysis, such as simplicity and robustness, clearly qualitative explanation; Based on fuzzy sets theory and the practical background of surveying data, some new concepts of Fuzzy Incidence Coefficient (FIC), Fuzzy Incidence Degree (FID) and Fuzzy Relative Weight (FRW) are proposed for surveying data information. On the basis of the concepts, a novel incidence pattern recognition algorithm is set up and applied to surveying data processing; On the basis of fuzzy sets theory, some new theories of fuzzy entropy measure and fuzzy cross entropy measure are established, and new concepts of Fuzzy Relative Mutual Informa...