Multi-scale Classification Method Based On Fractal Theory

With the advent of the big data era,it becomes more urgent to excavate the rich and valuable knowledge behind the massive data.Classification mining as an important data mining and analysis method,has been widely used in daily life(such as: electronic commerce,finance,biology,communications,insurance,medical,etc.)as well as scientific research(such as image recognition,voice recognition,natural language processing,machine learning,etc.).Classification mining is a kind of supervised learning method,the essence of which is to forecast the label of new data,by a classification model,learned through the analysis of the distribution characteristics of the train data sets,which label is known.The purpose of multi-scale data mining is to carry out multi-scale and comprehensive analysis of data,and its core lies in scale transformation,which the result can be used for multiple times as soon as learned.Multi-scale classification is a typical interdisciplinary topic,the essence of which is combining multi-scale science and classification,multi-scale,all aspects of analytical data characteristics,then obtain many classification models of different levels,finally research the scale conversion mechanism and the scale effects due to scale conversion problem.At present,there have been many researches on the application of multi-scale data mining in general data sets,such as multi-scale association rules and multi-scale clustering.However,in general data sets,multi-scale data mining is seldom used in the field of classification algorithms.Fractal theory,as an important tool and means in nonlinear complex scientific research,produce the generalized fractal theory which opens up its application prospect in general data processing.The self-similarity is the most notable features of fractal,it emphasizes the relationship between commonness and individuality of the whole and partial,which as similar as multi-scale classification concept.Therefore,in this paper,the fractal theory as the macro guiding ideology,provides a new thought and method for the multiple scale classification research.This thesis based on the self-similar structure of fractal theory,constructs the multi-scale data set model by combining the hierarchy theory and the inclusion degree theory.And it discussed the knowledge of the choice of scale,the scale conversion and scale effect,defined the concept of scale conversion object,put forward the definition of multi-scale classification,discussed the essence of the multi-scale classification,finally constructed the multi-scale classification mining system structure;On the basis of this,a similarity measure method based on hausdorff distance is proposed based on the fractal dimension,and then a multi-scale classification scale-up algorithm based on fractal theory is proposed;Finally,this paper analyzes the essence of fractal interpolation,puts forward the concept of generalized fractal interpolation,combines the theory of inverse distance weighting,and then proposes a multi-scale classification scale-down algorithm based on generalized fractal interpolation.Regarding the multi-scale classification as the research core,this thesis mainly completes the following works:1)The research of the multi-scale classification theoretical basisAiming at the problems existing in multi-scale classification,this paper studies and improves the multi-scale classification theory basis from three aspects of constructing multi-scale data sets,scale transformation and multi-scale classification system.First of all,on the basis of the structure of self-similar fractal theory,combined with the theory of hierarchy and inclusion degree,this paper forms a partial order structure by discretizating data characteristic,and then puts forward general method of structuring the multi-scale data set model;Secondly,analyzing the scale conversion of the multi-scale classification mining from the types and methods of scale conversion,benchmark scale selection,scale conversion object,scale conversion mechanism,scale effect and so on several aspects.Finally,the definition and essence of multi-scale classification mining are proposed,and the task of multi-scale classification is analyzed,it provides a theoretical basis and method for the study of multi-scale classification algorithms.2)The proposal of multi-scale classification algorithmThe multi-scale classification mining theory system provides the guiding ideology for the scale conversion algorithm.Combined with the generalized fractal dimension,a similarity measure method is proposed based on the hausdorff distance,improved the method of structuring similarity matrix,and then put forward the multi-scale classification scale-up algorithm based on the fractal theory MSCSUA(Multi-Scale Classification Scaling-Up Algorithm);The essence of the fractal interpolation is analyzed,and puts forward the concept of the generalized fractal interpolation,both consider the overall distribution and the local inherent characteristics of the known samples,from different aspects to measure the contribution of the known samples to the unknown sample points,then combining with the inverse distance weighting theory,and put forward the multi-scale classification scale-down algorithm based on the generalized fractal interpolation theory MSCSDA(Multi-Scale Classification Scaling-Down Algorithm).3)Verification experiments on the multi-scale classification algorithmThe multi-scale classification algorithm was analyzed by using 4 groups of UCI common benchmark data sets and 1 of real data set(part population of H province).The results show that the multi-scale classification ideas and MSCSUA,MSCSDA algorithm of this paper proposed with higher accuracy compared with the traditional algorithms(KNN,Decision Tree,LIBSVM),with the increasing of the number of data scale and category labels,little float operation of the run time,so the algorithms with better stability,and is feasible and effective.