The Three Kinds Of Uncertain Support Vector Machines And Applications

Support vector machine is a universal machine learning algorithm, which is based on VCdimension and structural risk minimization principle of statistical learning theory. It solvesthe practical problems of traditional learning methods, such as small sample, high dimensionand nonlinearity, and has good generalization capability. Since it was proposed, supportvector machine has won the favor with many experts and engineering and technical personnel,and has been successfully applied into face recognition, remote sensing image analysis, textclassification, etc.However, with the wide range of applications, support vector machine has somelimitations in some practical problems. For example, support vector machine is sensitive tonoises, and has low performance for imbalance data set. Another example, the trainingsamples of support vector machine are real random variables. While, in some practicalproblems, the training samples are non-real random variables (random set, fuzzy, etc.). Inorder to solve aforementioned problems, three kinds of uncertain support vector machines aregiven to handle the noise uncertainty samples, random set uncertainty input samples, andfuzzy etc. uncertainty output samples accordingly.The main contributions are as follows:(1) The support vector machine and multi-class support vector machine based onintuitionistic fuzzy numbers are proposed. Intuitionistic fuzzy number as an extension offuzzy membership can describe the fuzziness of the objective world more accurately. Thesupport vector machine based on intuitionistic fuzzy numbers assign each training samplewith a corresponding intuitionistic fuzzy number by the use of kernel function, and a newscore function of the intuitionistic fuzzy number is proposed to measure the contribution ofeach training sample and distinguish from the noises and support vectors. Then, themulti-class support vector machine of one-against-one and one-against-all are given based onthe above support vector machine. In order to solve the misclassification problem resultedfrom the imbalance samples of different classes in the construction of one-against-all supportvector machine, different weights are assigned to differed class sample. The effectiveness ofthe above uncertain support vector machines are verified by numerical experiments.(2) The support vector machine and multi-class support vector machine based on randomset input samples are constructed. Random set as an important extension of real valued random variable, can well deal with the fuzzy and experimental data of complicated uncertainenvironments. The support vector machine based on random set input samples takesmeasurable selections are taken as the main feature of random set. Then the classification ofrandom set input samples is transformed into the classification of measurable selections. Themulti-class support vector machine transform the multi-classification of random input samplesinto the multi-classification of real-valued samples by the use of fuzzy C-means clusteringalgorithm. Numerical experiments show the effective of this kind of uncertain support vectormachine(3) The support vector machine based on fuzzy output samples in credibility space andthe support vector machine based on uncertainty output samples in uncertainty space aregiven. In credibility space, the support vector machine based on fuzzy output samples proposea dynamic division method of class label by the use of credibility measure and the confidencelevel, and construct a dynamic classification hyperplane to effectively deal with thefuzziness of fuzzy output samples. Similarly, in uncertain space, the support vector machinebased on uncertain output samples also give a dynamic division method of class label by theuse of uncertain measure and the confidence level, and then construct a correspondingdynamic classification hyperplane to handle the uncertainty of uncertain output samples. Thesimulation experiments show the effective of this kind of uncertain support vector machine.(4) Two kinds of uncertain support vector machine are applied into the face recognition.Due to the impact of lighting condition, gesture and facial expression, there are muchuncertain information such as noise, fuzzy, intuitionistic fuzzy and random set. In order todeal with the above uncertain information, two kinds of uncertain support vector machineproposed in this paper are applied into the face recognition, and experiments show theeffective of the two algorithms.