The Application Of Smooth Technology In Multi-class Classification Problems

Data mining is the process to find non-obvious but effective information from massive data. It is the integration of machine learning, database technology and other cutting-edge technologies. Currently, data mining has been widely used in many fields, such as communications, biosciences, weather analysis and so on. It shows good prospects and potential value.Clustering and classification are extremely important machine learning methods of data mining. In the study of data mining, clustering and classification have been the focus of academic research. Clustering is the unsupervised machine learning which is based on the similarity of the objects’properties. Within the same cluster, objects have higher similarity properties. But objects have quite differences between each cluster. A cluster is usually expressed by its center, so the core of clustering problem is the class center problem. Classification is the supervised machine learning, it through the training set of known categories of analysis to find the classification rules, in order to predict unknown samples’ category.In this paper, some of the clustering and classification algorithms are discussed and studied based on smooth technique. The main work and achievements of this thesis are as follows:(1)A smooth cluster-center algorithm is studied. The clustering center problem is a non-convex non-smooth mathematical optimization problem. Most of the classic fast optimization algorithms are not suitable for solving this problem. A smooth clustering-center algorithm is proposed based on filled function. Theoretical analysis and numerical results proof that the algorithm can solve the clustering problem effectively.(2)Smooth support vector machine is studied. Standard support vector machine is a convex quadratic programming problem and the objective function is non-smooth non-differentiable. Smooth support vector machine has better classification performance than SVM based on a smooth function. A Piecewise Entropy Smooth Support Vector Machine and a Third-order Piecewise Smooth Support Vector Machine are proposed to solve classification problems. Newton-Armijo algorithm which has quadratic convergence rate can be used to solve these classification machine models. Both theoretical analysis and numerical results illustrate that the new models have good classification performance.(3)Multi-class classification methods of smooth-SVM are studied. Smooth Support Vector Machine is designed for solving the second-class classification problems. But in real life, most of the problems are multi-class classification problems. Multi-class classification smooth support vector machine is proposed and validated. The theoretical analysis and numerical results show this method is feasible and effective.(4)Face recognition based on multi-class classification smooth support vector machine is studied. Face recognition problem is a multi-class classification problem. PCA is employed to extract the main feature of face image set, and multi-class classification smooth-SVM is used for face recognition. The face database experiments show that smooth support vector machine method is better than the traditional identification methods.