Support Vector Machine And Its Applications

Statistical Learning Theory focuses on the machine learning theory for small samples. The main idea of the theory is to control the generalization ability of learning machine by controlling the complexity of its models. Support Vector Machine (SVM) is a new general machine learning algorithm developed from Statistical Learning Theory. It mostly outperformed traditional methods in theory and practice. SVM solved the problems such as small samples, high dimensions, nonlinear and local minimum problem. It has shown good performance in many fields such as pattern recognition and regression. SVM for regression is the expansion of SVM for classfication to regression problems. In this dissertation, kernel function, selection of ultra-parameters, training algorithm of SVM for regression were discussed, and SVM methods were introduced to the field of intelligent modeling of helicopter. The main works of this dissertation are as follows:Firstly, construction of kernel function and selection of parameters for SVM were studied. Presently usual kernel function can not generate the whole basis of the square-integrable space by translation. So SVM can not approximate arbitrary nonlinear function in this space with arbitrary precision. To deal with this problem, Marr wavelet was used to construct wavelet kernel, and the rationality of the wavelet kernel was proved. Modified chaotic particle swarm optimization was adpoted to select parameters of SVM. It is shown by simulation that SVM with wavelet kernel has higher convergence precision than SVM with Gaussian kernel.Then, sequential minimal optimization algorithm for training SVM was studied. KKT condition was usually used for halt criteria in sequential minimal optimization algorithm. This halt criteria for iterative optimization always causes slow convergence before over. The global minimum of a quadratic programming will be reached when the dual gap is zero. According this property, the halt criteria in the sequential minimal optimization algorithm was modified, and a modified sequential minimal optimization algorithm was proposed. It is shown by simulation that the modified algorithm can improve convergence speed effectively with similar generalization and test precision.Next, online algorithms for training SVM were studied. Online algorithms are efficient to run, easy to implement comparing with batch algorithms. Presently online algorithms for training SVM usually need all samples in training set. The number of support vectors will increase at least linearly with the size of the training set. It has a significant impact on the time of training and predicting if keep too much support vectors. To deal with this problem, a modified online algorithm for training SVM based on exist greedy online algorithm was proposed, witch have a budget parameter and a process to delete samples. It is shown by simulation that the modified online algorithm can reduce and control the number of support vectors effectively, as while as can improve speed of training and predicting.Lastly, Simulation model of helicopter based on SVM was studed. Aimed at building simulation model of helicopter with high precision, SVM method was introduced to the field of intelligent modeling of helicopter. Rotator speed model for landing process of a helicopter with rotator self-rotating and fishlike flight model were built based on two special flight states. The methods of modeling with SVM avoid complex aerodynamic knowledge needed by mechanism modeling, and reduce the complexity of the simulation model greatly. Compared with a neural networks model, the SVM simulation model of the helicopter owns some advantages such as simple structure, fast convergence speed and high generalization ability.