机器学习--SVM分类器

SVM分类器的介绍：https://en.wikipedia.org/wiki/Support_vector_machine


在本例中，调用的accrod-net来实现，使用的SMO算法，主要基于公式（拉格朗日的对偶形式）：
Max(alpha[i], i∈[1,n]) - 1/2 * y[i]*y[j]*Kernal(x[i],x[j])*alpha[i]*alpha[j]
其中,alpha[i]为拉格朗日乘子，对上式进行迭代，在符合KKT条件(https://en.wikipedia.org/wiki/Karush–Kuhn–Tucker_conditions)下，进行迭代。调整alpha[i]和alpha[j]，直到收敛。
核函数Kernal(x[i],x[j])的作用是将数据提升维度，达到线性可分。


实例代码：


  

  public static class SVMDEmo
    {
        public static void Execute()
        {
            double[][] inputs =
            {
                new double[] { 1, 3 }, //-1
                new double[] { -1, 3 },//1
                new double[] { 2, 5 }, //-1
                new double[] { 3, -4 },//1
                new double[] { -3, 6 },//-1
                new double[] { 7, 2 }, //1
                new double[] { 2, 9 }, //-1
                new double[] { 10, 1 },//1
                new double[] { 1, 8 }, //-1
                new double[] { 3, 10 },//1
             };


            // Dichotomy SVM outputs should be given as [-1;+1]
            int[] labels =
            {
                -1,1,
                -1,1,
                -1,1,
                -1,1,
                -1,1
            };


            // Create a Support Vector Machine for the given inputs
            SupportVectorMachine machine = new SupportVectorMachine(inputs[0].Length);


            // Instantiate a new learning algorithm for SVMs
            SequentialMinimalOptimization smo = new SequentialMinimalOptimization(machine, inputs, labels);


            // Set up the learning algorithm
            smo.Complexity = 1.0;


            // Run the learning algorithm
            double error = smo.Run();


            // Compute the decision output for one of the input vectors
            int decision = Math.Sign(machine.Compute(new double[] { 10, 12 }));


            Console.WriteLine(decision);
        }
    }


static void Main(string[] args)
        {
            SVMDEmo.Execute();
            Console.ReadLine();
        }