Machine Learning实验3】SoftMax regression

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神奇的SoftMax regression，搞了一晚上搞不定，凌晨3点起来继续搞，刚刚终于调通。我算是彻底理解了，哈哈。代码试验了Andrew Ng的第四课上提到的SoftMax regression算法，并参考了http://ufldl.stanford.edu/wiki/index.php/Softmax_Regression

最终收敛到这个结果，巨爽。

smaple 0: 0.983690,0.004888,0.011422,likelyhood:-0.016445
smaple 1: 0.940236,0.047957,0.011807,likelyhood:-0.061625
smaple 2: 0.818187,0.001651,0.180162,likelyhood:-0.200665
smaple 3: 0.000187,0.999813,0.000000,likelyhood:-0.000187
smaple 4: 0.007913,0.992087,0.000000,likelyhood:-0.007945
smaple 5: 0.001585,0.998415,0.000000,likelyhood:-0.001587
smaple 6: 0.020159,0.000001,0.979840,likelyhood:-0.020366
smaple 7: 0.018230,0.000000,0.981770,likelyhood:-0.018398

smaple 8: 0.025072,0.000000,0.974928,likelyhood:-0.025392

#include "stdio.h"#include "math.h"double matrix[9][4]={{1,47,76,24}, //include x0=1              {1,46,77,23},              {1,48,74,22},              {1,34,76,21},              {1,35,75,24},              {1,34,77,25},              {1,55,76,21},              {1,56,74,22},              {1,55,72,22},                };double result[]={1,                 1,                 1,                 2,                 2,                 2,                 3,                 3,                 3,};double theta[2][4]={                 {0.3,0.3,0.01,0.01},                 {0.5,0.5,0.01,0.01}}; // include theta0double function_g(double x){        double ex = pow(2.718281828,x);        return ex/(1+ex);}double function_e(double x){        return pow(2.718281828,x);}int main(void){        double likelyhood = 0.0;        for(int j = 0;j<9;++j)        {                double sum = 1.0; // this is very important, because exp(thetak x)=1                for(int l = 0;l<2;++l)                {                        double xi = 0.0;                        for(int k=0;k<4;++k)                        {                                xi += matrix[j][k]*theta[l][k];                        }                        sum += function_e(xi);                }                double xi = 0.0;                for(int k=0;k<4;++k)                {                        xi += matrix[j][k]*theta[0][k];                }                double p1 = function_e(xi)/sum;                xi = 0.0;                for(int k=0;k<4;++k)                {                        xi += matrix[j][k]*theta[1][k];                }                double p2 = function_e(xi)/sum;                double p3 = 1-p1-p2;               double ltheta = 0.0;               if(result[j]==1)                        ltheta = log(p1);               else if(result[j]==2)                        ltheta = log(p2);               else if(result[j]==3)                        ltheta = log(p3);               else               {}                printf("smaple %d: %f,%f,%f,likelyhood:%f\n",j,p1,p2,p3,ltheta);        }        for(int i =0 ;i<1000;++i)        {                for(int j=0;j<9;++j)                {                        double sum = 1.0; // this is very important, because exp(thetak x)=1                        for(int l = 0;l<2;++l)                        {                                double xi = 0.0;                                for(int k=0;k<4;++k)                                {                                        xi += matrix[j][k]*theta[l][k];                                }                                sum += function_e(xi);                        }                        double xi = 0.0;                        for(int k=0;k<4;++k)                        {                                xi += matrix[j][k]*theta[0][k];                        }                        double p1 = function_e(xi)/sum;                        xi = 0.0;                        for(int k=0;k<4;++k)                        {                                xi += matrix[j][k]*theta[1][k];                        }                        double p2 = function_e(xi)/sum;                        double p3 = 1-p1-p2;                        for(int m = 0; m<4; ++m)                        {                                if(result[j]==1)                                {                                        theta[0][m] = theta[0][m] + 0.001*(1-p1)*matrix[j][m];                                }                                else                                {                                        theta[0][m] = theta[0][m] + 0.001*(-p1)*matrix[j][m];                                }                                if(result[j]==2)                                {                                        theta[1][m] = theta[1][m] + 0.001*(1-p2)*matrix[j][m];                                }                                else                                {                                        theta[1][m] = theta[1][m] + 0.001*(-p2)*matrix[j][m];                                }                        }                }                double likelyhood = 0.0;                for(int j = 0;j<9;++j)                {                        double sum = 1.0; // this is very important, because exp(thetak x)=1                        for(int l = 0;l<2;++l)                        {                                double xi = 0.0;                                for(int k=0;k<4;++k)                                {                                        xi += matrix[j][k]*theta[l][k];                                }                                sum += function_e(xi);                        }                        double xi = 0.0;                        for(int k=0;k<4;++k)                        {                                xi += matrix[j][k]*theta[0][k];                        }                        double p1 = function_e(xi)/sum;                        xi = 0.0;                        for(int k=0;k<4;++k)                        {                                xi += matrix[j][k]*theta[1][k];                        }                        double p2 = function_e(xi)/sum;                        double p3 = 1-p1-p2;                        double ltheta = 0.0;                        if(result[j]==1)                                ltheta = log(p1);                        else if(result[j]==2)                                ltheta = log(p2);                        else if(result[j]==3)                                ltheta = log(p3);                        else                        {}                        printf("smaple %d: %f,%f,%f,likelyhood:%f\n",j,p1,p2,p3,ltheta);                }        }        return 0;}

from: http://blog.csdn.net/pennyliang/article/details/7048291

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