http://eric-yuan.me/softmax-regression-cv. I did not test the code but hopefully it should be good. I will write when a test is done.
The code below is a copy from Eric Yuan's blog http://eric-yuan.me/softmax-regression-cv.
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// ----------------------------------------------------------------------------------------- //
// Softmax regression
#include "opencv2/core/core.hpp"
#include "opencv2/imgproc/imgproc.hpp"
#include "opencv2/highgui/highgui.hpp"
#include <math.h>
#include <iostream>
using namespace cv;
using namespace std;
#define elif else if
#define AT at<double>
#define MAX_ITER 100000
double cost = 0.0;
Mat grad;
double lrate = 0.1;
double lambda = 0.0;
int nclasses = 2;
Mat vec2mat(vector<vector<double> >&vec){
int cols = vec.size();
int rows = vec[0].size();
Mat result(rows, cols, CV_64FC1);
double *pData;
for(int i = 0; i<rows; i++){
pData = result.ptr<double>(i);
for(int j=0; j<cols; j++){
pData[j] = vec[j][i];
}
}
return result;
}
Mat vec2colvec(vector<double>& vec){
int length = vec.size();
Mat A(length, 1, CV_64FC1);
for(int i=0; i<length; i++){
A.AT(i, 0) = vec[i];
}
return A;
}
Mat vec2rowvec(vector<double>& vec){
Mat A = vec2colvec(vec);
return A.t();
}
void update_CostFunction_and_Gradient(Mat x, Mat y, Mat weightsMatrix, double lambda){
int nsamples = x.cols;
int nfeatures = x.rows;
//calculate cost function
Mat theta(weightsMatrix);
Mat M = theta * x;
Mat temp, temp2;
temp = Mat::ones(1, M.cols, CV_64FC1);
reduce(M, temp, 0, CV_REDUCE_SUM);
temp2 = repeat(temp, nclasses, 1);
M -= temp2;
exp(M, M);
temp = Mat::ones(1, M.cols, CV_64FC1);
reduce(M, temp, 0, CV_REDUCE_SUM);
temp2 = repeat(temp, nclasses, 1);
divide(M, temp2, M);
Mat groundTruth = Mat::zeros(nclasses, nsamples, CV_64FC1);
for(int i=0; i<nsamples; i++){
groundTruth.AT(y.AT(0, i), i) = 1.0;
}
Mat logM;
log(M, logM);
temp = groundTruth.mul(logM);
cost = - sum(temp)[0] / nsamples;
Mat theta2;
pow(theta, 2.0, theta2);
cost += sum(theta2)[0] * lambda / 2;
//calculate gradient
temp = groundTruth - M;
temp = temp * x.t();
grad = - temp / nsamples;
grad += lambda * theta;
}
Mat calculateY(Mat x, Mat weightsMatrix){
int nsamples = x.cols;
int nfeatures = x.rows;
//calculate cost function
Mat theta(weightsMatrix);
Mat M = theta * x;
Mat temp, temp2;
temp = Mat::ones(1, M.cols, CV_64FC1);
reduce(M, temp, 0, CV_REDUCE_SUM);
temp2 = repeat(temp, nclasses, 1);
M -= temp2;
exp(M, M);
temp = Mat::ones(1, M.cols, CV_64FC1);
reduce(M, temp, 0, CV_REDUCE_SUM);
temp2 = repeat(temp, nclasses, 1);
divide(M, temp2, M);
log(M, M);
Mat result = Mat::ones(1, M.cols, CV_64FC1);
for(int i=0; i<M.cols; i++){
double maxele = M.AT(0, i);
int which = 0;
for(int j=1; j<M.rows; j++){
if(M.AT(j, i) > maxele){
maxele = M.AT(j, i);
which = j;
}
}
result.AT(0, i) = which;
}
return result;
}
void softmax(vector<vector<double> >&vecX, vector<double> &vecY, vector<vector<double> >& testX, vector<double>& testY){
int nsamples = vecX.size();
int nfeatures = vecX[0].size();
//change vecX and vecY into matrix or vector.
Mat y = vec2rowvec(vecY);
Mat x = vec2mat(vecX);
double init_epsilon = 0.12;
Mat weightsMatrix = Mat::ones(nclasses, nfeatures, CV_64FC1);
double *pData;
for(int i = 0; i<nclasses; i++){
pData = weightsMatrix.ptr<double>(i);
for(int j=0; j<nfeatures; j++){
pData[j] = randu<double>();
}
}
weightsMatrix = weightsMatrix * (2 * init_epsilon) - init_epsilon;
grad = Mat::zeros(nclasses, nfeatures, CV_64FC1);
/*
//Gradient Checking (remember to disable this part after you're sure the
//cost function and dJ function are correct)
update_CostFunction_and_Gradient(x, y, weightsMatrix, lambda);
Mat dJ(grad);
// grad.copyTo(dJ);
cout<<"test!!!!"<<endl;
double epsilon = 1e-4;
for(int i=0; i<weightsMatrix.rows; i++){
for(int j=0; j<weightsMatrix.cols; j++){
double memo = weightsMatrix.AT(i, j);
weightsMatrix.AT(i, j) = memo + epsilon;
update_CostFunction_and_Gradient(x, y, weightsMatrix, lambda);
double value1 = cost;
weightsMatrix.AT(i, j) = memo - epsilon;
update_CostFunction_and_Gradient(x, y, weightsMatrix, lambda);
double value2 = cost;
double tp = (value1 - value2) / (2 * epsilon);
cout<<i<<", "<<j<<", "<<tp<<", "<<dJ.AT(i, j)<<", "<<dJ.AT(i, j) / tp<<endl;
weightsMatrix.AT(i, j) = memo;
}
}
*/
int converge = 0;
double lastcost = 0.0;
while(converge < MAX_ITER){
update_CostFunction_and_Gradient(x, y, weightsMatrix, lambda);
weightsMatrix -= lrate * grad;
cout<<"learning step: "<<converge<<", Cost function value = "<<cost<<endl;
if(fabs((cost - lastcost) ) <= 5e-6 && converge > 0) break;
lastcost = cost;
++ converge;
}
cout<<"############result#############"<<endl;
Mat yT = vec2rowvec(testY);
Mat xT = vec2mat(testX);
Mat result = calculateY(xT, weightsMatrix);
Mat err(yT);
err -= result;
int correct = err.cols;
for(int i=0; i<err.cols; i++){
if(err.AT(0, i) != 0) --correct;
}
cout<<"correct: "<<correct<<", total: "<<err.cols<<", accuracy: "<<double(correct) / (double)(err.cols)<<endl;
}
int main(int argc, char** argv)
{
long start, end;
//read training X from .txt file
FILE *streamX, *streamY;
streamX = fopen("trainX.txt", "r");
int numofX = 30;
vector<vector<double> > vecX;
double tpdouble;
int counter = 0;
while(1){
if(fscanf(streamX, "%lf", &tpdouble)==EOF) break;
if(counter / numofX >= vecX.size()){
vector<double> tpvec;
vecX.push_back(tpvec);
}
vecX[counter / numofX].push_back(tpdouble);
++ counter;
}
fclose(streamX);
cout<<vecX.size()<<", "<<vecX[0].size()<<endl;
//read training Y from .txt file
streamY = fopen("trainY.txt", "r");
vector<double> vecY;
while(1){
if(fscanf(streamY, "%lf", &tpdouble)==EOF) break;
vecY.push_back(tpdouble);
}
fclose(streamY);
for(int i = 1; i<vecX.size(); i++){
if(vecX[i].size() != vecX[i - 1].size()) return 0;
}
if(vecX.size() != vecY.size()) return 0;
streamX = fopen("testX.txt", "r");
vector<vector<double> > vecTX;
counter = 0;
while(1){
if(fscanf(streamX, "%lf", &tpdouble)==EOF) break;
if(counter / numofX >= vecTX.size()){
vector<double> tpvec;
vecTX.push_back(tpvec);
}
vecTX[counter / numofX].push_back(tpdouble);
++ counter;
}
fclose(streamX);
streamY = fopen("testY.txt", "r");
vector<double> vecTY;
while(1){
if(fscanf(streamY, "%lf", &tpdouble)==EOF) break;
vecTY.push_back(tpdouble);
}
fclose(streamY);
start = clock();
softmax(vecX, vecY, vecTX, vecTY);
end = clock();
cout<<"Training used time: "<<((double)(end - start)) / CLOCKS_PER_SEC<<" second"<<endl;
return 0;
}
// EOF //
|
Read http://eric-yuan.me/softmax/ about Softmax. The final part of the page says as follows:
SOFTMAX VS MULTI-BINARY CLASSIFIERS
Now let’s retrieve back to the above question about softmax VS multi-binary classifiers. As Prof. Andrew Ng says, which algorithm to use depend on whether the classes are mutually exclusive, which means, whether the classes are mixed. For example:
- Case 1. classes are [1, 2, 3, 4, 5, 6]
- Case 2. classes are [1, 2, 3, odd, even, positive]
For case 1, Softmax regression classifier would be fine, in the second case, use multi-logistic regression.
