LWR 局部加权线性回归算法

http://blog.csdn.net/tianguokaka/article/details/14227187

分类： 统计学习方法2013-11-06
14:44 1649人阅读 评论(3) 收藏 举报

看了机器学习的第三课，实现了一下LWR算法。

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#include<iostream>

using namespace std;

const int Number = 6;

const int Dimesion = 3;

const float learningRate=0.001;

const float errorThr=1; //variance threshold

const int MAX=1000; //Max times of iteration

typedef struct Data{

float vectorComponent[Dimesion];

}vectorData;

vectorData x[Number] = {

/* {1,1,4},

{1,2,5},

{1,5,1},

{1,4,2},*/

{1,1,1},

{1,1,3},

{1,1,2},

{1,2,3},

{1,2,1},

{1,2,2},

};

float y[Number]={2,10,5,13,5,8};

/lwr(局部线性回归)

float weightValue(vectorData xi,vectorData x){

float weight = 0.0;

for(int i=0;i<Dimesion;i++){

weight+=pow(xi.vectorComponent[i]-x.vectorComponent[i],2);

}

float tempWeight = exp(-(weight/(2*36)));

if(tempWeight<0.02)

tempWeight = 0.0;

return tempWeight;

}

float multiPly(vectorData x1,vectorData x2){

float temp = 0.0;

for(int i=0;i<Dimesion;i++){

temp += x1.vectorComponent[i]*x2.vectorComponent[i];

}

return temp;

}

vectorData addVectorData(vectorData x1,vectorData x2){

vectorData temp;

for(int i=0;i<Dimesion;i++)

temp.vectorComponent[i] = x1.vectorComponent[i]+x2.vectorComponent[i];

return temp;

}

vectorData minusVectorData(vectorData x1,vectorData x2){

vectorData temp;

for(int i=0;i<Dimesion;i++)

temp.vectorComponent[i] = x1.vectorComponent[i]-x2.vectorComponent[i];

return temp;

}

vectorData numberMultiVectorData(float para,vectorData x1){

vectorData temp;

for(int i=0;i<Dimesion;i++)

temp.vectorComponent[i] = x1.vectorComponent[i]*para;

return temp;

}

float costFunction(vectorData parameter[],vectorData inputData[],float inputResultData[],vectorData object){

float costValue = 0.0;

float tempValue = 0.0;

float weightedValue = 0.0;

for(int i=0;i<Number;i++){

tempValue = 0.0;

//consider all the parameters although most of them is zero

for(int j=0;j<Number;j++)

tempValue += multiPly(parameter[j],inputData[i]);

costValue += weightValue(inputData[i],object)*pow((inputResultData[i]-tempValue),2);

}

return (costValue/2*4);

}

int LocallyWeightedAgression(vectorData parameter[],vectorData inputData[],float resultData[],vectorData objectVector){

float tempValue = 0.0;

float errorCost = 0.0;

float weightedValue = 0.0;

errorCost=costFunction(parameter,inputData,resultData,objectVector);

if(errorCost<errorThr)

return 1;

for(int iteration=0;iteration<MAX;iteration++){

//stochastic

for(int i=0;i<Number;i++){

//calculate the h(x)

weightedValue = weightValue(inputData[i],objectVector);

tempValue=0.0;

for(int j=0;j<Number;j++)

tempValue+=multiPly(parameter[j],inputData[i]);

//update the parameter by stochastic(随机梯度下降)

printf("the next parameter is ");

for(int ii=0;ii<Number;ii++){

parameter[ii] = addVectorData(parameter[ii],numberMultiVectorData(weightedValue*learningRate*(resultData[i]-tempValue),inputData[i]));

if(multiPly(parameter[ii],parameter[ii])!=0){

for(int jj=0;jj<Dimesion;jj++){

printf("%f ",parameter[ii].vectorComponent[jj]);

}

}

}

printf("\n");

errorCost=costFunction(parameter,inputData,resultData,objectVector);

printf("error cost is %f\n",errorCost);

if(errorCost<errorThr)

break;

}//end stochastic one time

}//end when the iteration becomes MAX

//calculate the object vector

float resultValue = 0.0;

for(int i=0;i<Number;i++){

resultValue += weightValue(inputData[i],objectVector)*multiPly(parameter[i],objectVector);

}

printf("result value is %f \n",resultValue);

return 1;

}

int testLWA(){

vectorData objectData = {1,1.5,1.5};

vectorData localParameter[Number] = {0.0};

LocallyWeightedAgression(localParameter,x,y,objectData);

return 1;

}

int main(){

// DescendAlgorithm(parameter,x,y);

// system("pause");

//clearParameter(parameter);

//Stochastic(parameter,x,y);

//float ForTestData[] = {1,10,20};

//testData(ForTestData);

testLWA();

system("pause");

return 1;

}

设定的目标函数是平面方程 z=x^2+y^2

实验数据是1.5,1.5

计算结果是 5.124