分享程序员开发的那些事...
更新时间：2022-11-29 14:45:48
在你目前的code，感知成功学的决策边界的方向，但不能的翻译的吧。
Y Y ^ ^ | - + \\ + | - \\ + | - + \\ + | - \\ +++ | - - \\ + | - - \\ + | - - + \\ + | - - \\ + ---------------------系列> X --------------------系列> X 坚持这样的需要得到这样的
问题在于，你的感知没有偏项，即连接到价值1输入第三组份的事实。
W0 ----- x ----> | | | F | ---->输出（+ 1 / -1） Ÿ----> | | W1 ----- ^ W2 1（偏差）--- |
下面是我如何修正这个问题：
的#include＆LT; stdio.h中＆GT;
＃包括＆LT; stdlib.h中＆GT;
＃包括＆LT;文件math.h＆GT;
＃包括＆LT; time.h中＆GT;
＃定义LEARNING_RATE 0.1
＃定义MAX_ITERATION 100
浮动randomFloat（）
{
返程（浮点）兰特（）/（浮点）RAND_MAX;
}
INT calculateOutput（浮动权[]，浮法X，浮动Y）
{
浮总和= X *重量[0] + Y *权重[1] +砝码[2];
返回（总和＆GT; = 0）？ 1：-1;
}
INT主（INT ARGC，字符* argv的[]）
{
函数srand（时间（NULL））;
浮法X [208]，Y [208]，权重[3]，localError，globalError;
INT输出[208]，patternCount，I，P，迭代，输出;
FILE * FP;
如果（（FP = FOPEN（test1.txt的，R））== NULL）{
的printf（不能打开文件\ñ。）;
出口（1）;
}
I = 0;
而（的fscanf（FP，％F％F％D，＆安培; X [I]中，＆安培;值Y [i]，＆安培;输出[I]）= EOF！）{
如果（输出[I] == 0）{
输出[I] = -1;
}
我++;
}
patternCount =我;
权重[0] = randomFloat（）;
权重[1] = randomFloat（）;
权重[2] = randomFloat（）;
迭代= 0;
做 {
迭代++;
globalError = 0;
为（p值= 0; P＆所述; patternCount，P ++）{
输出= calculateOutput（权重中，x [P]，Y [P]）;
localError =输出[P] - 输出;
权重[0] + = LEARNING_RATE * localError * X [P];
权重[1] + = LEARNING_RATE * localError * Y [P];
权重[2] + = LEARNING_RATE * localError;
globalError + =（localError * localError）;
}
/ *均方根误差* /
的printf（迭代％D：RMSE =％.4f \ N，迭代，
的sqrt（globalError / patternCount））;
}而（globalError = 0＆放大器;！＆安培;迭代＆LT; = MAX_ITERATION）;
的printf（\ nDecision边界（线）公式：％.2f * X +％.2f * Y +％.2f = 0 \ N，
权重[0]，权重[1]，权重[2]）;
返回0;
}
......与下面的输出：
迭代1：RMSE = 0.7206
迭代2：RMSE = 0.5189
迭代3：RMSE = 0.4804
迭代4：RMSE = 0.4804
迭代5：RMSE = 0.3101
迭代6：RMSE = 0.4160
迭代7：RMSE = 0.4599
迭代8：RMSE = 0.3922
迭代9：RMSE = 0.0000
决策边界（线）公式：-2.37 * X + -2.51 * Y + -7.55 = 0
编辑：我创建的code以上使用MATLAB一个动画短片。请查看以下视频：
Here is my perceptron implementation in ANSI C:
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
float randomFloat()
{
srand(time(NULL));
float r = (float)rand() / (float)RAND_MAX;
return r;
}
int calculateOutput(float weights[], float x, float y)
{
float sum = x * weights[0] + y * weights[1];
return (sum >= 0) ? 1 : -1;
}
int main(int argc, char *argv[])
{
// X, Y coordinates of the training set.
float x[208], y[208];
// Training set outputs.
int outputs[208];
int i = 0; // iterator
FILE *fp;
if ((fp = fopen("test1.txt", "r")) == NULL)
{
printf("Cannot open file.\n");
}
else
{
while (fscanf(fp, "%f %f %d", &x[i], &y[i], &outputs[i]) != EOF)
{
if (outputs[i] == 0)
{
outputs[i] = -1;
}
printf("%f %f %d\n", x[i], y[i], outputs[i]);
i++;
}
}
system("PAUSE");
int patternCount = sizeof(x) / sizeof(int);
float weights[2];
weights[0] = randomFloat();
weights[1] = randomFloat();
float learningRate = 0.1;
int iteration = 0;
float globalError;
do {
globalError = 0;
int p = 0; // iterator
for (p = 0; p < patternCount; p++)
{
// Calculate output.
int output = calculateOutput(weights, x[p], y[p]);
// Calculate error.
float localError = outputs[p] - output;
if (localError != 0)
{
// Update weights.
for (i = 0; i < 2; i++)
{
float add = learningRate * localError;
if (i == 0)
{
add *= x[p];
}
else if (i == 1)
{
add *= y[p];
}
weights[i] += add;
}
}
// Convert error to absolute value.
globalError += fabs(localError);
printf("Iteration %d Error %.2f %.2f\n", iteration, globalError, localError);
iteration++;
}
system("PAUSE");
} while (globalError != 0);
system("PAUSE");
return 0;
}
The training set I'm using: Data Set
I have removed all irrelevant code. Basically what it does now it reads test1.txt file and loads values from it to three arrays: x, y, outputs.
Then there is a perceptron learning algorithm which, for some reason, is not converging to 0 (globalError should converge to 0) and therefore I get an infinite do while loop.
When I use a smaller training set (like 5 points), it works pretty well. Any ideas where could be the problem?
I wrote this algorithm very similar to this C# Perceptron algorithm:
EDIT:
Here is an example with a smaller training set:
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
float randomFloat()
{
float r = (float)rand() / (float)RAND_MAX;
return r;
}
int calculateOutput(float weights[], float x, float y)
{
float sum = x * weights[0] + y * weights[1];
return (sum >= 0) ? 1 : -1;
}
int main(int argc, char *argv[])
{
srand(time(NULL));
// X coordinates of the training set.
float x[] = { -3.2, 1.1, 2.7, -1 };
// Y coordinates of the training set.
float y[] = { 1.5, 3.3, 5.12, 2.1 };
// The training set outputs.
int outputs[] = { 1, -1, -1, 1 };
int i = 0; // iterator
FILE *fp;
system("PAUSE");
int patternCount = sizeof(x) / sizeof(int);
float weights[2];
weights[0] = randomFloat();
weights[1] = randomFloat();
float learningRate = 0.1;
int iteration = 0;
float globalError;
do {
globalError = 0;
int p = 0; // iterator
for (p = 0; p < patternCount; p++)
{
// Calculate output.
int output = calculateOutput(weights, x[p], y[p]);
// Calculate error.
float localError = outputs[p] - output;
if (localError != 0)
{
// Update weights.
for (i = 0; i < 2; i++)
{
float add = learningRate * localError;
if (i == 0)
{
add *= x[p];
}
else if (i == 1)
{
add *= y[p];
}
weights[i] += add;
}
}
// Convert error to absolute value.
globalError += fabs(localError);
printf("Iteration %d Error %.2f\n", iteration, globalError);
}
iteration++;
} while (globalError != 0);
// Display network generalisation.
printf("X Y Output\n");
float j, k;
for (j = -1; j <= 1; j += .5)
{
for (j = -1; j <= 1; j += .5)
{
// Calculate output.
int output = calculateOutput(weights, j, k);
printf("%.2f %.2f %s\n", j, k, (output == 1) ? "Blue" : "Red");
}
}
// Display modified weights.
printf("Modified weights: %.2f %.2f\n", weights[0], weights[1]);
system("PAUSE");
return 0;
}
In your current code, the perceptron successfully learns the direction of the decision boundary BUT is unable to translate it.
y y
^ ^
| - + \\ + | - \\ + +
| - +\\ + + | - \\ + + +
| - - \\ + | - - \\ +
| - - + \\ + | - - \\ + +
---------------------> x --------------------> x
stuck like this need to get like this
The problem lies in the fact that your perceptron has no bias term, i.e. a third weight component connected to an input of value 1.
w0 -----
x ---->| |
| f |----> output (+1/-1)
y ---->| |
w1 -----
^ w2
1(bias) ---|
The following is how I corrected the problem:
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#define LEARNING_RATE 0.1
#define MAX_ITERATION 100
float randomFloat()
{
return (float)rand() / (float)RAND_MAX;
}
int calculateOutput(float weights[], float x, float y)
{
float sum = x * weights[0] + y * weights[1] + weights[2];
return (sum >= 0) ? 1 : -1;
}
int main(int argc, char *argv[])
{
srand(time(NULL));
float x[208], y[208], weights[3], localError, globalError;
int outputs[208], patternCount, i, p, iteration, output;
FILE *fp;
if ((fp = fopen("test1.txt", "r")) == NULL) {
printf("Cannot open file.\n");
exit(1);
}
i = 0;
while (fscanf(fp, "%f %f %d", &x[i], &y[i], &outputs[i]) != EOF) {
if (outputs[i] == 0) {
outputs[i] = -1;
}
i++;
}
patternCount = i;
weights[0] = randomFloat();
weights[1] = randomFloat();
weights[2] = randomFloat();
iteration = 0;
do {
iteration++;
globalError = 0;
for (p = 0; p < patternCount; p++) {
output = calculateOutput(weights, x[p], y[p]);
localError = outputs[p] - output;
weights[0] += LEARNING_RATE * localError * x[p];
weights[1] += LEARNING_RATE * localError * y[p];
weights[2] += LEARNING_RATE * localError;
globalError += (localError*localError);
}
/* Root Mean Squared Error */
printf("Iteration %d : RMSE = %.4f\n", iteration,
sqrt(globalError/patternCount));
} while (globalError != 0 && iteration<=MAX_ITERATION);
printf("\nDecision boundary (line) equation: %.2f*x + %.2f*y + %.2f = 0\n",
weights[0], weights[1], weights[2]);
return 0;
}
... with the following output:
Iteration 1 : RMSE = 0.7206
Iteration 2 : RMSE = 0.5189
Iteration 3 : RMSE = 0.4804
Iteration 4 : RMSE = 0.4804
Iteration 5 : RMSE = 0.3101
Iteration 6 : RMSE = 0.4160
Iteration 7 : RMSE = 0.4599
Iteration 8 : RMSE = 0.3922
Iteration 9 : RMSE = 0.0000
Decision boundary (line) equation: -2.37*x + -2.51*y + -7.55 = 0
EDIT: I created a short animation of the code above using MATLAB. Check out the following video: