adaline_learning.c File Reference

Adaptive Linear Neuron (ADALINE) implementation More...

#include <assert.h>
#include <limits.h>
#include <math.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h>

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Data Structures
struct	adaline
	structure to hold adaline model parameters More...

Macros
#define	MAX_ITER   500
	Maximum number of iterations to learn.
#define	ACCURACY   1e-5
	convergence accuracy \(=1\times10^{-5}\)

Functions
struct adaline	new_adaline (const int num_features, const double eta)
	Default constructor. More...
void	delete_adaline (struct adaline *ada)
	delete dynamically allocated memory More...
int	activation (double x)
	Heaviside activation function
char *	get_weights_str (struct adaline *ada)
	Operator to print the weights of the model.
int	predict (struct adaline *ada, const double *x, double *out)
	predict the output of the model for given set of features More...
double	fit_sample (struct adaline *ada, const double *x, const int y)
	Update the weights of the model using supervised learning for one feature vector. More...
void	fit (struct adaline *ada, double **X, const int *y, const int N)
	Update the weights of the model using supervised learning for an array of vectors. More...
void	test1 (double eta)
	test function to predict points in a 2D coordinate system above the line \(x=y\) as +1 and others as -1. More...
void	test2 (double eta)
	test function to predict points in a 2D coordinate system above the line \(x+3y=-1\) as +1 and others as -1. More...
void	test3 (double eta)
	test function to predict points in a 3D coordinate system lying within the sphere of radius 1 and centre at origin as +1 and others as -1. More...
int	main (int argc, char **argv)
	Main function.

Detailed Description

Adaptive Linear Neuron (ADALINE) implementation

Author

Krishna Vedala

source ADALINE is one of the first and simplest single layer artificial neural network. The algorithm essentially implements a linear function

\[ f\left(x_0,x_1,x_2,\ldots\right) = \sum_j x_jw_j+\theta \]

where \(x_j\) are the input features of a sample, \(w_j\) are the coefficients of the linear function and \(\theta\) is a constant. If we know the \(w_j\), then for any given set of features, \(y\) can be computed. Computing the \(w_j\) is a supervised learning algorithm wherein a set of features and their corresponding outputs are given and weights are computed using stochastic gradient descent method.

Function Documentation

delete_adaline()

void delete_adaline

(

struct adaline *

ada

)

delete dynamically allocated memory

Parameters

[in]

ada

model from which the memory is to be freeed.

{
    if (ada == NULL)
        return;
 
    free(ada->weights);
};

fit()

void fit	(	struct adaline *	ada,
		double **	X,
		const int *	y,
		const int	N
	)

Update the weights of the model using supervised learning for an array of vectors.

Parameters

[in]	ada	adaline model to train
[in]	X	array of feature vector
[in]	y	known output value for each feature vector
[in]	N	number of training samples

{
    double avg_pred_error = 1.f;
 
    int iter;
    for (iter = 0; (iter < MAX_ITER) && (avg_pred_error > ACCURACY); iter++)
    {
        avg_pred_error = 0.f;
 
        // perform fit for each sample
        for (int i = 0; i < N; i++)
        {
            double err = fit_sample(ada, X[i], y[i]);
            avg_pred_error += fabs(err);
        }
        avg_pred_error /= N;
 
        // Print updates every 200th iteration
        // if (iter % 100 == 0)
        printf("\tIter %3d: Training weights: %s\tAvg error: %.4f\n", iter,
               get_weights_str(ada), avg_pred_error);
    }
 
    if (iter < MAX_ITER)
        printf("Converged after %d iterations.\n", iter);
    else
        printf("Did not converged after %d iterations.\n", iter);
}

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fit_sample()

double fit_sample	(	struct adaline *	ada,
		const double *	x,
		const int	y
	)

Update the weights of the model using supervised learning for one feature vector.

Parameters

[in]	ada	adaline model to fit
[in]	x	feature vector
[in]	y	known output value

Returns

correction factor

{
    /* output of the model with current weights */
    int p = predict(ada, x, NULL);
    int prediction_error = y - p;  // error in estimation
    double correction_factor = ada->eta * prediction_error;
 
    /* update each weight, the last weight is the bias term */
    for (int i = 0; i < ada->num_weights - 1; i++)
    {
        ada->weights[i] += correction_factor * x[i];
    }
    ada->weights[ada->num_weights - 1] += correction_factor;  // update bias
 
    return correction_factor;
}

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new_adaline()

struct adaline new_adaline	(	const int	num_features,
		const double	eta
	)

Default constructor.

Parameters

[in]	num_features	number of features present
[in]	eta	learning rate (optional, default=0.1)

Returns

new adaline model

{
    if (eta <= 0.f || eta >= 1.f)
    {
        fprintf(stderr, "learning rate should be > 0 and < 1\n");
        exit(EXIT_FAILURE);
    }
 
    // additional weight is for the constant bias term
    int num_weights = num_features + 1;
    struct adaline ada;
    ada.eta = eta;
    ada.num_weights = num_weights;
    ada.weights = (double *)malloc(num_weights * sizeof(double));
    if (!ada.weights)
    {
        perror("Unable to allocate error for weights!");
        return ada;
    }
 
    // initialize with random weights in the range [-50, 49]
    for (int i = 0; i < num_weights; i++) ada.weights[i] = 1.f;
    // ada.weights[i] = (double)(rand() % 100) - 50);
 
    return ada;
}

predict()

int predict	(	struct adaline *	ada,
		const double *	x,
		double *	out
	)

predict the output of the model for given set of features

Parameters

[in]	ada	adaline model to predict
[in]	x	input vector
[out]	out	optional argument to return neuron output before applying activation function (NULL to ignore)

Returns

model prediction output

{
    double y = ada->weights[ada->num_weights - 1];  // assign bias value
 
    for (int i = 0; i < ada->num_weights - 1; i++) y += x[i] * ada->weights[i];
 
    if (out)  // if out variable is not NULL
        *out = y;
 
    return activation(y);  // quantizer: apply ADALINE threshold function
}

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test1()

void test1

(

double

eta

)

test function to predict points in a 2D coordinate system above the line \(x=y\) as +1 and others as -1.

Note that each point is defined by 2 values or 2 features.

Parameters

[in]

eta

learning rate (optional, default=0.01)

{
    struct adaline ada = new_adaline(2, eta);  // 2 features
 
    const int N = 10;  // number of sample points
    const double saved_X[10][2] = {{0, 1},  {1, -2},   {2, 3},   {3, -1},
                                   {4, 1},  {6, -5},   {-7, -3}, {-8, 5},
                                   {-9, 2}, {-10, -15}};
 
    double **X = (double **)malloc(N * sizeof(double *));
    const int Y[10] = {1,  -1, 1, -1, -1,
                       -1, 1,  1, 1,  -1};  // corresponding y-values
    for (int i = 0; i < N; i++)
    {
        X[i] = (double *)saved_X[i];
    }
 
    printf("------- Test 1 -------\n");
    printf("Model before fit: %s", get_weights_str(&ada));
 
    fit(&ada, X, Y, N);
    printf("Model after fit: %s\n", get_weights_str(&ada));
 
    double test_x[] = {5, -3};
    int pred = predict(&ada, test_x, NULL);
    printf("Predict for x=(5,-3): % d", pred);
    assert(pred == -1);
    printf(" ...passed\n");
 
    double test_x2[] = {5, 8};
    pred = predict(&ada, test_x2, NULL);
    printf("Predict for x=(5, 8): % d", pred);
    assert(pred == 1);
    printf(" ...passed\n");
 
    // for (int i = 0; i < N; i++)
    //     free(X[i]);
    free(X);
    delete_adaline(&ada);
}

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test2()

void test2

(

double

eta

)

test function to predict points in a 2D coordinate system above the line \(x+3y=-1\) as +1 and others as -1.

Note that each point is defined by 2 values or 2 features. The function will create random sample points for training and test purposes.

Parameters

[in]

eta

learning rate (optional, default=0.01)

{
    struct adaline ada = new_adaline(2, eta);  // 2 features
 
    const int N = 50;  // number of sample points
 
    double **X = (double **)malloc(N * sizeof(double *));
    int *Y = (int *)malloc(N * sizeof(int));  // corresponding y-values
    for (int i = 0; i < N; i++) X[i] = (double *)malloc(2 * sizeof(double));
 
    // generate sample points in the interval
    // [-range2/100 , (range2-1)/100]
    int range = 500;          // sample points full-range
    int range2 = range >> 1;  // sample points half-range
    for (int i = 0; i < N; i++)
    {
        double x0 = ((rand() % range) - range2) / 100.f;
        double x1 = ((rand() % range) - range2) / 100.f;
        X[i][0] = x0;
        X[i][1] = x1;
        Y[i] = (x0 + 3. * x1) > -1 ? 1 : -1;
    }
 
    printf("------- Test 2 -------\n");
    printf("Model before fit: %s", get_weights_str(&ada));
 
    fit(&ada, X, Y, N);
    printf("Model after fit: %s\n", get_weights_str(&ada));
 
    int N_test_cases = 5;
    double test_x[2];
    for (int i = 0; i < N_test_cases; i++)
    {
        double x0 = ((rand() % range) - range2) / 100.f;
        double x1 = ((rand() % range) - range2) / 100.f;
 
        test_x[0] = x0;
        test_x[1] = x1;
        int pred = predict(&ada, test_x, NULL);
        printf("Predict for x=(% 3.2f,% 3.2f): % d", x0, x1, pred);
 
        int expected_val = (x0 + 3. * x1) > -1 ? 1 : -1;
        assert(pred == expected_val);
        printf(" ...passed\n");
    }
 
    for (int i = 0; i < N; i++) free(X[i]);
    free(X);
    free(Y);
    delete_adaline(&ada);
}

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test3()

void test3

(

double

eta

)

test function to predict points in a 3D coordinate system lying within the sphere of radius 1 and centre at origin as +1 and others as -1.

Note that each point is defined by 3 values but we use 6 features. The function will create random sample points for training and test purposes. The sphere centred at origin and radius 1 is defined as: \(x^2+y^2+z^2=r^2=1\) and if the \(r^2<1\), point lies within the sphere else, outside.

Parameters

[in]

eta

learning rate (optional, default=0.01)

{
    struct adaline ada = new_adaline(6, eta);  // 2 features
 
    const int N = 50;  // number of sample points
 
    double **X = (double **)malloc(N * sizeof(double *));
    int *Y = (int *)malloc(N * sizeof(int));  // corresponding y-values
    for (int i = 0; i < N; i++) X[i] = (double *)malloc(6 * sizeof(double));
 
    // generate sample points in the interval
    // [-range2/100 , (range2-1)/100]
    int range = 200;          // sample points full-range
    int range2 = range >> 1;  // sample points half-range
    for (int i = 0; i < N; i++)
    {
        double x0 = ((rand() % range) - range2) / 100.f;
        double x1 = ((rand() % range) - range2) / 100.f;
        double x2 = ((rand() % range) - range2) / 100.f;
        X[i][0] = x0;
        X[i][1] = x1;
        X[i][2] = x2;
        X[i][3] = x0 * x0;
        X[i][4] = x1 * x1;
        X[i][5] = x2 * x2;
        Y[i] = (x0 * x0 + x1 * x1 + x2 * x2) <= 1 ? 1 : -1;
    }
 
    printf("------- Test 3 -------\n");
    printf("Model before fit: %s", get_weights_str(&ada));
 
    fit(&ada, X, Y, N);
    printf("Model after fit: %s\n", get_weights_str(&ada));
 
    int N_test_cases = 5;
    double test_x[6];
    for (int i = 0; i < N_test_cases; i++)
    {
        double x0 = ((rand() % range) - range2) / 100.f;
        double x1 = ((rand() % range) - range2) / 100.f;
        double x2 = ((rand() % range) - range2) / 100.f;
        test_x[0] = x0;
        test_x[1] = x1;
        test_x[2] = x2;
        test_x[3] = x0 * x0;
        test_x[4] = x1 * x1;
        test_x[5] = x2 * x2;
        int pred = predict(&ada, test_x, NULL);
        printf("Predict for x=(% 3.2f,% 3.2f): % d", x0, x1, pred);
 
        int expected_val = (x0 * x0 + x1 * x1 + x2 * x2) <= 1 ? 1 : -1;
        assert(pred == expected_val);
        printf(" ...passed\n");
    }
 
    for (int i = 0; i < N; i++) free(X[i]);
    free(X);
    free(Y);
    delete_adaline(&ada);
}

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