adaline_learning.cpp File Reference

Adaptive Linear Neuron (ADALINE) implementation More...

#include <array>
#include <cassert>
#include <climits>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <iostream>
#include <numeric>
#include <vector>

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Classes
class	machine_learning::adaline

Namespaces
namespace	machine_learning
	A* search algorithm

Functions
void	test1 (double eta=0.01)
void	test2 (double eta=0.01)
void	test3 (double eta=0.01)
int	main (int argc, char **argv)

Variables
constexpr int	MAX_ITER = 500

Detailed Description

Adaptive Linear Neuron (ADALINE) implementation

Author

Krishna Vedala

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

main()

int main	(	int	argc,
		char **	argv )

Main function

                                {
    std::srand(std::time(nullptr));  // initialize random number generator
 
    double eta = 0.1;  // default value of eta
    if (argc == 2) {   // read eta value from commandline argument if present
        eta = strtof(argv[1], nullptr);
    }
 
    test1(eta);
 
    std::cout << "Press ENTER to continue..." << std::endl;
    std::cin.get();
 
    test2(eta);
 
    std::cout << "Press ENTER to continue..." << std::endl;
    std::cin.get();
 
    test3(eta);
 
    return 0;
}

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test1()

void test1

(

double

eta = 0.01

)

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)

                              {
    adaline ada(2, eta);  // 2 features
 
    const int N = 10;  // number of sample points
 
    std::array<std::vector<double>, N> X = {
        std::vector<double>({0, 1}),   std::vector<double>({1, -2}),
        std::vector<double>({2, 3}),   std::vector<double>({3, -1}),
        std::vector<double>({4, 1}),   std::vector<double>({6, -5}),
        std::vector<double>({-7, -3}), std::vector<double>({-8, 5}),
        std::vector<double>({-9, 2}),  std::vector<double>({-10, -15})};
    std::array<int, N> y = {1,  -1, 1, -1, -1,
                            -1, 1,  1, 1,  -1};  // corresponding y-values
 
    std::cout << "------- Test 1 -------" << std::endl;
    std::cout << "Model before fit: " << ada << std::endl;
 
    ada.fit<N>(X, y);
    std::cout << "Model after fit: " << ada << std::endl;
 
    int predict = ada.predict({5, -3});
    std::cout << "Predict for x=(5,-3): " << predict;
    assert(predict == -1);
    std::cout << " ...passed" << std::endl;
 
    predict = ada.predict({5, 8});
    std::cout << "Predict for x=(5,8): " << predict;
    assert(predict == 1);
    std::cout << " ...passed" << std::endl;
}

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test2()

void test2

(

double

eta = 0.01

)

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)

                              {
    adaline ada(2, eta);  // 2 features
 
    const int N = 50;  // number of sample points
 
    std::array<std::vector<double>, N> X;
    std::array<int, N> Y{};  // corresponding y-values
 
    // 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 = (static_cast<double>(std::rand() % range) - range2) / 100.f;
        double x1 = (static_cast<double>(std::rand() % range) - range2) / 100.f;
        X[i] = std::vector<double>({x0, x1});
        Y[i] = (x0 + 3. * x1) > -1 ? 1 : -1;
    }
 
    std::cout << "------- Test 2 -------" << std::endl;
    std::cout << "Model before fit: " << ada << std::endl;
 
    ada.fit(X, Y);
    std::cout << "Model after fit: " << ada << std::endl;
 
    int N_test_cases = 5;
    for (int i = 0; i < N_test_cases; i++) {
        double x0 = (static_cast<double>(std::rand() % range) - range2) / 100.f;
        double x1 = (static_cast<double>(std::rand() % range) - range2) / 100.f;
 
        int predict = ada.predict({x0, x1});
 
        std::cout << "Predict for x=(" << x0 << "," << x1 << "): " << predict;
 
        int expected_val = (x0 + 3. * x1) > -1 ? 1 : -1;
        assert(predict == expected_val);
        std::cout << " ...passed" << std::endl;
    }
}

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test3()

void test3

(

double

eta = 0.01

)

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)

                              {
    adaline ada(6, eta);  // 2 features
 
    const int N = 100;  // number of sample points
 
    std::array<std::vector<double>, N> X;
    std::array<int, N> Y{};  // corresponding y-values
 
    // 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 = (static_cast<double>(std::rand() % range) - range2) / 100.f;
        double x1 = (static_cast<double>(std::rand() % range) - range2) / 100.f;
        double x2 = (static_cast<double>(std::rand() % range) - range2) / 100.f;
        X[i] = std::vector<double>({x0, x1, x2, x0 * x0, x1 * x1, x2 * x2});
        Y[i] = ((x0 * x0) + (x1 * x1) + (x2 * x2)) <= 1.f ? 1 : -1;
    }
 
    std::cout << "------- Test 3 -------" << std::endl;
    std::cout << "Model before fit: " << ada << std::endl;
 
    ada.fit(X, Y);
    std::cout << "Model after fit: " << ada << std::endl;
 
    int N_test_cases = 5;
    for (int i = 0; i < N_test_cases; i++) {
        double x0 = (static_cast<double>(std::rand() % range) - range2) / 100.f;
        double x1 = (static_cast<double>(std::rand() % range) - range2) / 100.f;
        double x2 = (static_cast<double>(std::rand() % range) - range2) / 100.f;
 
        int predict = ada.predict({x0, x1, x2, x0 * x0, x1 * x1, x2 * x2});
 
        std::cout << "Predict for x=(" << x0 << "," << x1 << "," << x2
                  << "): " << predict;
 
        int expected_val = ((x0 * x0) + (x1 * x1) + (x2 * x2)) <= 1.f ? 1 : -1;
        assert(predict == expected_val);
        std::cout << " ...passed" << std::endl;
    }
}

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