From 1836baa4a08eed7ab5477b4aa0b1ca3c4032aaaf Mon Sep 17 00:00:00 2001
From: Krishna Vedala <7001608+kvedala@users.noreply.github.com>
Date: Sun, 31 May 2020 12:43:17 -0400
Subject: [PATCH] adaline learning algorithm
---
machine_learning/adaline_learning.c | 392 ++++++++++++++++++++++++++++
1 file changed, 392 insertions(+)
create mode 100644 machine_learning/adaline_learning.c
diff --git a/machine_learning/adaline_learning.c b/machine_learning/adaline_learning.c
new file mode 100644
index 00000000..fc38ac3f
--- /dev/null
+++ b/machine_learning/adaline_learning.c
@@ -0,0 +1,392 @@
+/**
+ * \file
+ * \brief [Adaptive Linear Neuron
+ * (ADALINE)](https://en.wikipedia.org/wiki/ADALINE) implementation
+ *
+ * 
+ * [source](https://commons.wikimedia.org/wiki/File:Adaline_flow_chart.gif)
+ * ADALINE is one of the first and simplest single layer artificial neural
+ * network. The algorithm essentially implements a linear function
+ * \f[ f\left(x_0,x_1,x_2,\ldots\right) =
+ * \sum_j x_jw_j+\theta
+ * \f]
+ * where \f$x_j\f$ are the input features of a sample, \f$w_j\f$ are the
+ * coefficients of the linear function and \f$\theta\f$ is a constant. If we
+ * know the \f$w_j\f$, then for any given set of features, \f$y\f$ can be
+ * computed. Computing the \f$w_j\f$ 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.
+ */
+
+#include
+#include
+#include
+#include
+#include
+#include
+#include
+
+#define MAX_ITER 500 // INT_MAX ///< Maximum number of iterations to learn
+
+/** structure to hold adaline model parameters */
+struct adaline
+{
+
+ double eta; ///< learning rate of the algorithm
+ double *weights; ///< weights of the neural network
+ int num_weights; ///< number of weights of the neural network
+};
+
+#define ACCURACY 1e-5 ///< convergence accuracy \f$=1\times10^{-5}\f$
+
+/**
+ * Default constructor
+ * \param[in] num_features number of features present
+ * \param[in] eta learning rate (optional, default=0.1)
+ * \returns new adaline model
+ */
+struct adaline new_adaline(const int num_features, const double eta)
+{
+ 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;
+}
+
+/** delete dynamically allocated memory
+ * \param[in] ada model from which the memory is to be freeed.
+ */
+void delete_adaline(struct adaline *ada)
+{
+ if (ada == NULL)
+ return;
+
+ free(ada->weights);
+};
+
+/** [Heaviside activation
+ * function](https://en.wikipedia.org/wiki/Heaviside_step_function) 
+ */
+int activation(double x) { return x > 0 ? 1 : -1; }
+
+/**
+ * Operator to print the weights of the model
+ */
+char *get_weights_str(struct adaline *ada)
+{
+ static char out[100]; // static so the value is persistent
+
+ sprintf(out, "<");
+ for (int i = 0; i < ada->num_weights; i++)
+ {
+ sprintf(out, "%s%.4g", out, ada->weights[i]);
+ if (i < ada->num_weights - 1)
+ sprintf(out, "%s, ", out);
+ }
+ sprintf(out, "%s>", out);
+ return out;
+}
+
+/**
+ * predict the output of the model for given set of features
+ *
+ * \param[in] ada adaline model to predict
+ * \param[in] x input vector
+ * \param[out] out optional argument to return neuron output before applying
+ * activation function (`NULL` to ignore)
+ * \returns model prediction output
+ */
+int predict(struct adaline *ada, const double *x, double *out)
+{
+ 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
+}
+
+/**
+ * Update the weights of the model using supervised learning for one feature
+ * vector
+ *
+ * \param[in] ada adaline model to fit
+ * \param[in] x feature vector
+ * \param[in] y known output value
+ * \returns correction factor
+ */
+double fit_sample(struct adaline *ada, const double *x, const int y)
+{
+ /* 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;
+}
+
+/**
+ * Update the weights of the model using supervised learning for an array of
+ * vectors.
+ *
+ * \param[in] ada adaline model to train
+ * \param[in] X array of feature vector
+ * \param[in] y known output value for each feature vector
+ * \param[in] N number of training samples
+ */
+void fit(struct adaline *ada, const double **X, const int *y, const int N)
+{
+ 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);
+}
+
+/**
+ * test function to predict points in a 2D coordinate system above the line
+ * \f$x=y\f$ as +1 and others as -1.
+ * Note that each point is defined by 2 values or 2 features.
+ * \param[in] eta learning rate (optional, default=0.01)
+ */
+void test1(double eta)
+{
+ const int num_features = 2;
+ struct adaline ada = new_adaline(num_features, eta); // 2 features
+
+ const int N = 10; // number of sample points
+
+ const double X[10][2] = {{0, 1}, {1, -2}, {2, 3}, {3, -1}, {4, 1},
+ {6, -5}, {-7, -3}, {-8, 5}, {-9, 2}, {-10, -15}};
+ const int y[10] = {1, -1, 1, -1, -1,
+ -1, 1, 1, 1, -1}; // corresponding y-values
+
+ 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\n", pred);
+ assert(pred == 1);
+ printf(" ...passed\n");
+}
+
+/**
+ * test function to predict points in a 2D coordinate system above the line
+ * \f$x+3y=-1\f$ 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.
+ * \param[in] eta learning rate (optional, default=0.01)
+ */
+void test2(double eta)
+{
+ 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);
+}
+
+/**
+ * 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:
+ * \f$x^2+y^2+z^2=r^2=1\f$ and if the \f$r^2<1\f$, point lies within the sphere
+ * else, outside.
+ *
+ * \param[in] eta learning rate (optional, default=0.01)
+ */
+void test3(double eta)
+{
+ 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);
+}
+
+/** Main function */
+int main(int argc, char **argv)
+{
+ srand(time(NULL)); // 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], NULL);
+
+ // test1(eta);
+
+ printf("Press ENTER to continue...\n");
+ getchar();
+
+ test2(eta);
+
+ printf("Press ENTER to continue...\n");
+ getchar();
+
+ test3(eta);
+
+ return 0;
+}