{ "cells": [ { "cell_type": "markdown", "id": "b73176c5", "metadata": {}, "source": [ "# Goal: Implement the Perceptron Algorithm and Investigate the Initialization of the Perceptron Algorithm using the Null Vector." ] }, { "cell_type": "markdown", "id": "a54e3d45", "metadata": {}, "source": [ "*An algorithm for the perceptron was used from the following website: https://towardsdatascience.com/perceptron-algorithm-in-python-f3ac89d2e537\n", "\n", "\n" ] }, { "cell_type": "markdown", "id": "2fada544", "metadata": {}, "source": [ "This algoritm was adjusted so the variable names were symnonmous to the variable names used in lectures. As perceptrons deal with binary data, a dataset was created which contained 2 features. These datasets are in R**2. Graphcally these are represented as blue squares and red circles. 4 different datasets were created with different parameters.\n", "\n", "Dataset 1 contains 100 samples and the standard deviation of the clustors is 1.\n", "Dataset 2 contains 500 samples and the standard deviation of the clustors is 1. This is to investigate the impact that the increase of the sample size has on the output.\n", "Dataset 3 contains 500 samples and the standard deviation of the clustors is 1.2. This is to investigate the impact that the increase of the standard deviation has on the output.\n", "Dataset 4 contains 500 samples and the standard deviation is increaed so that the dataset is no longer linerarly seperable. This is to graphically show that the perceptron cannot deal with non-linearly seperable data.\n", "\n", "The 4 datasets are plotted below." ] }, { "cell_type": "code", "execution_count": 1, "id": "ba43e21c", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from sklearn import datasets\n", "\n", "x_1, y_1 = datasets.make_blobs(n_samples=100,n_features=2,\n", " centers=2,cluster_std=1.0,\n", " random_state=2)\n", "\n", "x_2, y_2 = datasets.make_blobs(n_samples=500,n_features=2,\n", " centers=2,cluster_std=1.0,\n", " random_state=2)\n", "\n", "x_3, y_3 = datasets.make_blobs(n_samples=500,n_features=2,\n", " centers=2,cluster_std=1.2,\n", " random_state=2)\n", "\n", "x_4, y_4 = datasets.make_blobs(n_samples=500,n_features=2,\n", " centers=2,cluster_std=1.8,\n", " random_state=2)\n", "\n", "\n", "fig, axs = plt.subplots(nrows=2, ncols=2, figsize=(20,15))\n", "axs[0, 0].plot(x_1[:, 0][y_1 == 0], x_1[:, 1][y_1 == 0], 'bs')\n", "axs[0, 0].plot(x_1[:, 0][y_1 == 1], x_1[:, 1][y_1 == 1], 'ro')\n", "axs[0, 0].set_title('Sample of 100, Standard Deviation of 1')\n", "\n", "axs[0, 1].plot(x_2[:, 0][y_2 == 0], x_2[:, 1][y_2 == 0], 'bs')\n", "axs[0, 1].plot(x_2[:, 0][y_2 == 1], x_2[:, 1][y_2 == 1], 'ro')\n", "axs[0, 1].set_title('Sample of 500, Standard Deviation of 1')\n", "\n", "axs[1, 0].plot(x_3[:, 0][y_3 == 0], x_3[:, 1][y_3 == 0], 'bs')\n", "axs[1, 0].plot(x_3[:, 0][y_3 == 1], x_3[:, 1][y_3 == 1], 'ro')\n", "axs[1, 0].set_title('Sample of 500, Standard Deviation of 1.2')\n", "\n", "axs[1, 1].plot(x_4[:, 0][y_4 == 0], x_4[:, 1][y_4 == 0], 'bs')\n", "axs[1, 1].plot(x_4[:, 0][y_4 == 1], x_4[:, 1][y_4 == 1], 'ro')\n", "axs[1, 1].set_title('Sample of 500, Standard Deviation of 1.5')\n", "\n", "plt.suptitle('Random Classification Data with 2 classes', weight='bold', y=1.0, fontsize=18)\n", "\n", "\n", "for ax in axs.flat:\n", " ax.set(xlabel='feature 1', ylabel='feature 2')\n", "\n", "\n", "plt.tight_layout()\n" ] }, { "cell_type": "markdown", "id": "309df889", "metadata": {}, "source": [ "The perceptron I am looking at is a Perceptron with a hard threshold which means to say that the function is a step function which returns a value of 0 or 1." ] }, { "cell_type": "code", "execution_count": 2, "id": "53c57933", "metadata": {}, "outputs": [], "source": [ "def step_func(z):\n", " return 1.0 if (z > 0) else 0.0" ] }, { "cell_type": "markdown", "id": "68c4abaf", "metadata": {}, "source": [ "The perceptron alogrithm has 4 imput parameters. The first is the number of training examples and the second is the number of features (which should always be 2). The Perceptron algorithm is initialized with the null vector. This will be updated later to a non-null vector to look at the effects on the learning coefficient(n). The learning coefficent is the third argument and the forth is the number of iterations. After each iteration, the number of misclassified data features are stored in a list. " ] }, { "cell_type": "code", "execution_count": 3, "id": "82348a3c", "metadata": {}, "outputs": [], "source": [ "def perceptron(x, y, lr, num_iterations):\n", " \n", " m, n = x.shape\n", " \n", " # Initializing parapeters(w) to zeros.\n", " # +1 in n+1 for the bias term.\n", " \n", " w = np.zeros((n+1,1))\n", " \n", " # Empty list to store how many examples were \n", " # misclassified at every iteration.\n", " n_miss_list = []\n", " \n", " # Training.\n", " for num in range(num_iterations):\n", " \n", " # variable to store #misclassified.\n", " n_miss = 0\n", " \n", " # looping for every example.\n", " for idx, x_i in enumerate(x):\n", " \n", " # Insering 1 for bias, X0 = 1.\n", " x_i = np.insert(x_i, 0, 1).reshape(-1,1)\n", " \n", " # Calculating prediction/hypothesis.\n", " y_hat = step_func(np.dot(x_i.T, w))\n", " \n", " # Updating if the example is misclassified.\n", " if (np.squeeze(y_hat) - y[idx]) != 0:\n", " w += lr*((y[idx] - y_hat)*x_i)\n", " \n", " # Incrementing by 1.\n", " n_miss += 1\n", " \n", " # Appending number of misclassified examples\n", " # at every iteration.\n", " n_miss_list.append(n_miss)\n", " \n", " return w, n_miss_list" ] }, { "cell_type": "markdown", "id": "0886b999", "metadata": {}, "source": [ "A defiition is created to plot the decision boundary that the perceptron algorithm has output." ] }, { "cell_type": "code", "execution_count": 4, "id": "e2f6d88a", "metadata": {}, "outputs": [], "source": [ "def plot_decision_boundary(x,y,w):\n", " \n", " # The Line is y=mx+c\n", " # So, Equate mx+c = theta0.X0 + theta1.X1 + theta2.X2\n", " # Solving we find m and c\n", " x1 = [min(x[:,0]), max(x[:,0])]\n", " m = -w[1]/w[2]\n", " c = -w[0]/w[2]\n", " x2 = m*x1 + c\n", " \n", " # Plotting\n", " fig = plt.figure(figsize=(10,8))\n", " plt.plot(x[:, 0][y == 0], x[:, 1][y == 0], 'bs')\n", " plt.plot(x[:, 0][y == 1], x[:, 1][y == 1], 'ro')\n", " plt.xlabel(\"feature 1\")\n", " plt.ylabel(\"feature 2\")\n", " plt.title(\"Perceptron Algorithm\")\n", " plt.plot(x1, x2, 'y-')" ] }, { "cell_type": "code", "execution_count": 5, "id": "5fe9cba4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The number of mislabeled classes for the first interation of sample = 100 is 11\n", "\n", "The number of mislabeled classes for the first interation of sample = 500 is 24\n", "\n", "The number of mislabeled classes for the first interation of sample = 500 \n", " but with an increased standard deviation is 32\n" ] } ], "source": [ "w_1, miss_l_1 = perceptron(x_1, y_1, 0.5, 10)\n", "w_2, miss_l_2 = perceptron(x_2, y_2, 0.5, 10)\n", "w_3, miss_l_3 = perceptron(x_3, y_3, 0.5, 10)\n", "\n", "print('The number of mislabeled classes for the first interation of sample = 100 is', miss_l_1[0])\n", "print('')\n", "print('The number of mislabeled classes for the first interation of sample = 500 is', miss_l_2[0])\n", "print('')\n", "print(f'The number of mislabeled classes for the first interation of sample = 500 \\n but with an increased standard deviation is', miss_l_3[0])" ] }, { "cell_type": "markdown", "id": "dca9b4d3", "metadata": {}, "source": [ "The above indicates that a larger the dataset and a larger varience causes the percetron algorithm in this case to misidentify more points on the first iteration. For all cases, these do converge using further iterations to a boundry which classifys all points correctly. One of the cases is below with the second dataset, initially 24 points are misclassified but by the 6th iteration, 0 points are misclassified. This shows nicely the convergence of the perceptron algorithm on linearly classified data. Graphically this can be seen as the yellow line splits the datset in two with the red dots above the line and the blue squares below the line." ] }, { "cell_type": "code", "execution_count": 6, "id": "9826ad21", "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[24, 13, 10, 4, 3, 0, 0, 0, 0, 0]\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_decision_boundary(x_2, y_2, w_2)\n", "print(miss_l_2)" ] }, { "cell_type": "markdown", "id": "682da16a", "metadata": {}, "source": [ "Below it can be shown how the perceptron algroritm fails on non linearly seperable data. It can be clearly seen visually that no line can seperate this data. The perceptron algoritm is run for 50 iterations and it can be seen that the number of misclassified points is remaining largely the same and will not converge down to 0." ] }, { "cell_type": "code", "execution_count": 7, "id": "85a84dc3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[50, 30, 24, 18, 17, 14, 15, 15, 14, 14, 12, 14, 12, 13, 13, 10, 13, 15, 10, 13, 8, 13, 13, 8, 9, 10, 9, 10, 14, 10, 8, 13, 10, 10, 8, 8, 14, 8, 8, 11, 8, 8, 11, 8, 8, 11, 13, 10, 10, 8]\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "w_4, miss_l_4 = perceptron(x_4, y_4, 0.5, 50)\n", "plot_decision_boundary(x_4, y_4, w_4)\n", "print(miss_l_4)" ] }, { "cell_type": "markdown", "id": "cf5885cd", "metadata": {}, "source": [ "A second definition of the perceptron algoritm is created but initialising the weights with values of 1 rather than a null vector as previously used above. The datasets used are the same as above. It can be seen that the learning rate causes the number of misclassified points to converge to 0 at a slower rate." ] }, { "cell_type": "code", "execution_count": 8, "id": "953c7e4f", "metadata": {}, "outputs": [], "source": [ "def perceptron_2(x, y, lr, num_iterations):\n", " \n", " m, n = x.shape\n", " \n", " # Initializing parapeters(w) to zeros.\n", " # +1 in n+1 for the bias term.\n", " \n", " w = np.ones((n+1,1))\n", " \n", " # Empty list to store how many examples were \n", " # misclassified at every iteration.\n", " n_miss_list = []\n", " \n", " # Training.\n", " for num in range(num_iterations):\n", " \n", " # variable to store #misclassified.\n", " n_miss = 0\n", " \n", " # looping for every example.\n", " for idx, x_i in enumerate(x):\n", " \n", " # Insering 1 for bias, X0 = 1.\n", " x_i = np.insert(x_i, 0, 1).reshape(-1,1)\n", " \n", " # Calculating prediction/hypothesis.\n", " y_hat = step_func(np.dot(x_i.T, w))\n", " \n", " # Updating if the example is misclassified.\n", " if (np.squeeze(y_hat) - y[idx]) != 0:\n", " w += lr*((y[idx] - y_hat)*x_i)\n", " \n", " # Incrementing by 1.\n", " n_miss += 1\n", " \n", " # Appending number of misclassified examples\n", " # at every iteration.\n", " n_miss_list.append(n_miss)\n", " \n", " return w, n_miss_list" ] }, { "cell_type": "markdown", "id": "da2ba94c", "metadata": {}, "source": [ "In the cases below, the learning rate and the inizialisation of the original weighted vector are the only parameters that are changing.\n", "\n", "In the first example, the null vector is used w = (0, 0, 0). The learning rate is a value between 0 and 1. Thus a small learning rate of 0.001 is compared against the largest learning rate possible of 1. The problem with using a large learning rate is the perceptron algorithm could converge too quickly to a suboptimal solution. In contract, using a small learning rate can cause the algorithm to converge too slowly causing the process to get stuck. The purpose of this comparision is to show the impact that the null vector has on the learning rate so neither of the above issues about the size of the learning rate are considered.\n", "\n", "It can be seen that using the null vector the increase or decrease of the elarning rate does not have an impact on how fast the misclassification of points converge to zero. They both converge to 0 misclassifications after 6 iterations." ] }, { "cell_type": "code", "execution_count": 9, "id": "8fe3a410", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "With a null initialisation vector and a learning rate of 0.001: [24, 13, 10, 4, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n", "With a null initialisation vector and a learning rate of 1: [24, 13, 10, 4, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n" ] } ], "source": [ "w_2_sml_lp_zeros, miss_l_2_sml_lp_zeros = perceptron(x_2, y_2, 0.001, 50)\n", "w_2_lrge_lp_zeros, miss_2_lrge_lp_zeros = perceptron(x_2, y_2, 1, 50)\n", "print(\"With a null initialisation vector and a learning rate of 0.001: \", miss_l_2_sml_lp_zeros)\n", "print(\"With a null initialisation vector and a learning rate of 1: \", miss_2_lrge_lp_zeros)" ] }, { "cell_type": "markdown", "id": "0598d69a", "metadata": {}, "source": [ "In the second example, when the initialation vector is non-null, w = (1,1,1), the learning rate has a significant effect on the convergence. When the learning rate is small, even after 50 iterations the algorithm is still misclassifing points although they are clearly converging to 0 over time. This is a large contrast to the learning algoritm of 1 which causes the algorithm to converge after 2 iterations." ] }, { "cell_type": "code", "execution_count": 10, "id": "d30284e0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "With a non-null initialisation vector and a learning rate of 0.001: [73, 53, 39, 30, 23, 17, 15, 13, 12, 10, 10, 9, 9, 9, 8, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 7, 6, 6, 7, 6, 6, 6, 7, 6, 6, 6, 5, 4, 4, 4, 3, 3, 3, 3, 3, 3]\n", "With a non-null initialisation vector and a learning rate of 0.001: [26, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n" ] } ], "source": [ "w_2_sml_lp, miss_l_2_sml_lp = perceptron_2(x_2, y_2, 0.001, 50)\n", "w_2_lrge_lp, miss_2_lrge_lp = perceptron_2(x_2, y_2, 1, 50)\n", "print(\"With a non-null initialisation vector and a learning rate of 0.001: \", miss_l_2_sml_lp)\n", "print(\"With a non-null initialisation vector and a learning rate of 0.001: \", miss_2_lrge_lp)" ] }, { "cell_type": "markdown", "id": "80ca2cf3", "metadata": {}, "source": [ "A graphical representation of the non null initialisation vectors discussed above.\n", "\n", "The first graph shows the small learning rate while the second graph shows the output with the large learning rate." ] }, { "cell_type": "code", "execution_count": 11, "id": "9aef0a43", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_decision_boundary(x_2, y_2, w_2_sml_lp)\n", "\n", "plot_decision_boundary(x_2, y_2, w_2_lrge_lp)" ] }, { "cell_type": "markdown", "id": "a0c197cd", "metadata": {}, "source": [ "In conclusion, the perceptron algotion was implemented on 4 different datasets. It was shown that the perceptron algorithm works with binary and linearly sperable data. It was also shown that the perceptron algorithm terminates in a finite number of sets if the data is linearly seperable. It can be seen that if the perceptron algorithm uses the null vector to initialise the weights, then the learning coeffiecient 'neta' does not affect the learning rate." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.12" } }, "nbformat": 4, "nbformat_minor": 5 }