upload solution for assignment 5
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assignment 5/iml_assignmnet5_solved.ipynb
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assignment 5/iml_assignmnet5_solved.ipynb
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{
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"cells": [
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{
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"cell_type": "markdown",
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"source": [
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"### Solution for Assignment 5 of the course \"Introduction to Machine Learning\" at the University of Leoben.\n",
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"##### Author: Fotios Lygerakis\n",
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"##### Semester: SS 2022/2023"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"# Perceptron Algorithm for Classification of Iris Dataset"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"(150, 4)\n",
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"(150,)\n"
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]
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}
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],
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"source": [
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"# load the iris dataset\n",
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"from sklearn.datasets import load_iris\n",
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"from sklearn.metrics import accuracy_score\n",
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"import numpy as np\n",
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"\n",
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"iris = load_iris()\n",
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"X = iris.data\n",
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"y = iris.target\n",
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"print(X.shape)\n",
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"print(y.shape)"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"Preprocess the data"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"outputs": [],
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"source": [
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"# Preprocess the data\n",
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"from sklearn.model_selection import train_test_split\n",
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"\n",
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"# split the scaled data into train and test sets\n",
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"X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"Define the perceptron algorithm"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"outputs": [],
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"source": [
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"# Define the perceptron algorithm\n",
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"class MultiClassPerceptron:\n",
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" def __init__(self, input_dim, output_dim, lr=0.01, epochs=1000):\n",
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" self.W = np.random.randn(input_dim, output_dim)\n",
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" self.b = np.zeros((1, output_dim))\n",
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" self.lr = lr\n",
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" self.epochs = epochs\n",
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"\n",
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" def forward(self, X):\n",
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" self.z = np.dot(X, self.W) + self.b\n",
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" self.y_hat = np.exp(self.z) / np.sum(np.exp(self.z), axis=1, keepdims=True)\n",
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"\n",
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" def backward(self, X, y):\n",
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" m = X.shape[0] # number of samples\n",
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" # Calculate the gradients\n",
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" grad_z = self.y_hat # shape (m, C)\n",
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" # Subtract 1 from the predicted class for each sample\n",
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" grad_z[range(m), y] -= 1 # shape (m, C)\n",
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" # Calculate the gradients with respect to the parameters\n",
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" grad_W = np.dot(X.T, grad_z) # shape (n, C)\n",
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" # Reshape the gradients into a 2-D array\n",
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" grad_b = np.sum(grad_z, axis=0, keepdims=True) # shape (1, C)\n",
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" # Update the parameters\n",
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" self.W -= self.lr * grad_W # shape (n, C)\n",
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" self.b -= self.lr * grad_b # shape (1, C)\n",
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"\n",
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" def fit(self, X, y):\n",
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" for epoch in range(self.epochs):\n",
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" self.forward(X)\n",
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" self.backward(X, y)\n",
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"\n",
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" def predict(self, X):\n",
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" self.forward(X)\n",
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" return np.argmax(self.y_hat, axis=1)"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"Train the model"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"outputs": [],
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"source": [
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"# Train the model\n",
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"p = MultiClassPerceptron(input_dim=X_train.shape[1], output_dim=3, lr=0.01, epochs=1000)\n",
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"p.fit(X_train, y_train)\n",
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"predictions_train = p.predict(X_train)\n",
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"predictions = p.predict(X_test)"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"Evaluate the model"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Perceptron classification train accuracy 0.975\n",
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"Perceptron classification accuracy 1.0\n"
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]
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}
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],
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"source": [
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"# evaluate train accuracy\n",
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"print(\"Perceptron classification train accuracy\", accuracy_score(y_train, predictions_train))\n",
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"print(\"Perceptron classification accuracy\", accuracy_score(y_test, predictions))"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"Non-linear feature transformation on the concrete compressive strength dataset"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"outputs": [],
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"source": [
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"def polynomial_features(X, degree):\n",
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" \"\"\"\n",
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" Creates a new feature matrix consisting of all polynomial combinations of the features with degree less than or equal to the specified degree.\n",
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" For example, if an input sample is two dimensional and of the form [a, b], the degree-2 polynomial features are [1, a, b, a^2, ab, b^2].\n",
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" Parameters\n",
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" ----------\n",
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" X : array-like, shape (n_samples, n_features)\n",
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" The input samples.\n",
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" degree : int\n",
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" The degree of the polynomial features.\n",
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" Returns\n",
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" -------\n",
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" X_new : array-like, shape (n_samples, 1 + n_features + n_features*(n_features+1)/2)\n",
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" The polynomial features with degree `degree`.\n",
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" \"\"\"\n",
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" n_samples, n_features = np.shape(X)\n",
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" new_features = np.ones(shape=(n_samples, 1))\n",
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"\n",
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" for i in range(n_features):\n",
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" for j in range(1, degree+1):\n",
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" # create a new column for each feature, with values raised to the power of j\n",
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" new_col = np.power(X[:, i], j) # shape (n_samples, 1)\n",
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" # reshape the new column to a 2-D array\n",
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" new_col = new_col.reshape(n_samples, 1) # shape (n_samples, 1)\n",
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" # append the new column to the new_features array\n",
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" new_features = np.hstack((new_features, new_col)) # shape (n_samples, j+1)\n",
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"\n",
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" return new_features"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"outputs": [],
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"source": [
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"# Non-linear feature transformation\n",
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"import pandas as pd\n",
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"from sklearn.preprocessing import PolynomialFeatures\n",
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"from sklearn.linear_model import LinearRegression\n",
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"from sklearn.metrics import mean_squared_error, r2_score\n",
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"\n",
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"# load the concrete compressive strength dataset\n",
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"df = pd.read_excel('Concrete_Data.xls')\n",
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"\n",
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"# split the data into train and test sets\n",
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"X = df.drop(['Concrete compressive strength(MPa, megapascals) '], axis=1)\n",
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"y = df['Concrete compressive strength(MPa, megapascals) ']\n",
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"X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n",
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"\n",
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"# transform the features into second degree polynomial features\n",
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"poly = PolynomialFeatures(degree=2)\n",
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"X_train_poly = poly.fit_transform(X_train)\n",
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"X_test_poly = poly.transform(X_test)\n",
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"\n",
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"X_train_poly_custom = polynomial_features(X_train.values, degree=2)\n",
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"X_test_poly_custom = polynomial_features(X_test.values, degree=2)\n"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"Train the linear regression model"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Mean squared error (train poly custom): 64.55\n",
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"Mean squared error (test poly custom): 58.28\n",
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"Mean squared error (train): 110.66\n",
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"Mean squared error (test): 95.98\n",
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"R^2 (train poly custom): 0.77\n",
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"R^2 (test poly custom): 0.77\n",
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"R^2 (train): 0.61\n",
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"R^2 (test): 0.63\n"
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]
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}
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],
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"source": [
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"# Train the model\n",
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"lr_poly_custom = LinearRegression()\n",
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"lr = LinearRegression()\n",
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"# fit the model\n",
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"lr_poly_custom.fit(X_train_poly_custom, y_train)\n",
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"lr.fit(X_train, y_train)\n",
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"# predict values from the polynomial transformed features\n",
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"predictions_poly_custom_train = lr_poly_custom.predict(X_train_poly_custom)\n",
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"predictions_poly_custom = lr_poly_custom.predict(X_test_poly_custom)\n",
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"# predict values from the original features\n",
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"predictions_train = lr.predict(X_train)\n",
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"predictions = lr.predict(X_test)\n",
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"\n",
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"# mean squared error\n",
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"print(\"Mean squared error (train poly custom): {:.2f}\".format(mean_squared_error(y_train, predictions_poly_custom_train)))\n",
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"print(\"Mean squared error (test poly custom): {:.2f}\".format(mean_squared_error(y_test, predictions_poly_custom)))\n",
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"print(\"Mean squared error (train): {:.2f}\".format(mean_squared_error(y_train, predictions_train)))\n",
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"print(\"Mean squared error (test): {:.2f}\".format(mean_squared_error(y_test, predictions)))\n",
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"\n",
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"# coefficient of determination (R^2)\n",
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"print(\"R^2 (train poly custom): {:.2f}\".format(r2_score(y_train, predictions_poly_custom_train)))\n",
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"print(\"R^2 (test poly custom): {:.2f}\".format(r2_score(y_test, predictions_poly_custom)))\n",
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"print(\"R^2 (train): {:.2f}\".format(r2_score(y_train, predictions_train)))\n",
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"print(\"R^2 (test): {:.2f}\".format(r2_score(y_test, predictions)))\n",
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"\n"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"RBFs on the California Housing Prices dataset"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"outputs": [],
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"source": [
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"def rbf_kernel(X, centers, gamma):\n",
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" # Pairwise Euclidean distances calculation:\n",
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" # Compute the squared Euclidean distances between each sample and each center using broadcasting:\n",
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" # - Subtract each center from each sample to get a difference matrix of shape (n_samples, n_centers, n_features)\n",
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" # - Square each element in the difference matrix\n",
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" # - Sum the squared differences along the feature axis to get the squared distances matrix of shape (n_samples, n_centers)\n",
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" # - Take the square root of each element in the squared distances matrix to obtain the pairwise Euclidean distances matrix of shape (n_samples, n_centers)\n",
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" dists = np.sqrt(((X[:, np.newaxis] - centers)**2).sum(axis=2)) # shape (n_samples, n_centers)\n",
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" # Compute the RBF values for each distance using the Gaussian kernel\n",
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" rbf_vals = np.exp(-gamma * dists**2) # shape (n_samples, n_centers)\n",
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" return rbf_vals"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Linear regression on original data:\n",
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"MSE: 0.5558915986952443\n",
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"R^2: 0.5757877060324508\n",
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"\n",
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"Linear regression on RBF-transformed data:\n",
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"MSE: 0.37106446913117447\n",
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"R^2: 0.7168330839511696\n"
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]
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}
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],
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"source": [
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"from sklearn.datasets import fetch_california_housing\n",
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"from sklearn.preprocessing import StandardScaler\n",
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"from sklearn.model_selection import train_test_split\n",
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"from sklearn.linear_model import LinearRegression\n",
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"from sklearn.metrics import mean_squared_error, r2_score\n",
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"\n",
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"# Load the California Housing Prices dataset\n",
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"data = fetch_california_housing()\n",
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"X = data['data']\n",
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"y = data['target']\n",
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"\n",
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"# Split the data into training and testing sets\n",
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"X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n",
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"\n",
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"# Standardize the features\n",
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"scaler = StandardScaler()\n",
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"X_train_std = scaler.fit_transform(X_train)\n",
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"X_test_std = scaler.transform(X_test)\n",
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"\n",
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"# Choose the number of centroids and the RBF kernel width\n",
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"num_centroids = 100\n",
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"gamma = 0.1\n",
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"\n",
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"# Randomly select the centroids from the training set\n",
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"np.random.seed(42)\n",
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"idx = np.random.choice(X_train_std.shape[0], num_centroids, replace=False)\n",
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"centroids = X_train_std[idx] # (100, 8)\n",
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"\n",
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"# Compute the RBF features for the training and testing sets\n",
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"rbf_train = rbf_kernel(X_train_std, centroids, gamma) # (16512, 100)\n",
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"rbf_test = rbf_kernel(X_test_std, centroids, gamma) # (4128, 100)\n",
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"\n",
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"# Fit a linear regression model on the original and RBF-transformed data\n",
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"linreg_orig = LinearRegression().fit(X_train_std, y_train)\n",
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"linreg_rbf = LinearRegression().fit(rbf_train, y_train)\n",
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"\n",
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"# Evaluate the models on the testing set\n",
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"y_pred_orig = linreg_orig.predict(X_test_std)\n",
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"mse_orig = mean_squared_error(y_test, y_pred_orig)\n",
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"r2_orig = r2_score(y_test, y_pred_orig)\n",
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"\n",
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"y_pred_rbf = linreg_rbf.predict(rbf_test)\n",
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"mse_rbf = mean_squared_error(y_test, y_pred_rbf)\n",
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"r2_rbf = r2_score(y_test, y_pred_rbf)\n",
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"\n",
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"# Print the results\n",
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"print(\"Linear regression on original data:\")\n",
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"print(\"MSE:\", mse_orig)\n",
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"print(\"R^2:\", r2_orig)\n",
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"\n",
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"print(\"\\nLinear regression on RBF-transformed data:\")\n",
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"print(\"MSE:\", mse_rbf)\n",
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"print(\"R^2:\", r2_rbf)\n"
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],
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"metadata": {
|
||||
"collapsed": false
|
||||
}
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||||
},
|
||||
{
|
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"cell_type": "markdown",
|
||||
"source": [
|
||||
"# **(Bonus)** Multilayer Perceptron Algorithm for Regression of Concrete Compressive Strength Dataset"
|
||||
],
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
}
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"source": [
|
||||
"Download the Concrete Compressive Strength Dataset from the UCI Machine Learning Repository."
|
||||
],
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
}
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 11,
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"(1030, 9)\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"# Download the Concrete Compressive Strength Dataset from the UCI Machine Learning Repository.\n",
|
||||
"import pandas as pd\n",
|
||||
"from sklearn.model_selection import train_test_split\n",
|
||||
"from sklearn.preprocessing import StandardScaler\n",
|
||||
"import numpy as np\n",
|
||||
"\n",
|
||||
"df = pd.read_excel('Concrete_Data.xls')\n",
|
||||
"print(df.shape)\n",
|
||||
"# df.head()"
|
||||
],
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
}
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"source": [
|
||||
"Preprocess the data"
|
||||
],
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
}
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 12,
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"# Preprocess the data\n",
|
||||
"X = df.iloc[:, :-1].values\n",
|
||||
"y = df.iloc[:, -1].values.reshape(-1, 1)\n",
|
||||
"\n",
|
||||
"# Normalize the features\n",
|
||||
"X_norm = StandardScaler().fit_transform(X)\n",
|
||||
"\n",
|
||||
"# Split the data into training and testing sets\n",
|
||||
"X_train, X_test, y_train, y_test = train_test_split(X_norm, y, test_size=0.2, random_state=42)"
|
||||
],
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
}
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"source": [
|
||||
"Define the multilayer perceptron algorithm"
|
||||
],
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
}
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 13,
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"# a multilayer perceptron algorithm class for regression problems\n",
|
||||
"class MLP:\n",
|
||||
" def __init__(self, input_dim, hidden_dim, output_dim, lr=0.01, epochs=1000):\n",
|
||||
" self.W1 = np.random.randn(input_dim, hidden_dim)\n",
|
||||
" self.b1 = np.zeros((1, hidden_dim))\n",
|
||||
" self.W2 = np.random.randn(hidden_dim, output_dim)\n",
|
||||
" self.b2 = np.zeros((1, output_dim))\n",
|
||||
" self.lr = lr\n",
|
||||
" self.epochs = epochs\n",
|
||||
"\n",
|
||||
" def forward(self, X):\n",
|
||||
" # forward propagation through our network\n",
|
||||
" self.z1 = np.dot(X, self.W1) + self.b1\n",
|
||||
" # activation function\n",
|
||||
" self.a1 = np.tanh(self.z1)\n",
|
||||
" # output layer\n",
|
||||
" self.z2 = np.dot(self.a1, self.W2) + self.b2\n",
|
||||
" # final activation function\n",
|
||||
" self.y_hat = self.z2\n",
|
||||
"\n",
|
||||
" def backward(self, X, y):\n",
|
||||
" # number of samples\n",
|
||||
" m = X.shape[0]\n",
|
||||
" # output layer gradient\n",
|
||||
" self.loss = np.mean((self.y_hat - y) ** 2) # MSE loss. shape (n_samples, output_dim)\n",
|
||||
" # output layer gradient\n",
|
||||
" delta2 = (self.y_hat - y) # shape (n_samples, output_dim)\n",
|
||||
" # hidden layer gradient\n",
|
||||
" dW2 = np.dot(self.a1.T, delta2) # shape (hidden_dim, output_dim)\n",
|
||||
" # bias gradient\n",
|
||||
" db2 = np.sum(delta2, axis=0, keepdims=True) # shape (1, output_dim)\n",
|
||||
" # hidden layer gradient\n",
|
||||
" delta1 = np.dot(delta2, self.W2.T) * (1 - np.power(self.a1, 2)) # shape (n_samples, hidden_dim)\n",
|
||||
" # input layer gradient\n",
|
||||
" dW1 = np.dot(X.T, delta1) # shape (input_dim, hidden_dim)\n",
|
||||
" # bias gradient\n",
|
||||
" db1 = np.sum(delta1, axis=0) # shape (1, hidden_dim)\n",
|
||||
" # update parameters\n",
|
||||
" self.W2 -= self.lr * dW2 / m\n",
|
||||
" self.b2 -= self.lr * db2 / m\n",
|
||||
" self.W1 -= self.lr * dW1 / m\n",
|
||||
" self.b1 -= self.lr * db1 / m\n",
|
||||
"\n",
|
||||
" def fit(self, X, y):\n",
|
||||
" for epoch in range(self.epochs):\n",
|
||||
" self.forward(X)\n",
|
||||
" self.backward(X, y)\n",
|
||||
"\n",
|
||||
" def predict(self, X):\n",
|
||||
" self.forward(X)\n",
|
||||
" return self.y_hat\n"
|
||||
],
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
}
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"source": [
|
||||
"Train the model"
|
||||
],
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
}
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 14,
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"# Create an instance of the MLP class\n",
|
||||
"mlp = MLP(input_dim=X_train.shape[1], hidden_dim=10, output_dim=1, lr=0.01, epochs=1000)\n",
|
||||
"# Train the model\n",
|
||||
"mlp.fit(X_train, y_train)"
|
||||
],
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
}
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"source": [
|
||||
"Evaluate the model"
|
||||
],
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
}
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 15,
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Mean Squared Error: 36.8911071801165\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"# Evaluate the model\n",
|
||||
"from sklearn.metrics import mean_squared_error\n",
|
||||
"\n",
|
||||
"y_pred = mlp.predict(X_test)\n",
|
||||
"print(\"Mean Squared Error:\", mean_squared_error(y_test, y_pred))"
|
||||
],
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
}
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"source": [
|
||||
"Compare the results with the linear regression model"
|
||||
],
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
}
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 16,
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Mean Squared Error: 95.97548435337708\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"# Compare the results with the linear regression model\n",
|
||||
"from sklearn.linear_model import LinearRegression\n",
|
||||
"\n",
|
||||
"lr = LinearRegression()\n",
|
||||
"lr.fit(X_train, y_train)\n",
|
||||
"y_pred = lr.predict(X_test)\n",
|
||||
"print(\"Mean Squared Error:\", mean_squared_error(y_test, y_pred))"
|
||||
],
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
}
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Python 3",
|
||||
"language": "python",
|
||||
"name": "python3"
|
||||
},
|
||||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 2
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython2",
|
||||
"version": "2.7.6"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 0
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user