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{
"cells": [
{
"cell_type": "markdown",
"source": [
"### Solution for Assignment 5 of the course \"Introduction to Machine Learning\" at the University of Leoben.\n",
"##### Author: Fotios Lygerakis\n",
"##### Semester: SS 2022/2023"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "markdown",
"source": [
"# Perceptron Algorithm for Classification of Iris Dataset"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "code",
"execution_count": 1,
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(150, 4)\n",
"(150,)\n"
]
}
],
"source": [
"# load the iris dataset\n",
"from sklearn.datasets import load_iris\n",
"from sklearn.metrics import accuracy_score\n",
"import numpy as np\n",
"\n",
"iris = load_iris()\n",
"X = iris.data\n",
"y = iris.target\n",
"print(X.shape)\n",
"print(y.shape)"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "markdown",
"source": [
"Preprocess the data"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "code",
"execution_count": 2,
"outputs": [],
"source": [
"# Preprocess the data\n",
"from sklearn.model_selection import train_test_split\n",
"\n",
"# split the scaled data into train and test sets\n",
"X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "markdown",
"source": [
"Define the perceptron algorithm"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "code",
"execution_count": 3,
"outputs": [],
"source": [
"# Define the perceptron algorithm\n",
"class MultiClassPerceptron:\n",
" def __init__(self, input_dim, output_dim, lr=0.01, epochs=1000):\n",
" self.W = np.random.randn(input_dim, output_dim)\n",
" self.b = np.zeros((1, output_dim))\n",
" self.lr = lr\n",
" self.epochs = epochs\n",
"\n",
" def forward(self, X):\n",
" self.z = np.dot(X, self.W) + self.b\n",
" self.y_hat = np.exp(self.z) / np.sum(np.exp(self.z), axis=1, keepdims=True)\n",
"\n",
" def backward(self, X, y):\n",
" m = X.shape[0] # number of samples\n",
" # Calculate the gradients\n",
" grad_z = self.y_hat # shape (m, C)\n",
" # Subtract 1 from the predicted class for each sample\n",
" grad_z[range(m), y] -= 1 # shape (m, C)\n",
" # Calculate the gradients with respect to the parameters\n",
" grad_W = np.dot(X.T, grad_z) # shape (n, C)\n",
" # Reshape the gradients into a 2-D array\n",
" grad_b = np.sum(grad_z, axis=0, keepdims=True) # shape (1, C)\n",
" # Update the parameters\n",
" self.W -= self.lr * grad_W # shape (n, C)\n",
" self.b -= self.lr * grad_b # shape (1, C)\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 np.argmax(self.y_hat, axis=1)"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "markdown",
"source": [
"Train the model"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "code",
"execution_count": 4,
"outputs": [],
"source": [
"# Train the model\n",
"p = MultiClassPerceptron(input_dim=X_train.shape[1], output_dim=3, lr=0.01, epochs=1000)\n",
"p.fit(X_train, y_train)\n",
"predictions_train = p.predict(X_train)\n",
"predictions = p.predict(X_test)"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "markdown",
"source": [
"Evaluate the model"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "code",
"execution_count": 5,
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Perceptron classification train accuracy 0.975\n",
"Perceptron classification accuracy 1.0\n"
]
}
],
"source": [
"# evaluate train accuracy\n",
"print(\"Perceptron classification train accuracy\", accuracy_score(y_train, predictions_train))\n",
"print(\"Perceptron classification accuracy\", accuracy_score(y_test, predictions))"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "markdown",
"source": [
"Non-linear feature transformation on the concrete compressive strength dataset"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "code",
"execution_count": 6,
"outputs": [],
"source": [
"def polynomial_features(X, degree):\n",
" \"\"\"\n",
" Creates a new feature matrix consisting of all polynomial combinations of the features with degree less than or equal to the specified degree.\n",
" 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",
" Parameters\n",
" ----------\n",
" X : array-like, shape (n_samples, n_features)\n",
" The input samples.\n",
" degree : int\n",
" The degree of the polynomial features.\n",
" Returns\n",
" -------\n",
" X_new : array-like, shape (n_samples, 1 + n_features + n_features*(n_features+1)/2)\n",
" The polynomial features with degree `degree`.\n",
" \"\"\"\n",
" n_samples, n_features = np.shape(X)\n",
" new_features = np.ones(shape=(n_samples, 1))\n",
"\n",
" for i in range(n_features):\n",
" for j in range(1, degree+1):\n",
" # create a new column for each feature, with values raised to the power of j\n",
" new_col = np.power(X[:, i], j) # shape (n_samples, 1)\n",
" # reshape the new column to a 2-D array\n",
" new_col = new_col.reshape(n_samples, 1) # shape (n_samples, 1)\n",
" # append the new column to the new_features array\n",
" new_features = np.hstack((new_features, new_col)) # shape (n_samples, j+1)\n",
"\n",
" return new_features"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "code",
"execution_count": 7,
"outputs": [],
"source": [
"# Non-linear feature transformation\n",
"import pandas as pd\n",
"from sklearn.preprocessing import PolynomialFeatures\n",
"from sklearn.linear_model import LinearRegression\n",
"from sklearn.metrics import mean_squared_error, r2_score\n",
"\n",
"# load the concrete compressive strength dataset\n",
"df = pd.read_excel('Concrete_Data.xls')\n",
"\n",
"# split the data into train and test sets\n",
"X = df.drop(['Concrete compressive strength(MPa, megapascals) '], axis=1)\n",
"y = df['Concrete compressive strength(MPa, megapascals) ']\n",
"X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n",
"\n",
"# transform the features into second degree polynomial features\n",
"poly = PolynomialFeatures(degree=2)\n",
"X_train_poly = poly.fit_transform(X_train)\n",
"X_test_poly = poly.transform(X_test)\n",
"\n",
"X_train_poly_custom = polynomial_features(X_train.values, degree=2)\n",
"X_test_poly_custom = polynomial_features(X_test.values, degree=2)\n"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "markdown",
"source": [
"Train the linear regression model"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "code",
"execution_count": 8,
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mean squared error (train poly custom): 64.55\n",
"Mean squared error (test poly custom): 58.28\n",
"Mean squared error (train): 110.66\n",
"Mean squared error (test): 95.98\n",
"R^2 (train poly custom): 0.77\n",
"R^2 (test poly custom): 0.77\n",
"R^2 (train): 0.61\n",
"R^2 (test): 0.63\n"
]
}
],
"source": [
"# Train the model\n",
"lr_poly_custom = LinearRegression()\n",
"lr = LinearRegression()\n",
"# fit the model\n",
"lr_poly_custom.fit(X_train_poly_custom, y_train)\n",
"lr.fit(X_train, y_train)\n",
"# predict values from the polynomial transformed features\n",
"predictions_poly_custom_train = lr_poly_custom.predict(X_train_poly_custom)\n",
"predictions_poly_custom = lr_poly_custom.predict(X_test_poly_custom)\n",
"# predict values from the original features\n",
"predictions_train = lr.predict(X_train)\n",
"predictions = lr.predict(X_test)\n",
"\n",
"# mean squared error\n",
"print(\"Mean squared error (train poly custom): {:.2f}\".format(mean_squared_error(y_train, predictions_poly_custom_train)))\n",
"print(\"Mean squared error (test poly custom): {:.2f}\".format(mean_squared_error(y_test, predictions_poly_custom)))\n",
"print(\"Mean squared error (train): {:.2f}\".format(mean_squared_error(y_train, predictions_train)))\n",
"print(\"Mean squared error (test): {:.2f}\".format(mean_squared_error(y_test, predictions)))\n",
"\n",
"# coefficient of determination (R^2)\n",
"print(\"R^2 (train poly custom): {:.2f}\".format(r2_score(y_train, predictions_poly_custom_train)))\n",
"print(\"R^2 (test poly custom): {:.2f}\".format(r2_score(y_test, predictions_poly_custom)))\n",
"print(\"R^2 (train): {:.2f}\".format(r2_score(y_train, predictions_train)))\n",
"print(\"R^2 (test): {:.2f}\".format(r2_score(y_test, predictions)))\n",
"\n"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "markdown",
"source": [
"RBFs on the California Housing Prices dataset"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "code",
"execution_count": 9,
"outputs": [],
"source": [
"def rbf_kernel(X, centers, gamma):\n",
" # Pairwise Euclidean distances calculation:\n",
" # Compute the squared Euclidean distances between each sample and each center using broadcasting:\n",
" # - Subtract each center from each sample to get a difference matrix of shape (n_samples, n_centers, n_features)\n",
" # - Square each element in the difference matrix\n",
" # - Sum the squared differences along the feature axis to get the squared distances matrix of shape (n_samples, n_centers)\n",
" # - 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",
" dists = np.sqrt(((X[:, np.newaxis] - centers)**2).sum(axis=2)) # shape (n_samples, n_centers)\n",
" # Compute the RBF values for each distance using the Gaussian kernel\n",
" rbf_vals = np.exp(-gamma * dists**2) # shape (n_samples, n_centers)\n",
" return rbf_vals"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "code",
"execution_count": 10,
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Linear regression on original data:\n",
"MSE: 0.5558915986952443\n",
"R^2: 0.5757877060324508\n",
"\n",
"Linear regression on RBF-transformed data:\n",
"MSE: 0.37106446913117447\n",
"R^2: 0.7168330839511696\n"
]
}
],
"source": [
"from sklearn.datasets import fetch_california_housing\n",
"from sklearn.preprocessing import StandardScaler\n",
"from sklearn.model_selection import train_test_split\n",
"from sklearn.linear_model import LinearRegression\n",
"from sklearn.metrics import mean_squared_error, r2_score\n",
"\n",
"# Load the California Housing Prices dataset\n",
"data = fetch_california_housing()\n",
"X = data['data']\n",
"y = data['target']\n",
"\n",
"# Split the data into training and testing sets\n",
"X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n",
"\n",
"# Standardize the features\n",
"scaler = StandardScaler()\n",
"X_train_std = scaler.fit_transform(X_train)\n",
"X_test_std = scaler.transform(X_test)\n",
"\n",
"# Choose the number of centroids and the RBF kernel width\n",
"num_centroids = 100\n",
"gamma = 0.1\n",
"\n",
"# Randomly select the centroids from the training set\n",
"np.random.seed(42)\n",
"idx = np.random.choice(X_train_std.shape[0], num_centroids, replace=False)\n",
"centroids = X_train_std[idx] # (100, 8)\n",
"\n",
"# Compute the RBF features for the training and testing sets\n",
"rbf_train = rbf_kernel(X_train_std, centroids, gamma) # (16512, 100)\n",
"rbf_test = rbf_kernel(X_test_std, centroids, gamma) # (4128, 100)\n",
"\n",
"# Fit a linear regression model on the original and RBF-transformed data\n",
"linreg_orig = LinearRegression().fit(X_train_std, y_train)\n",
"linreg_rbf = LinearRegression().fit(rbf_train, y_train)\n",
"\n",
"# Evaluate the models on the testing set\n",
"y_pred_orig = linreg_orig.predict(X_test_std)\n",
"mse_orig = mean_squared_error(y_test, y_pred_orig)\n",
"r2_orig = r2_score(y_test, y_pred_orig)\n",
"\n",
"y_pred_rbf = linreg_rbf.predict(rbf_test)\n",
"mse_rbf = mean_squared_error(y_test, y_pred_rbf)\n",
"r2_rbf = r2_score(y_test, y_pred_rbf)\n",
"\n",
"# Print the results\n",
"print(\"Linear regression on original data:\")\n",
"print(\"MSE:\", mse_orig)\n",
"print(\"R^2:\", r2_orig)\n",
"\n",
"print(\"\\nLinear regression on RBF-transformed data:\")\n",
"print(\"MSE:\", mse_rbf)\n",
"print(\"R^2:\", r2_rbf)\n"
],
"metadata": {
"collapsed": false
}
},
{
"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
}
}
],
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"display_name": "Python 3",
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