{ "cells": [ { "cell_type": "markdown", "id": "dba0131e", "metadata": {}, "source": [ "## Machine Learning\n", "### RBF network (with stochastic gradient descent)\n", "The RBF network $F$ with a bias term $w_{K+1}$is expressed by:\n", "
$\\large F(\\boldsymbol{x})=\\sum_{k=1}^K w_k \\phi_k(||\\boldsymbol{x}-\\boldsymbol{c}_k||)+w_{K+1}$ (1)\n", "
where $\\boldsymbol{c}_k$ are $K$ distinct center points. And $w_{K+1}$ is the bias term, which is considerdd as a part of the weight vector $\\boldsymbol{w}=[w_1,w_2,...,w_K,w_{K+1}]^T$. Morover, we usually choose $\\phi_k(r)=exp(-\\frac{r^2}{2\\sigma_k^2})$\n", "
The loss function for a single training sample $(\\boldsymbol{x}_i,yi)$ is defined by:\n", "
$\\large L_i=\\frac{1}{2}(y_i-F(x_i))^2+\\frac{1}{2}\\lambda \\sum_{k=1}^K w_k^2$\n", "
Then, the gradient of $L_i$ with respect to weight $w_k$ is:\n", "
$\\large \\frac{\\partial L_i}{\\partial w_k}=(y_i-F(\\boldsymbol{x}_i))\\phi_k(||\\boldsymbol{x}_i-\\boldsymbol{c}_k||)+\\lambda w_k$ for $k=1,2,...,K$\n", "
and for the bias term $w_{K+1}$\n", "
$\\large \\frac{\\partial L_i}{\\partial w_{K+1}}=(y_i-F(\\boldsymbol{x}_i))$\n", "
Then, according tothe stochastic gradeint descent (SGD), we update weights by:\n", "
$\\large w_k\\leftarrow w_k-\\eta \\frac{\\partial L_i}{\\partial w_k}$ for $k=1,2,...,K,K+1$\n", "
\n", "Finally, we implement the RBF network with SGD (stochastic gradient descent) and bias term and regualarization without affecting the bias term.\n", "
\n", "The Python code at: https://github.com/ostad-ai/Machine-Learning\n", "
Explanation: https://www.pinterest.com/HamedShahHosseini/Machine-Learning/" ] }, { "cell_type": "code", "execution_count": 1, "id": "045f50a2", "metadata": {}, "outputs": [], "source": [ "# Import required modules\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "from scipy.spatial.distance import cdist\n", "from sklearn.cluster import KMeans" ] }, { "cell_type": "code", "execution_count": 2, "id": "a142fac0", "metadata": {}, "outputs": [], "source": [ "# The RBF network with SGD+regulariztion and bias term\n", "class RBFNetworkSGD:\n", " def __init__(self, n_centers=10, sigma=None, lambda_reg=0.01, learning_rate=0.01, epochs=100):\n", " \"\"\"\n", " Parameters:\n", " - n_centers: Number of RBF neurons (int)\n", " - sigma: Width of RBFs (float). If None, computed automatically.\n", " - lambda_reg: L2 regularization strength (float)\n", " - learning_rate: SGD step size (float)\n", " - epochs: Number of training passes (int)\n", " \"\"\"\n", " self.n_centers = n_centers\n", " self.sigma = sigma\n", " self.lambda_reg = lambda_reg\n", " self.learning_rate = learning_rate\n", " self.epochs = epochs\n", " self.centers = None\n", " self.weights = None # Includes bias as last element (w_K+1)\n", " self.loss_history = []\n", "\n", " def _rbf_activation(self, X):\n", " \"\"\"Compute RBF activations (without bias term). Shape: (N, K)\"\"\"\n", " r = cdist(X, self.centers)\n", " return np.exp(-0.5 * (r ** 2) / (self.sigma ** 2))\n", "\n", " def fit(self, X, y):\n", " # Step 1: Initialize RBF centers using K-means\n", " kmeans = KMeans(n_clusters=self.n_centers,n_init='auto')\n", " kmeans.fit(X)\n", " self.centers = kmeans.cluster_centers_\n", "\n", " # Step 2: Set RBF width if not provided\n", " if self.sigma is None:\n", " D = cdist(self.centers, self.centers)\n", " np.fill_diagonal(D, np.inf) # Ignore self-distance\n", " self.sigma = np.mean(np.min(D, axis=1)) # Avg dist to nearest center\n", "\n", " # Step 3: Initialize weights (including bias)\n", " self.weights = np.random.randn(self.n_centers + 1) * 0.01 # K weights + 1 bias\n", "\n", " # Step 4: SGD Training\n", " n_samples = len(X) \n", " \n", " for epoch in range(self.epochs):\n", " epoch_loss = 0\n", " for i in range(n_samples):\n", " # Compute RBF activations for the current sample using _rbf_activation\n", " phi_i = self._rbf_activation(X[i].reshape(1, -1)).flatten() # Shape: (K,)\n", " \n", " # Add bias term (1.0) to create extended activation vector\n", " phi_i_plus = np.append(phi_i, 1.0) # Shape: (K + 1,)\n", " \n", " # Compute error\n", " error = np.dot(self.weights, phi_i_plus) - y[i]\n", " \n", " # Update weights (with L2 regularization excluding bias)\n", " self.weights -= self.learning_rate * (\n", " error * phi_i_plus + self.lambda_reg * np.append(self.weights[:-1],0.))\n", "\n", " # Accumulate loss (MSE + L2)\n", " epoch_loss += 0.5 * error ** 2\n", "\n", " # Record average epoch loss\n", " epoch_loss = epoch_loss / n_samples + 0.5 * self.lambda_reg * np.sum(self.weights[:-1] ** 2)\n", " self.loss_history.append(epoch_loss)\n", "\n", " # Print progress\n", " if epoch % 10 == 0:\n", " print(f\"Epoch {epoch:4d}, Loss: {epoch_loss:.4f}\")\n", "\n", " def predict(self, X):\n", " \"\"\"Predict outputs for new inputs.\"\"\"\n", " # Compute RBF activations and add bias term\n", " phi = self._rbf_activation(X)\n", " phi_plus = np.column_stack([phi, np.ones(len(X))]) # Shape: (N, K + 1)\n", " return phi_plus @ self.weights" ] }, { "cell_type": "code", "execution_count": 3, "id": "54d312e3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Epoch 0, Loss: 0.0692\n", "Epoch 10, Loss: 0.0297\n", "Epoch 20, Loss: 0.0295\n", "Epoch 30, Loss: 0.0295\n", "Epoch 40, Loss: 0.0295\n", "Epoch 50, Loss: 0.0295\n", "Epoch 60, Loss: 0.0295\n", "Epoch 70, Loss: 0.0295\n", "Epoch 80, Loss: 0.0295\n", "Epoch 90, Loss: 0.0295\n", "Epoch 100, Loss: 0.0295\n", "Epoch 110, Loss: 0.0295\n", "Epoch 120, Loss: 0.0295\n", "Epoch 130, Loss: 0.0295\n", "Epoch 140, Loss: 0.0295\n", "Epoch 150, Loss: 0.0295\n", "Epoch 160, Loss: 0.0295\n", "Epoch 170, Loss: 0.0295\n", "Epoch 180, Loss: 0.0295\n", "Epoch 190, Loss: 0.0295\n" ] }, { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Generate synthetic data\n", "X = np.linspace(0, 10, 100).reshape(-1, 1)\n", "y = np.sin(X.flatten()) + 0.1 * np.random.randn(100)\n", "\n", "# Initialize and train\n", "model = RBFNetworkSGD(\n", " n_centers=10,\n", " sigma=None,\n", " lambda_reg=0.02,\n", " learning_rate=0.05,\n", " epochs=200,)\n", "\n", "model.fit(X, y)\n", "\n", "# Predictions\n", "X_test = np.linspace(0, 10, 200).reshape(-1, 1)\n", "y_pred = model.predict(X_test)\n", "\n", "# Plot results\n", "plt.figure(figsize=(10, 5))\n", "plt.scatter(X, y, label=\"Training Data\", alpha=0.6)\n", "plt.plot(X_test, y_pred, 'r-', label=\"RBF Network Prediction\", linewidth=2)\n", "plt.title(\"RBF Network with SGD Training\")\n", "plt.xlabel(\"Input (x)\")\n", "plt.ylabel(\"Output (y)\")\n", "plt.legend()\n", "plt.grid(True)\n", "plt.show()\n", "\n", "# Plot training loss\n", "plt.figure(figsize=(10, 4))\n", "plt.plot(model.loss_history)\n", "plt.title(\"Training Loss (MSE + L2)\")\n", "plt.xlabel(\"Epoch\")\n", "plt.ylabel(\"Loss\")\n", "plt.grid(True)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "5fba0e71", "metadata": {}, "outputs": [], "source": [] } ], "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": "3.11.1" } }, "nbformat": 4, "nbformat_minor": 5 }