From 77753feae1b590b35e1ecbe8c0b735fbf894b3d3 Mon Sep 17 00:00:00 2001 From: Oleksii Trekhleb Date: Thu, 20 Dec 2018 16:37:24 +0200 Subject: [PATCH] Add multilayer perceptron. --- homemade/neural_network/README.md | 2 + .../multilayer_perceptron_demo.ipynb | 110 ++++++++++++++++-- 2 files changed, 104 insertions(+), 8 deletions(-) diff --git a/homemade/neural_network/README.md b/homemade/neural_network/README.md index c4d67a2..fcfcddb 100644 --- a/homemade/neural_network/README.md +++ b/homemade/neural_network/README.md @@ -20,6 +20,8 @@ In common ANN implementations, the signal at a connection between artificial neu ![Neural Network](https://upload.wikimedia.org/wikipedia/commons/4/46/Colored_neural_network.svg) +A **multilayer perceptron (MLP)** is a class of feedforward artificial neural network. An MLP consists of, at least, three layers of nodes: an input layer, a hidden layer and an output layer. Except for the input nodes, each node is a neuron that uses a nonlinear activation function. MLP utilizes a supervised learning technique called backpropagation for training. Its multiple layers and non-linear activation distinguish MLP from a linear perceptron. It can distinguish data that is not linearly separable. + ## Neuron Model (Logistic Unit) Here is a model of one neuron unit. diff --git a/notebooks/neural_network/multilayer_perceptron_demo.ipynb b/notebooks/neural_network/multilayer_perceptron_demo.ipynb index f673250..f024743 100644 --- a/notebooks/neural_network/multilayer_perceptron_demo.ipynb +++ b/notebooks/neural_network/multilayer_perceptron_demo.ipynb @@ -1,5 +1,22 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Neural Network (Multilayer Perceptron) Demo\n", + "\n", + "> ☝Before moving on with this demo you might want to take a look at:\n", + "> - 📗[Math behind the Neural Networks](https://github.com/trekhleb/homemade-machine-learning/tree/master/homemade/neural_network)\n", + "> - ⚙️[Neural Network Source Code](https://github.com/trekhleb/homemade-machine-learning/blob/master/homemade/neural_network/multilayer_perceptron.py)\n", + "\n", + "**Artificial neural networks (ANN)** or connectionist systems are computing systems vaguely inspired by the biological neural networks that constitute animal brains. The neural network itself isn't an algorithm, but rather a framework for many different machine learning algorithms to work together and process complex data inputs. Such systems \"learn\" to perform tasks by considering examples, generally without being programmed with any task-specific rules.\n", + "\n", + "A **multilayer perceptron (MLP)** is a class of feedforward artificial neural network. An MLP consists of, at least, three layers of nodes: an input layer, a hidden layer and an output layer. Except for the input nodes, each node is a neuron that uses a nonlinear activation function. MLP utilizes a supervised learning technique called backpropagation for training. Its multiple layers and non-linear activation distinguish MLP from a linear perceptron. It can distinguish data that is not linearly separable.\n", + "\n", + "> **Demo Project:** In this example we will train handwritten digits (0-9) classifier using simple multilayer perceptron." + ] + }, { "cell_type": "code", "execution_count": 1, @@ -465,7 +482,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ @@ -479,7 +496,7 @@ "test_data = pd_test_data.values\n", "\n", "# Extract training/test labels and features.\n", - "num_training_examples = 3000\n", + "num_training_examples = 5000\n", "x_train = train_data[:num_training_examples, 1:]\n", "y_train = train_data[:num_training_examples, [0]]\n", "\n", @@ -487,14 +504,29 @@ "y_test = test_data[:, [0]]" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Init and Train MLP Model\n", + "\n", + "> ☝🏻This is the place where you might want to play with model configuration.\n", + "\n", + "- `layers` - configuration of the multilayer perceptron layers (array of numbers where every number represents the number of nayron in specific layer).\n", + "- `max_iterations` - this is the maximum number of iterations that gradient descent algorithm will use to find the minimum of a cost function. Low numbers may prevent gradient descent from reaching the minimum. High numbers will make the algorithm work longer without improving its accuracy.\n", + "- `regularization_param` - parameter that will fight overfitting. The higher the parameter, the simplier is the model will be.\n", + "- `normalize_data` - boolean flag that indicates whether data normalization is needed or not.\n", + "- `alpha` - the size of gradient descent steps. You may need to reduce the step size if gradient descent can't find the cost function minimum. " + ] + }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 6, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -514,7 +546,7 @@ "];\n", "normalize_data = True # Flag that detects whether we want to do features normalization or not.\n", "epsilon = 0.12 # Defines the range for initial theta values.\n", - "max_iterations = 100 # Max number of gradient descent iterations.\n", + "max_iterations = 500 # Max number of gradient descent iterations.\n", "regularization_param = 1 # Helps to fight model overfitting.\n", "alpha = 0.1 # Gradient descent step size.\n", "\n", @@ -541,15 +573,15 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Training Precision: 81.8667%\n", - "Test Precision: 79.6000%\n" + "Training Precision: 93.5400%\n", + "Test Precision: 90.1500%\n" ] } ], @@ -565,6 +597,68 @@ "print('Training Precision: {:5.4f}%'.format(train_precision))\n", "print('Test Precision: {:5.4f}%'.format(test_precision))" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Plot Test Dataset Predictions\n", + "\n", + "In order to illustrate how our model classifies unknown examples let's plot first 64 predictions for testing dataset. All green digits on the plot below have been recognized corrctly but all the red digits have not been recognized correctly by our classifier. On top of each digit image you may see the class (the number) that has been recognized on the image." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# How many numbers to display.\n", + "numbers_to_display = 64\n", + "\n", + "# Calculate the number of cells that will hold all the numbers.\n", + "num_cells = math.ceil(math.sqrt(numbers_to_display))\n", + "\n", + "# Make the plot a little bit bigger than default one.\n", + "plt.figure(figsize=(15, 15))\n", + "\n", + "# Go through the first numbers in a test set and plot them.\n", + "for plot_index in range(numbers_to_display):\n", + " # Extrace digit data.\n", + " digit_label = y_test[plot_index, 0]\n", + " digit_pixels = x_test[plot_index, :]\n", + " \n", + " # Predicted label.\n", + " predicted_label = y_test_predictions[plot_index][0]\n", + "\n", + " # Calculate image size (remember that each picture has square proportions).\n", + " image_size = int(math.sqrt(digit_pixels.shape[0]))\n", + " \n", + " # Convert image vector into the matrix of pixels.\n", + " frame = digit_pixels.reshape((image_size, image_size))\n", + " \n", + " # Plot the number matrix.\n", + " color_map = 'Greens' if predicted_label == digit_label else 'Reds'\n", + " plt.subplot(num_cells, num_cells, plot_index + 1)\n", + " plt.imshow(frame, cmap=color_map)\n", + " plt.title(predicted_label)\n", + " plt.tick_params(axis='both', which='both', bottom=False, left=False, labelbottom=False, labelleft=False)\n", + "\n", + "# Plot all subplots.\n", + "plt.subplots_adjust(hspace=0.5, wspace=0.5)\n", + "plt.show()" + ] } ], "metadata": {