{ "cells": [ { "cell_type": "markdown", "id": "c55e7f27-9b86-4222-95f3-17b251b81f95", "metadata": { "tags": [] }, "source": [ "# Homework 1\n", "\n", "Due Thursday, September 12 by 11:59 PM via Blackboard.\n", "\n", "This homework will give you experience using Python notebooks, scikit learn, the Digits dataset, and Perceptrons. You'll also think about what learned weights tell you about the underlying data. \n", "\n", "Here's what to do:\n", "* Open this notebook either in Google's Colab or download it to your local machine and run Jupyter there.\n", "* Read through the documentation and code below to get familiar with what's here.\n", "* In cells that start with \"Task ...\" you'll find instructions on what to do. You'll write a couple of lines of code and repond to a few questions.\n", "* Add cells to the notebook as needed for code, and create markdown cells for text that you write.\n", "* When you're done, send a copy of the notebook in ipynb form to the TA via slack." ] }, { "cell_type": "markdown", "id": "5299668e-1085-4132-abd3-e99be149e319", "metadata": {}, "source": [ "## Task 0: Learn about Python notebooks\n", "\n", "If you're new to notebooks, there are lots of good resources on the web. Here's one that will get you started:\n", "\n", "https://realpython.com/jupyter-notebook-introduction/" ] }, { "cell_type": "code", "execution_count": 1, "id": "249b6ab3-ed7d-49c6-a426-7ba91653300c", "metadata": {}, "outputs": [], "source": [ "# Imports\n", "\n", "from sklearn.linear_model import Perceptron\n", "from sklearn.preprocessing import MinMaxScaler\n", "from sklearn.datasets import load_digits\n", "import matplotlib.pyplot as plt\n", "from sklearn.model_selection import train_test_split" ] }, { "cell_type": "code", "execution_count": 2, "id": "6fcbd5b6-eb94-4b85-89f1-94a2ec2fccde", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Digit = 0\n" ] }, { "data": { "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Digit = 1\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Digit = 2\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Digit = 3\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Digit = 4\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Digit = 5\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Digit = 6\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Digit = 7\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Digit = 8\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Digit = 9\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Load the digits dataset and look at a few examples\n", "\n", "digits = load_digits()\n", "plt.gray()\n", "\n", "for i in range(10):\n", " print('Digit = %d' % i)\n", " plt.matshow(digits.images[i])\n", " plt.show()\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "1aae5e44-8d71-455d-8892-e399b9a7a93c", "metadata": {}, "outputs": [], "source": [ "# Get the attribute vectors and the class labels\n", "\n", "X = digits.data\n", "y = digits.target" ] }, { "cell_type": "code", "execution_count": 4, "id": "680aba53-c977-4239-92db-916b9f869ca6", "metadata": {}, "outputs": [], "source": [ "# Convert 10 digit problem to one in which the goal is to tell if a digit is\n", "# 0 or not 0\n", "\n", "y = [1 if a == 0 else 0 for a in y]" ] }, { "cell_type": "markdown", "id": "128dee30-8848-411b-88cb-214af75977b4", "metadata": {}, "source": [ "## Task 1: Read about scikit's train/test splitter\n", "\n", "https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.train_test_split.html" ] }, { "cell_type": "code", "execution_count": 5, "id": "d8b2b79c-c71e-43d6-9fe7-b02999658d95", "metadata": {}, "outputs": [], "source": [ "# Split the data into a training set and a test set\n", "\n", "X_train, X_test, y_train, y_test = train_test_split(X, y, \n", " test_size=0.5, \n", " random_state=42)" ] }, { "cell_type": "markdown", "id": "da381813-439e-400b-bf3d-68b454e01615", "metadata": {}, "source": [ "## Task 2: Run the perceptron implementation from scikit\n", "\n", "Read the manual page for scikit's Perceptron class here:\n", "\n", "https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.Perceptron.html\n", "\n", "Below, write code to:\n", "* Train the perceptron on the training data using the fit() function\n", "* Print out the training set accuracy using the score() function\n", "* Print out the testing set accuracy using the score() function\n", "\n", "Briefly explain what the accuracies tell you about the difficulty of this problem and why the two accuracies are different." ] }, { "cell_type": "code", "execution_count": 6, "id": "f860cdb5-2fd7-4502-ab7c-2f67b979da1d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.0\n", "0.9933259176863182\n" ] } ], "source": [ "# YOUR CODE HERE\n", "\n", "# If you name your classifier object clf as below then the code for the next task \n", "# not need to be modified." ] }, { "cell_type": "markdown", "id": "b653662c-fc54-4e5a-a6f2-14ad07002cc2", "metadata": {}, "source": [ "## Task 3: Use the code below to show a visualization of the learned weights. \n", "\n", "The magnitude of the weight is conveyed by the grayscale intesity. Black means large negative weights and white means large positive weights. Note that all of the features, pixels, are positive. Also, the weights will be arranged in the image such that they get multiplied by the pixel in the digit at the same location in the digit image.\n", "\n", "Briefly explain why the learned weights make sense for the task of classifying zero digits as the positive class and all other digits as the negative class." ] }, { "cell_type": "code", "execution_count": 7, "id": "8b2a4f21-240f-4ac0-8c82-06e98292cd39", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# This cell will throw an error until you write the code above to train the perceptron\n", "plt.matshow(clf.coef_.reshape(8,8))" ] }, { "cell_type": "code", "execution_count": null, "id": "8f0df17a-7f01-43d8-af34-4011b507888e", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "1abe40be-08d7-421e-a12a-69429e57e5b6", "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": "3.12.4" } }, "nbformat": 4, "nbformat_minor": 5 }