__MACOSX/._A5_programming A5_programming/.DS_Store __MACOSX/A5_programming/._.DS_Store __MACOSX/A5_programming/._test __MACOSX/A5_programming/._train __MACOSX/A5_programming/._.ipynb_checkpoints...

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Machine learning assignment need to be done 6pm AEDT 25th Oct. Basically need those tasks done in the jupyter notebook file. Training and testing data to be provided later.


__MACOSX/._A5_programming A5_programming/.DS_Store __MACOSX/A5_programming/._.DS_Store __MACOSX/A5_programming/._test __MACOSX/A5_programming/._train __MACOSX/A5_programming/._.ipynb_checkpoints A5_programming/C3670_ass5.ipynb { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "**COMP3670 Assignment 5 - Matrix Decomposition & Dimensionality Reduction**\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Enter Your Student ID:**\n", "\n", "**Your Name:** \n", " \n", "\n", "**Submit:** You can write your answers in this file and submit a single Jupyter Notebook file (.ipynb) on Wattle. Rename this file with your student number as 'uXXXXXXX.ipynb'. Otherwise, you can write your programming questions in this file, and submit two files, 'uXXXXXXX.ipynb' for programming and 'uXXXXXXX.pdf' for theory. Please submit them separately instead of a zip file.\n", " \n", "**Enter Discussion Partner IDs Below:**\n", "- \n", "- \n", "- \n", " \n", "\n", "**Programming Section**\n", "- 1 = 10%\n", "- 2 = 15%\n", "- 3 = 30%\n", "- 4 = 10%\n", "- 5 = 20%\n", "- 6 = 15%" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "\n", "**PROGRAMMING SECTION**\n", "---\n", "\n", "For all of the following, program the solution yourself. Don't just call a library function that does the whole question for you, or you'll get zero (no, that doesn't mean you can't use any library functions, but it does mean that you have to show you understand how to compute the answer yourself).\n", "\n", "**All written answers** should be between 50 and 500 words. If you can describe all the necessary information in 50 words, that's better. However, you'll only be graded on whether you describe the necessary ideas.\n", "\n", "\n", "-----------\n", "\n", " **TASK 0.1:** You know the drill. Import Numpy and PyPlot. We're also going to generate a dataset.\n", "\n", "\n", "-----------" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D #This is for 3d scatter plots.\n", "import math\n", "import random\n", "from scipy.stats import multivariate_normal\n", "import os\n", "from matplotlib.pyplot import imread\n", "np.random.seed(13579201)\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(77760, 135)\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "width = 320\n", "height = 243\n", "images = []\n", "for file in os.listdir(\"./train\"):\n", " if file.endswith(\".pgm\"):\n", " im = imread(\"./train/\" + file)\n", " im = im.flatten('F') # flatten im into a vector\n", " images.append(im) \n", "A_pp = np.stack(images).T # build a matrix where each column is a flattened image\n", "print(A_pp.shape)\n", "plt.imshow(A_pp[:, 134].reshape(width, height).T)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "PROGRAMMING EXERCISE 1 \n", "-----------\n", "\n", "---\n", " **TASK 1.1:** Complete the function $laplace\\_expansion(A) = |A|$, where $A \\in \\mathbb{R}^{N \\times N}$, and $|A|$ is the determinant of $A$.\n", " \n", "**HINT:**\n", "- One way to find the determinant is to implement the Laplace Expansion algorithm. This is described in the matrix decomposition lecture slides.\n", "- $|A| \\neq 0$ iff $A$ is invertible.\n", "---\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "def det(A):\n", " # WRITE CODE HERE\n", " return det_A\n", "\n", "print(det(np.eye(2)))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "**TASK 1.2:** Let $A\\_{pp} \\in \\mathbb{R}^{D \\times N}$ be a matrix of data. Each column of $A\\_{pp}$ is a sample of data (1 training example for instance). The rows of $A\\_{pp}$ are thus the features (dimensions) of each of these samples. Complete the function $preprocess(A\\_{pp}) = A, Q\\_norms, A\\_means$, for which:\n", "\n", "$$Q_{i,:} = A\\_{pp}_{i,:} - \\mu_i$$\n", "\n", "...where $\\mu_i = \\frac{1}{m}\\sum_j A\\_{pp}_{ij}$ .\n", "\n", "$$A_{i,:} = \\frac{Q_{i,:}}{||Q_{i,:}||_\\infty }$$\n", "\n", "\n", "$A \\in \\mathbb{R}^{D \\times N}$\n", "\n", "$Q_{i,:}$ is the $i^{th}$ row of $Q$.\n", "\n", "$A_{i,:}$ is the $i^{th}$ row of $A$.\n", "\n", "$||Q_{i,:}||_\\infty$ is the infinity norm of $Q_{i,:}$.\n", "\n", "$Q\\_norms \\in \\mathbb{R}^{D}$ is a vector recording $||Q_{i,:}||_\\infty$ for every feature dimension $i$.\n", "\n", "$A\\_means \\in \\mathbb{R}^{D}$ is a vector recording $\\mu_i$ for every feature dimension $i$.\n", "\n", "\n", "**HINT:** \n", "- If the norm is 0, divide by 1 instead.\n", "\n", "---" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "def preprocess(A_pp):\n", " # WRITE CODE HERE\n", " return A, Q_norms, mu\n", "\n", "A, Q_norms, A_means = preprocess(A_pp)\n", "print(A)\n", "print(Q_norms)\n", "print(A_means)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "$A \\in \\mathbb{R}^{D \\times N}$ as above is a matrix of data where every column is a sample of data, and every row is a feature of that data. In this case, we're going to be working with images. Each column $A_{:,j}$ of $A$ is an image of a face. \n", "\n", "\"But an image is a square grid\" you might be thinking. Well, we've simply taken every column of the image and stacked them vertically, converting a $320$ column $ \\times 243$ row pixel image into a $77760 \\times 1$ dimensional vector.\n", "\n", "Hence $D = 77760$ and we have $N = 135$ images.\n", "\n", "According to our lecture, we should first compute the covariance matrix $AA^T$, and then calculate the eigenvalues and eigenvectors of this covariance matrix. However, in our case, $AA^T$ is a $77760 \\times 77760$ dimensional matrix. \n", "\n", "Luckily, our lecture introduces an efficient method to work with such high-dimensional data. \n", "\n", "That is, we have the choice of either
Answered Same DayOct 24, 2021Australian National University

Answer To: __MACOSX/._A5_programming A5_programming/.DS_Store __MACOSX/A5_programming/._.DS_Store...

Sandeep Kumar answered on Nov 24 2021
149 Votes
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**COMP3670 Assignment 5 - Matrix Decomposition & Dimensionality Reduction**\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**En
ter Your Student ID:**\n",
"\n",
"**Your Name:** \n",
" \n",
"\n",
"**Submit:** You can write your answers in this file and submit a single Jupyter Notebook file (.ipynb) on Wattle. Rename this file with your student number as 'uXXXXXXX.ipynb'. Otherwise, you can write your programming questions in this file, and submit two files, 'uXXXXXXX.ipynb' for programming and 'uXXXXXXX.pdf' for theory. Please submit them separately instead of a zip file.\n",
" \n",
"**Enter Discussion Partner IDs Below:**\n",
"- \n",
"- \n",
"- \n",
" \n",
"\n",
"**Programming Section**\n",
"- 1 = 10%\n",
"- 2 = 15%\n",
"- 3 = 30%\n",
"- 4 = 10%\n",
"- 5 = 20%\n",
"- 6 = 15%"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"\n",
"**PROGRAMMING SECTION**\n",
"---\n",
"\n",
"For all of the following, program the solution yourself. Don't just call a library function that does the whole question for you, or you'll get zero (no, that doesn't mean you can't use any library functions, but it does mean that you have to show you understand how to compute the answer yourself).\n",
"\n",
"**All written answers** should be between 50 and 500 words. If you can describe all the necessary information in 50 words, that's better. However, you'll only be graded on whether you describe the necessary ideas.\n",
"\n",
"\n",
"-----------\n",
"\n",
" **TASK 0.1:** You know the drill. Import Numpy and PyPlot. We're also going to generate a dataset.\n",
"\n",
"\n",
"-----------"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from mpl_toolkits.mplot3d import Axes3D #This is for 3d scatter plots.\n",
"import math\n",
"import random\n",
"from scipy.stats import multivariate_normal\n",
"import os\n",
"from matplotlib.pyplot import imread\n",
"np.random.seed(13579201)\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(77760, 135)\n"
]
},
{
"data": {
"image/png":...
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