{ "cells": [ { "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\n", "import umap\n", "\n", "np.random.seed(32423)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Dimensionality reduction\n", "\n", "This notebook will present some of the main methodologies used to reduce dimensionality in a dataset.\n", "\n", "__add details on reasons for dr__" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The curse of dimensionality\n", "\n", "In many tasks related to machine learning, statistics, numerical analysis and data mining, problems arise when the dimensionality of the space (e.g. the feature space) increases to large numbers (> ~100-1000).\n", "\n", "The common underlying factor to these \"cursed\" phenomena is that when the space dimensionality increases, the volume increases so fast that most of the data becomes sparse. This sparsity becomes a significant burden for computational reasons and for tasks that rely on statistical significance" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "cd_data = np.random.rand(3, 32)\n", "\n", "fig = plt.figure(figsize=(16, 6))\n", "ax = [_]*3\n", "ax[0] = fig.add_subplot(1, 3, 1)\n", "ax[1] = fig.add_subplot(1, 3, 2)\n", "ax[2] = fig.add_subplot(1, 3, 3,projection='3d')\n", "\n", "ax[0].scatter(cd_data[0,:16], [0]*16, c=\"red\")\n", "ax[0].scatter(cd_data[0,16:], [0]*16, c=\"blue\")\n", "ax[0].set_xticks(np.arange(0, 1.1, 0.25))\n", "ax[0].grid(axis=\"x\")\n", "ax[0].set_title(\"1D: 4 regions\")\n", "\n", "\n", "ax[1].scatter(cd_data[0,:16], cd_data[1,:16], c=\"red\")\n", "ax[1].scatter(cd_data[0,16:], cd_data[1,16:], c=\"blue\")\n", "ax[1].set_xticks(np.arange(0, 1.1, 0.25))\n", "ax[1].set_yticks(np.arange(0, 1.1, 0.25))\n", "ax[1].grid(axis=\"both\")\n", "ax[1].set_title(\"2D: 16 regions\")\n", "\n", "\n", "\n", "ax[2].scatter(cd_data[0,:16], cd_data[1,:16], cd_data[2,:16], c=\"red\")\n", "ax[2].scatter(cd_data[0,16:], cd_data[1,16:], cd_data[2,16:], c=\"blue\")\n", "ax[2].set_xticks(np.arange(0, 1.1, 0.25))\n", "ax[2].set_yticks(np.arange(0, 1.1, 0.25))\n", "ax[2].set_zticks(np.arange(0, 1.1, 0.25))\n", "ax[2].set_title(\"3D: 64 regions\")\n", "ax[2].dist = 10\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In each unit region (strip, square, cube respectively) of the previous visualization are contained different amounts of datapoints. While each region of the 1D plot contains several points, each cube of the 3D plot contains only a few at most. This problem exacerbates as the number of dimensions increases." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Dimensionality reduction methods\n", "\n", "In general, dimensionality reduction techniques can be divided into two main categories: *feature selection*, and *feature projection/mapping*. \n", "\n", "\n", "__Feature selection__ is the selection of a subset of the original features, which means that the features present in the final subset are unaltered.\n", "\n", "__Feature extraction__ transforms the high-dimensional feature representation to a lower dimensional one, in which each new feature is some combination of one or more of the original features.\n", "\n", "\n", "This notebook is focused on this latter category of algorithms." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.7.6" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }