UDA Manifold Learning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# UDA Manifold Learning\n",
    "\n",
    "Author: George H. Chen (georgechen [at symbol] cmu.edu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('seaborn-v0_8')\n",
    "%config InlineBackend.figure_format = 'retina'  # if you use a Mac with Retina display\n",
    "np.set_printoptions(precision=2, suppress=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multi-dimensional scaling (MDS)\n",
    "\n",
    "Given a table of pairwise distances, MDS finds points that approximately have those pairwise distances. MDS is used within the Isomap algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1D coordinates:\n",
      "[[ 6.4]\n",
      " [ 6.6]\n",
      " [-0. ]\n",
      " [-4.6]\n",
      " [-8.4]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x550 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 466,
       "width": 684
      }
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "1D distance table:\n",
      "[[ 0.   0.2  6.4 11.  14.8]\n",
      " [ 0.2  0.   6.6 11.2 15. ]\n",
      " [ 6.4  6.6  0.   4.6  8.4]\n",
      " [11.  11.2  4.6  0.   3.8]\n",
      " [14.8 15.   8.4  3.8  0. ]]\n"
     ]
    }
   ],
   "source": [
    "point_names = ['A', 'B', 'C', 'D', 'E']\n",
    "distances = np.array([[0, 5, 8, 13, 16],\n",
    "                      [5, 0, 5, 10, 13],\n",
    "                      [8, 5, 0, 5, 8],\n",
    "                      [13, 10, 5, 0, 5],\n",
    "                      [16, 13, 8, 5, 0]])\n",
    "\n",
    "from sklearn.manifold import MDS\n",
    "\n",
    "# remove random_state=0 and re-running gives you different 1D representations of A, B, C, D, E\n",
    "mds = MDS(n_components=1, dissimilarity='precomputed', random_state=0)\n",
    "low_dimensional_points = mds.fit_transform(distances)\n",
    "print('1D coordinates:')\n",
    "print(low_dimensional_points)\n",
    "\n",
    "# plotting code (same idea as how we did the 1D PCA plot in the earlier demo)\n",
    "plt.scatter(low_dimensional_points,\n",
    "            np.zeros(len(low_dimensional_points)))\n",
    "for idx in range(len(point_names)):\n",
    "    plt.annotate(point_names[idx], (low_dimensional_points[idx], 0))\n",
    "plt.show()\n",
    "\n",
    "# this shows you the low-dimensional distance table:\n",
    "# - `pdist` computes pairwise distances between points, storing the results in a compact format\n",
    "# - `squareform` converts the compact format into a 2D distance table like the ones from lecture\n",
    "from scipy.spatial.distance import pdist, squareform\n",
    "low_dimensional_distances = squareform(pdist(low_dimensional_points))\n",
    "print()\n",
    "print('1D distance table:')\n",
    "print(low_dimensional_distances)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Isomap\n",
    "\n",
    "In practice, if you want to use Isomap, you don't need to write the MDS code yourself. Instead, you would use Isomap as follows (and Isomap's fitting procedure will do MDS under the hood without telling you about it):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# goes from outside to inside of the Swiss roll\n",
    "swiss_roll_2d = np.array([[479, -231],\n",
    "                          [515, -237],\n",
    "                          [551, -233],\n",
    "                          [581, -255],\n",
    "                          [597, -284],\n",
    "                          [610, -313],\n",
    "                          [619, -341],\n",
    "                          [623, -368],\n",
    "                          [617, -407],\n",
    "                          [591, -434],\n",
    "                          [573, -468],\n",
    "                          [542, -478],\n",
    "                          [507, -490],\n",
    "                          [471, -482],\n",
    "                          [437, -462],\n",
    "                          [398, -446],\n",
    "                          [383, -408],\n",
    "                          [403, -373],\n",
    "                          [430, -349],\n",
    "                          [470, -326],\n",
    "                          [507, -320],\n",
    "                          [531, -352],\n",
    "                          [527, -385],\n",
    "                          [487, -397]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(24, 2)\n"
     ]
    }
   ],
   "source": [
    "print(swiss_roll_2d.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 800x550 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 466,
       "width": 681
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(swiss_roll_2d[:, 0], swiss_roll_2d[:, 1],\n",
    "            c=list(range(len(swiss_roll_2d))),\n",
    "            cmap='Spectral')\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(n_components=1)\n",
    "swiss_roll_1d_pca = pca.fit_transform(swiss_roll_2d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_1d(data_1d, y_offset=-0.001):\n",
    "    plt.scatter(data_1d, np.zeros(len(data_1d)),\n",
    "                c=list(range(len(data_1d))), cmap='Spectral')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x550 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 466,
       "width": 684
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_1d(swiss_roll_1d_pca)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x550 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 466,
       "width": 684
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.manifold import Isomap\n",
    "\n",
    "isomap = Isomap(n_neighbors=2, n_components=1)\n",
    "swiss_roll_1d_isomap = isomap.fit_transform(swiss_roll_2d)\n",
    "plot_1d(swiss_roll_1d_isomap)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x550 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 466,
       "width": 684
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bad_isomap = Isomap(n_neighbors=23, n_components=1)\n",
    "swiss_roll_1d_bad_isomap = bad_isomap.fit_transform(swiss_roll_2d)\n",
    "\n",
    "plot_1d(swiss_roll_1d_bad_isomap)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# t-SNE\n",
    "\n",
    "In terms of using other manifold learning algorithms that scikit-learn provides, the code is similar to using PCA and Isomap; however, different methods have different parameters that you do have to play with. One of the most popular manifold learning methods used in practice is t-SNE. Here's an example usage case:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[t-SNE] Computing 10 nearest neighbors...\n",
      "[t-SNE] Indexed 24 samples in 0.000s...\n",
      "[t-SNE] Computed neighbors for 24 samples in 0.001s...\n",
      "[t-SNE] Computed conditional probabilities for sample 24 / 24\n",
      "[t-SNE] Mean sigma: 40.764802\n",
      "[t-SNE] KL divergence after 250 iterations with early exaggeration: 49.031513\n",
      "[t-SNE] KL divergence after 1000 iterations: 0.230493\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x550 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 466,
       "width": 684
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.manifold import TSNE\n",
    "\n",
    "# *WARNING*: *despite* what the sklearn documentation says for t-SNE, the perplexity parameter\n",
    "# does matter! a helpful article to read: https://distill.pub/2016/misread-tsne/\n",
    "tsne = TSNE(n_components=1, perplexity=3, learning_rate=0.1, max_iter=1000, init='random', verbose=1, random_state=0)\n",
    "swiss_roll_1d_tsne = tsne.fit_transform(swiss_roll_2d)\n",
    "plot_1d(swiss_roll_1d_tsne)"
   ]
  }
 ],
 "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": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}