95-865 Manifold Learning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 95-865: 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",
    "%matplotlib inline\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)\n",
    "\n",
    "# these next three lines are needed on my old Intel Mac laptop due to some weird software update issue\n",
    "import os\n",
    "import psutil\n",
    "os.environ['LOKY_MAX_CPU_COUNT'] = str(psutil.cpu_count(logical=False))"
   ]
  },
  {
   "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": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/georgehc/anaconda3/lib/python3.11/site-packages/sklearn/manifold/_mds.py:298: FutureWarning: The default value of `normalized_stress` will change to `'auto'` in version 1.4. To suppress this warning, manually set the value of `normalized_stress`.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1D coordinates:\n",
      "[[ 6.4]\n",
      " [ 6.6]\n",
      " [ 0. ]\n",
      " [-4.6]\n",
      " [-8.4]]\n",
      "\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"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x550 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 466,
       "width": 684
      }
     },
     "output_type": "display_data"
    }
   ],
   "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",
    "\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": {
      "text/plain": [
       "(371.0, 635.0, -502.95, -218.05)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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], c=list(range(len(swiss_roll_2d))), cmap='Spectral')\n",
    "plt.axis('equal')"
   ]
  },
  {
   "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')"
   ]
  },
  {
   "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": "markdown",
   "metadata": {},
   "source": [
    "In case you are wondering what distance matrix Isomap computed (using the nearest neighbor graph) to use with Isomap, you can print it out as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  0.    36.5   72.03 109.23 142.35 174.13 203.54 230.84 270.3  307.78\n",
      "  346.25 378.82 415.82 452.7  492.15 534.3  575.16 615.47 651.59 697.73\n",
      "  735.22 775.22 808.46 838.15]\n",
      " [ 36.5    0.    36.22  73.42 106.54 138.33 167.74 195.03 234.49 271.97\n",
      "  310.44 343.02 380.02 416.89 456.34 498.5  539.35 579.66 615.78 661.93\n",
      "  699.41 739.41 772.65 802.35]\n",
      " [ 72.03  36.22   0.    37.2   70.32 102.1  131.51 158.81 198.27 235.75\n",
      "  274.22 306.8  343.8  380.67 420.12 462.27 503.13 543.44 579.56 625.7\n",
      "  663.19 703.19 736.43 766.12]\n",
      " [109.23  73.42  37.2    0.    33.12  64.9   94.31 121.61 161.07 198.55\n",
      "  237.02 269.59 306.59 343.47 382.92 425.07 465.93 506.24 542.36 588.5\n",
      "  625.99 665.99 699.23 728.92]\n",
      " [142.35 106.54  70.32  33.12   0.    31.78  61.19  88.49 127.94 165.43\n",
      "  203.9  236.47 273.47 310.35 349.8  391.95 432.8  473.12 509.24 555.38\n",
      "  592.86 632.86 666.11 695.8 ]\n",
      " [174.13 138.33 102.1   64.9   31.78   0.    29.41  56.71  96.16 133.65\n",
      "  172.12 204.69 241.69 278.57 318.02 360.17 401.02 441.34 477.46 523.6\n",
      "  561.08 601.08 634.33 664.02]\n",
      " [203.54 167.74 131.51  94.31  61.19  29.41   0.    27.29  66.75 104.24\n",
      "  142.71 175.28 212.28 249.16 288.6  330.76 371.61 411.92 448.05 494.19\n",
      "  531.67 571.67 604.91 634.61]\n",
      " [230.84 195.03 158.81 121.61  88.49  56.71  27.29   0.    39.46  76.94\n",
      "  115.41 147.99 184.99 221.86 261.31 303.46 344.32 384.63 420.75 466.9\n",
      "  504.38 544.38 577.62 607.32]\n",
      " [270.3  234.49 198.27 161.07 127.94  96.16  66.75  39.46   0.    37.48\n",
      "   75.95 108.53 145.53 182.41 221.85 264.01 304.86 345.17 381.3  427.44\n",
      "  464.92 504.92 538.16 567.86]\n",
      " [307.78 271.97 235.75 198.55 165.43 133.65 104.24  76.94  37.48   0.\n",
      "   38.47  71.04 108.04 144.92 184.37 226.52 267.38 307.69 343.81 389.95\n",
      "  427.44 467.44 500.68 530.37]\n",
      " [346.25 310.44 274.22 237.02 203.9  172.12 142.71 115.41  75.95  38.47\n",
      "    0.    32.57  69.57 106.45 145.9  188.05 228.91 269.22 305.34 351.48\n",
      "  388.97 428.97 462.21 491.9 ]\n",
      " [378.82 343.02 306.8  269.59 236.47 204.69 175.28 147.99 108.53  71.04\n",
      "   32.57   0.    37.    73.88 113.32 155.48 196.33 236.64 272.77 318.91\n",
      "  356.39 396.39 429.63 459.33]\n",
      " [415.82 380.02 343.8  306.59 273.47 241.69 212.28 184.99 145.53 108.04\n",
      "   69.57  37.     0.    36.88  76.32 118.48 159.33 199.64 235.77 281.91\n",
      "  319.39 359.39 392.63 422.33]\n",
      " [452.7  416.89 380.67 343.47 310.35 278.57 249.16 221.86 182.41 144.92\n",
      "  106.45  73.88  36.88   0.    39.45  81.6  122.45 162.77 198.89 245.03\n",
      "  282.51 322.51 355.76 385.45]\n",
      " [492.15 456.34 420.12 382.92 349.8  318.02 288.6  261.31 221.85 184.37\n",
      "  145.9  113.32  76.32  39.45   0.    42.15  83.01 123.32 159.44 205.59\n",
      "  243.07 283.07 316.31 346.  ]\n",
      " [534.3  498.5  462.27 425.07 391.95 360.17 330.76 303.46 264.01 226.52\n",
      "  188.05 155.48 118.48  81.6   42.15   0.    40.85  81.16 117.29 163.43\n",
      "  200.91 240.91 274.16 303.85]\n",
      " [575.16 539.35 503.13 465.93 432.8  401.02 371.61 344.32 304.86 267.38\n",
      "  228.91 196.33 159.33 122.45  83.01  40.85   0.    40.31  76.44 122.58\n",
      "  160.06 200.06 233.3  263.  ]\n",
      " [615.47 579.66 543.44 506.24 473.12 441.34 411.92 384.63 345.17 307.69\n",
      "  269.22 236.64 199.64 162.77 123.32  81.16  40.31   0.    36.12  82.27\n",
      "  119.75 159.75 192.99 222.69]\n",
      " [651.59 615.78 579.56 542.36 509.24 477.46 448.05 420.75 381.3  343.81\n",
      "  305.34 272.77 235.77 198.89 159.44 117.29  76.44  36.12   0.    46.14\n",
      "   83.62 123.62 156.87 186.56]\n",
      " [697.73 661.93 625.7  588.5  555.38 523.6  494.19 466.9  427.44 389.95\n",
      "  351.48 318.91 281.91 245.03 205.59 163.43 122.58  82.27  46.14   0.\n",
      "   37.48  77.48 110.72 140.42]\n",
      " [735.22 699.41 663.19 625.99 592.86 561.08 531.67 504.38 464.92 427.44\n",
      "  388.97 356.39 319.39 282.51 243.07 200.91 160.06 119.75  83.62  37.48\n",
      "    0.    40.    73.24 102.94]\n",
      " [775.22 739.41 703.19 665.99 632.86 601.08 571.67 544.38 504.92 467.44\n",
      "  428.97 396.39 359.39 322.51 283.07 240.91 200.06 159.75 123.62  77.48\n",
      "   40.     0.    33.24  62.94]\n",
      " [808.46 772.65 736.43 699.23 666.11 634.33 604.91 577.62 538.16 500.68\n",
      "  462.21 429.63 392.63 355.76 316.31 274.16 233.3  192.99 156.87 110.72\n",
      "   73.24  33.24   0.    41.76]\n",
      " [838.15 802.35 766.12 728.92 695.8  664.02 634.61 607.32 567.86 530.37\n",
      "  491.9  459.33 422.33 385.45 346.   303.85 263.   222.69 186.56 140.42\n",
      "  102.94  62.94  41.76   0.  ]]\n"
     ]
    }
   ],
   "source": [
    "print(isomap.dist_matrix_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x13b0f5e90>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x550 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 466,
       "width": 553
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(isomap.dist_matrix_)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What happens if you choose the number of nearest neighbors to be too large?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x13b1f39d0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x550 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 466,
       "width": 553
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(bad_isomap.dist_matrix_)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x13b304450>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 800x550 with 4 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 451,
       "width": 677
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(1, 2, 1)\n",
    "plt.imshow(isomap.dist_matrix_)\n",
    "plt.colorbar()\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.imshow(bad_isomap.dist_matrix_)\n",
    "plt.colorbar()"
   ]
  },
  {
   "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": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[t-SNE] Computing 7 nearest neighbors...\n",
      "[t-SNE] Indexed 24 samples in 0.001s...\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: 23.784069\n",
      "[t-SNE] KL divergence after 250 iterations with early exaggeration: 49.421410\n",
      "[t-SNE] KL divergence after 1000 iterations: 0.371065\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=2, learning_rate=0.1, n_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": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}