persistence image of small values.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Persistance images from small values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from ripser import Rips\n",
    "from persim import PersistenceImager\n",
    "import glob\n",
    "import pickle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib as mpl\n",
    "mpl.rcParams.update(mpl.rcParamsDefault)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/h6x/anaconda3/envs/TDA/lib/python3.11/site-packages/pandas/core/arrays/masked.py:60: UserWarning: Pandas requires version '1.3.6' or newer of 'bottleneck' (version '1.3.5' currently installed).\n",
      "  from pandas.core import (\n"
     ]
    }
   ],
   "source": [
    "# import the data\n",
    "data = []\n",
    "for file in glob.glob(\"./tennessee/results/selected coordinates for each county/*.pkl\"):\n",
    "    with open(file, 'rb') as f:\n",
    "        data.append(pickle.load(f))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variable: EP_DISABL\n",
      "(80, 2)\n",
      "Variable: EP_NOHSDP\n",
      "(0,)\n",
      "Variable: EP_PCI\n",
      "(48, 2)\n",
      "Variable: EP_MOBILE\n",
      "(112, 2)\n",
      "Variable: EP_POV\n",
      "(42, 2)\n"
     ]
    }
   ],
   "source": [
    "# add the data(coordinates) to the list - for a single county - multiple variable\n",
    "data_coordinates_list = []\n",
    "for variable_name, selected_coordinates in data[7].items():\n",
    "    data_coordinates = np.array([np.array(coord) for coord in selected_coordinates['coords']])\n",
    "\n",
    "    print(f\"Variable: {variable_name}\")\n",
    "    print(data_coordinates.shape)\n",
    "\n",
    "    # append the data to the list\n",
    "    data_coordinates_list.append(data_coordinates)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# selecting single variable to plot\n",
    "data_ep_pci = data_coordinates_list[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the data_ep_pci for the county\n",
    "plt.rcParams[\"figure.figsize\"] = (6, 6)\n",
    "plt.scatter(data_ep_pci[:,0], data_ep_pci[:,1], label=\"data\", s=8)\n",
    "plt.axis('equal')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Persistance image "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rips(maxdim=1, thresh=inf, coeff=2, do_cocycles=False, n_perm = None, verbose=True)\n"
     ]
    }
   ],
   "source": [
    "# creating the persistence diagram from rips class\n",
    "rips = Rips(maxdim=1, coeff=2)\n",
    "dgms = rips.fit_transform(data_ep_pci)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# seperate the diagrams H0 and H1\n",
    "diagrams_h0 = dgms[0]\n",
    "diagrams_h1 = dgms[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# remove last data point in H0 diagram - it is infinity\n",
    "diagrams_h0_without_inf = diagrams_h0[0:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting the persistence diagram of H0 and H1\n",
    "plt.figure(figsize=(12,6))\n",
    "plt.subplot(121)\n",
    "\n",
    "rips.plot(diagrams_h0_without_inf, show=False)\n",
    "plt.title(\"PD of $H_0$\")\n",
    "\n",
    "plt.subplot(122)\n",
    "rips.plot(diagrams_h1, show=False)\n",
    "plt.title(\"PD of $H_1$\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# lifetime is y coordinates diagrams_h0_without_inf\n",
    "# only if used as weight in the persistence imager\n",
    "lifetime = diagrams_h1[:,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define custom weighting function that uses lifetime as weight \n",
    "# default weight function is 'persistance'\n",
    "def weight_by_lifetime(birth, persistence, lifetime, **kwargs):\n",
    "    # Use lifetime as weight\n",
    "    #return lifetime\n",
    "    return np.exp(lifetime)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# For the default bivariate normal Gaussian kernel, the parameter controlling the spread (sigma) may be specified \n",
    "# either by a float or a 2x2 covariance matrix\n",
    "# pimgr = PersistenceImager(pixel_size=0.1, weight=weight_by_lifetime, weight_params={'lifetime': lifetime})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Persistence image of H1 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pimgr_1 = PersistenceImager(pixel_size=0.1)\n",
    "pimgr_1.fit(diagrams_h1)\n",
    "\n",
    "pimgr_1.pixel_size = 0.005\n",
    "pimgr_1.birth_range = (-0.02, 0.1)\n",
    "pimgr_1.pers_range = (-0.02, 0.1)\n",
    "\n",
    "\n",
    "fig, axs = plt.subplots(1, 2, figsize=(20,5))\n",
    "pimgr_1.kernel_params = {'sigma': .1}\n",
    "pimgr_1.plot_diagram(diagrams_h1, skew=True, ax=axs[0])\n",
    "axs[0].set_title('Diagram', fontsize=16)\n",
    "\n",
    "pimgr_1.kernel_params = {'sigma': 0.000005}\n",
    "pimgr_1.plot_image(pimgr_1.transform(diagrams_h1), ax=axs[1])\n",
    "axs[1].set_title('Kernel Spread: 0.1', fontsize=16)\n",
    "\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Persistence image of H0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pimgr = PersistenceImager(pixel_size=0.1)\n",
    "pimgr.fit(diagrams_h0_without_inf)\n",
    "\n",
    "pimgr.pixel_size = 0.005\n",
    "pimgr.birth_range = (-0.02, 0.1)\n",
    "pimgr.pers_range = (-0.02, 0.1)\n",
    "\n",
    "\n",
    "# pixel size 1 and sigma 0.1\n",
    "fig, axs = plt.subplots(1, 2, figsize=(20,5))\n",
    "pimgr.kernel_params = {'sigma': .1}\n",
    "pimgr.plot_diagram(diagrams_h0_without_inf, skew=True, ax=axs[0])\n",
    "axs[0].set_title('Diagram', fontsize=16)\n",
    "\n",
    "pimgr.kernel_params = {'sigma': 0.000005}\n",
    "pimgr.plot_image(pimgr.transform(diagrams_h0_without_inf), ax=axs[1])\n",
    "axs[1].set_title('Kernel Spread: 0.1', fontsize=16)\n",
    "\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Persistence image of H1+H0 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = pimgr.transform(diagrams_h0_without_inf)\n",
    "B = pimgr_1.transform(diagrams_h1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# add A and B two images by making the shape of the final image 24,24\n",
    "# just multiply by 8 show the persistance more clearly\n",
    "C = A +8*B\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pimgr = PersistenceImager(pixel_size=0.1)\n",
    "pimgr.fit(diagrams_h0_without_inf)\n",
    "\n",
    "pimgr.pixel_size = 0.005\n",
    "pimgr.birth_range = (-0.02, 0.1)\n",
    "pimgr.pers_range = (-0.02, 0.1)\n",
    "\n",
    "\n",
    "# pixel size 1 and sigma 0.1\n",
    "fig, axs = plt.subplots(1, 2, figsize=(20,5))\n",
    "pimgr.kernel_params = {'sigma': .1}\n",
    "pimgr.plot_diagram(diagrams_h0_without_inf, skew=True, ax=axs[0])\n",
    "axs[0].set_title('Diagram', fontsize=16)\n",
    "\n",
    "pimgr.kernel_params = {'sigma': 0.000005}\n",
    "pimgr.plot_image(C, ax=axs[1])\n",
    "axs[1].set_title('Kernel Spread: 0.1', fontsize=16)\n",
    "\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Plotting only the persistence image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Rotate 90 degrees to the left(k=3), 90 degrees to the right(k=1), 180 degrees(k=2)\n",
    "C_rotated = np.rot90(C, k=1) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 240x240 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(2.4, 2.4))\n",
    "plt.imshow(C_rotated, cmap='viridis')  # Assuming 'viridis' colormap, change as needed\n",
    "plt.axis('off')  # Turn off axis\n",
    "\n",
    "plt.subplots_adjust(left=0, right=1, top=1, bottom=0)  # Adjust subplot parameters to remove borders\n",
    "# plt.savefig('./tennessee/results/persistence images/test.png')\n",
    "# plt.close()\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 240x240 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "C_rotated = np.rot90(C, k=1) \n",
    "\n",
    "plt.figure(figsize=(2.4, 2.4))\n",
    "plt.imshow(C_rotated, cmap='viridis')\n",
    "plt.axis('off')\n",
    "\n",
    "# save \n",
    "# plt.savefig('./tennessee/results/persistence images/testEEE.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Creating an empty image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create 24x24 numpy ndarray with zeros\n",
    "empty_image = np.zeros((24,24))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQQAAAEECAYAAADOCEoKAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAC6ElEQVR4nO3WsRGDUAwFwQ/j1lyCq3QJ9GY5u5iEgWA3VvCiG20zMwtgrbXfPQB4DkEAIghABAGIIAARBCCCAEQQgAgCkNfZw/f+uXIHcKHj9z1150MAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgAgCEEEAIghABAGIIAARBCCCAEQQgGwzM3ePAJ7BhwBEEIAIAhBBACIIQAQBiCAAEQQgggDkD3pkDQH8QRCDAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 240x240 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(2.4, 2.4))\n",
    "plt.imshow(empty_image, cmap='viridis')  # Assuming 'viridis' colormap, change as needed\n",
    "plt.axis('off')  # Turn off axis\n",
    "\n",
    "plt.subplots_adjust(left=0, right=1, top=1, bottom=0)  # Adjust subplot parameters to remove borders\n",
    "# plt.savefig('./tennessee/results/persistence images/test.png')\n",
    "# plt.close()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Shape of persisence image and creating a input vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(C_rotated)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(24, 24)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C_rotated.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create a empty image with RGB\n",
    "empty_image = np.zeros((24,24,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(24, 24, 3)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "empty_image.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 240x240 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the image\n",
    "plt.figure(figsize=(2.4, 2.4))\n",
    "plt.imshow(empty_image)  # Assuming 'viridis' colormap, change as needed\n",
    "plt.axis('off')  # Turn off axis\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# combine 3 of C_rotated to create a new RGB image without using the empty_image\n",
    "C_rotated_3d = np.stack((C_rotated, C_rotated, C_rotated), axis=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(24, 24, 3)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C_rotated_3d.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 240x240 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the image\n",
    "plt.figure(figsize=(2.4, 2.4))\n",
    "plt.imshow(C_rotated_3d)  # Assuming 'viridis' colormap, change as needed\n",
    "plt.axis('off')  # Turn off axis\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "# save C_rotated to a file\n",
    "np.save('./tennessee/results/persistence images/test', C_rotated)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "TDA",
   "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": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}