examples/example_preprocessing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1 id=\"tocheading\">Table of Contents</h1>\n",
    "<div id=\"toc\"></div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "$.getScript('https://kmahelona.github.io/ipython_notebook_goodies/ipython_notebook_toc.js')\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "%%javascript\n",
    "$.getScript('https://kmahelona.github.io/ipython_notebook_goodies/ipython_notebook_toc.js')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import some necessary modules\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import matplotlib as mpl\n",
    "import pandas as pd\n",
    "import time\n",
    "import scipy as sp\n",
    "import pickle\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import MuSiCal\n",
    "import musical"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Overview "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, we demonstrate the usage of the preprocessing module, which provides two complementary methods -- cohort stratification and outlier removal. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cohort stratification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the PCAWG ColoRect.AdenoCA dataset to demonstrate the usage of cohort stratification. We read in the mutation count matrix $X$, which contains 60 samples, and aim to investigate whether the dataset should be further stratified into subsets with distinct signature compositions. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(96, 60)\n"
     ]
    }
   ],
   "source": [
    "X = pd.read_csv('./data/preprocessing_example.ColoRect.AdenoCA.X.csv', index_col=0)\n",
    "print(X.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After an initial *de novo* signature discovery with the entire dataset of 60 samples, we obtain the following signature matrix $W$ and exposure matrix $H$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "W = pd.read_csv('./data/preprocessing_example.ColoRect.AdenoCA.W_denovo.csv', index_col=0)\n",
    "H = pd.read_csv('./data/preprocessing_example.ColoRect.AdenoCA.H_denovo.csv', index_col=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cohort stratification can be performed with the function `musical.preprocessing.stratify_samples()`. Briefly, it performs hierarchical clustering on the exposure matrix $H$ and selects the optimal number of clusters $k$ with the gap statistic. In this example, $k=3$ clusters are selected. Note that the optimal $k$ can be 1, which suggests that there is no subset structure within the dataset. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    }
   ],
   "source": [
    "k, clusters, Xs, model = musical.preprocessing.stratify_samples(X.values, H.values)\n",
    "print(k)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualize how the optimal $k$ is selected. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The indices of samples belonging to each cluster are stored in `clusters`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([52, 53, 54, 55, 56, 57, 58, 59]),\n",
       " array([0, 1, 2, 3, 4, 5, 6, 7, 8]),\n",
       " array([ 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25,\n",
       "        26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42,\n",
       "        43, 44, 45, 46, 47, 48, 49, 50, 51])]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clusters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the stratified mutation count matrices are stored in `Xs`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(96, 8)\n",
      "(96, 9)\n",
      "(96, 43)\n"
     ]
    }
   ],
   "source": [
    "for i in range(0, k):\n",
    "    print(Xs[i].shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sometimes it is helpful to check the silhouette scores of the selected clusters. Larger silhouette scores suggest clearer subset structures. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.79767023, 0.74100285, 0.59182553])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.silscorek_percluster[k]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, it is informative to look at the average mutational spectrum of each cluster. We can see that the first cluster corresponds to samples with POLE-exo mutations, the second cluster corresponds to MMRD samples, and the third cluster is the rest. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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AAGMECAAAAADGCBAAAAAAjBEgAAAAABgjQAAAAAAwRoAAAAAAYIwAAQAAAMAYAQIAAACAMQIEAAAAAGMECAAAAADG+nV3AwAAAN3l+aPJTsef/Z+DXVoL9GasQAAAAAAwxgoEAADoNPxWHvB9BAgAANAjED6A3oEAAQDosDNTJjgdH7H/kJc7AQB4C89AAAAAADBGgAAAAABgjAABAAAAwBjPQAAAAHgZD4yjN2MFAgAAAIAxViAAAADAqgiMsQIBAAAAwBgrEAAAn3L48GGn4+PHj/dyJwDgm1iBAAAAAGCMFQgAAIBehGcV0N0IED3ArANNTsc3T+7v5U4AAAAA97iFCQAAAIAxViAAAECv11W39XTX7ULOjsstSugpWIEAAAAAYIwVCPQaPCsCAADQ/QgQAPqkM1MmOB0fsf+QlzsBAO/hDU7oDAQIAAAAH0FAMHNhS4XT8bsfsXi5k96JAAGg1+qNqwi9sWcAAL6NAAEAHiIEAAD6MgIEPMbDzEDfQVgCOo7bieCrCBBewkU3gL6G8IGeggt5oHMRIAAAQI9HCAB6DgIEAPRxrBTAWwgBgG8gQACAE1xUAwDgnH93NwAAAACg92AFAgAAAPCC7voCu84+LgECAAAfdPjwYafj48eP93InAHwNtzABAAAAMMYKhA/juycAAF2B1Q2gbyNAAAAAwOd01/MGfQEBopP0xt/2d1XP7vbbGz8nAADQMzkLCQSErtfnAgQXsADQ83GLDNB3sFLQ+3QoQBw8eFBFRUWqrq5WRESE5syZo4ULF8rPz89lTVlZmUpKSnT+/HlFRUUpJydHs2bNstvm448/1ssvv6wTJ05o4MCBmjFjhp544gkFBgZ2pE0AQA/mLCR0d0DoiT0BQE/jcYA4fvy48vLylJaWpqVLl+rYsWMqLCxUS0uLcnNzndaUl5frqaee0rx585SUlKQ9e/Zo5cqVCgoK0owZMyRJNTU1ys7OVkJCQns4KSws1LVr1/S73/3u1s7SUE9cneiJPQEA7N3Kikl31QJAR3kcINasWaNRo0bplVdekSQlJyerublZJSUlys7OVnBwsENNUVGRLBaLVqxYIUlKSkrSlStXVFxc3B4g1q5dq5CQEL3++usKDAzUpEmTFBwcrOeff165ubkaPHjwrZwn+gBnK2Ctra1dst/O2je+xmcMuEZIAHAz3r4NzKMA0djYqCNHjmjx4sV24xaLRWvXrtWHH36on/3sZ3ZzFy5ckM1mc1pTXl4uq9WquLg4VVZWavLkyXa3K91///1atWqVKisrlZGR4em5AX0SF+Pwdd11Qc2FPADp5hfrfeGZDo8CxPnz59XU1KTY2Fi78SFDhkiSbDabQ4Corq6WJLc1UVFRunjxouLi4uy2iYiIUGhoqGw2mydtohP42q1TXFSbcfc58RnCFxA+vuGup57YL7qfuzceubtovpUL6r5wMd6mNwUTjwLE1atXJUmhoaF24yEhIZKk+vp6h5pr167dtMbVftu2c7bfNlOnTnU5Z7PZFBAQoKFDh7aP1V53vu3QYPdz7mrvuIXamx23q/bb23oy+Yydzn3r774j8zertVqtTufawrCz+e8GZWc6st+b7ftWz/Vmcx3pyeS4TZf+1+lc/5vMSeqWWnoyr71x44bDXFBQkMu5tnl3c11R2xN7Mqntrp4+v3HJ6dzbQUPdzknqltqe2JOr2u7u6asvvnSYC1g+wOVc27y7ua6o7dKeQrrufLz9OX17vk10dLTee+89p9t+m0cBoqWlRZLr31L6+/sb17T91tLf39/tbzDd/ebzZvz9/dWvn/0p3vH/F5uXLn39H0lUVJTRXHfV0pN5bVxcnNs5d7U326+r+Zvtt6PHvZX9mhyzI7Vdda43q+0fdVeH5rqrlp7Ma4OCgtzOuap1N9ddtfT0zXx4UFSH5rqrtif21Dbf03oKCBngds5Vrbu57qqlJ+fXBqY8ChBhYWGSHFcavvjiC0nOVxBc1TQ0NLTXDBo0yG4/392ubd6ZvXv3mrZvp23lwlm9u7nuqqWn3tvTrdTSEz3RU++qpSd6oqfeVUtPHeO4ZOBGTEyMAgICdO7cObvxtp+HDx/uUNP2m0V3NQMHDlRkZKTDNnV1daqvr3e6XwAAAADe51GACAoKUmJionbv3m1321FFRYXCwsIUHx/vUDNkyBBFR0eroqLCbryiokKxsbHtr2edOHGiDhw4oMbGxvZt3n33XQUEBPDQFgAAANBDePw9ELm5ucrOztaSJUs0c+ZMffTRR3rrrbe0bNkyBQcHq76+XmfPnlVMTIwiIiIkSXl5ecrPz1d4eLhSUlK0b98+lZeXq7CwsH2/OTk52rlzp3JycpSdnS2bzaaCggJlZGTc8n1aAAAAADqHRysQkjRhwgQVFxfLarVq0aJF2rFjh5YvX66cnBxJ0okTJ5SRkaEDBw6016Snp2vVqlV6//33tWjRIh09elQvvfSSHnjggfZthg0bpnXr1un69etavHix3n77bc2fP1/PPPPMrZ8lAAAAgE7h8QqEJE2bNk3Tpk1zOjdu3DidPn3aYXzOnDmaM2eO2/0mJibq73//e0daAgAAAOAFHq9AAAAAAOi7/Fr5GlkAAAAAhliBAAAAAGCMAAEAAADAGAECAAAAgDECBAAAAABjBAgAAAAAxggQAAAAAIwRIAAAAAAYI0AAAAAAMEaAAAAAAGCMAAEAAADA2P8BfjuHsgfdH+wAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(0, k):\n",
    "    fig = musical.sigplot_bar(np.mean(Xs[i], axis=1), title='Cluster ' + str(i + 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we note that the only required parameter of the function `musical.preprocessing.stratify_samples()` is $X$. When only $X$ is provided and $H$ is not, clustering will be performed on $X$ instead. Sometimes the subset structure in the dataset is strong enough such that clustering on $X$ can already be informative for the stratification. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Outlier removal "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the PCAWG CNS.GBM dataset to demonstrate the usage of outlier removal. We read in the mutation count matrix $X$, which contains 40 samples, and aim to investigate whether the dataset contains potential outliers, i.e., a small number of samples with strong exposures of signatures that are not present in other samples. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(96, 40)\n"
     ]
    }
   ],
   "source": [
    "X = pd.read_csv('./data/preprocessing_example.CNS.GBM.X.csv', index_col=0)\n",
    "print(X.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After an initial *de novo* signature discovery with the entire dataset of 40 samples, we obtain the following signature matrix $W$ and exposure matrix $H$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "W = pd.read_csv('./data/preprocessing_example.CNS.GBM.W_denovo.csv', index_col=0)\n",
    "H = pd.read_csv('./data/preprocessing_example.CNS.GBM.H_denovo.csv', index_col=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Outlier removal can be performed with the function `musical.preprocessing.remove_samples_based_on_gini()`. Briefly, it uses the Gini coefficient to detect signatures with nonhomogeneous exposure distributions and the corresponding outlier samples. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "dict_samples_to_keep, dict_X_to_keep, samples_to_keep = musical.preprocessing.remove_samples_based_on_gini(H, X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the output, the indices of retained non-outlier samples are stored in `samples_to_keep`. Thus the mutation count matrix after outlier removal can be obtained as follows. In this example, only 1 outlier is detected and removed. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(96, 39)\n"
     ]
    }
   ],
   "source": [
    "X_to_keep = pd.DataFrame.copy(X.iloc[:, samples_to_keep])\n",
    "print(X_to_keep.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To gain further information about why the outliers are removed, we can check `dict_samples_to_keep`, which is a dictionary. The keys of the dictionary are indices of signatures deemed to have nonhomogeneous exposure distributions. The values of the dictionary are indices of non-outlier samples corresponding to the signatures. In this example, one outlier (with sample index 16) is detected because it has an exceptionally large exposure of the signature with index 0. This sample is dominated by the temozolomide signature. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 17,\n",
       "        18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34,\n",
       "        35, 36, 37, 38, 39])}"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dict_samples_to_keep"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = musical.sigplot_bar(W.iloc[:, 0], title='Signature')\n",
    "fig = musical.sigplot_bar(X.iloc[:, 16], title=X.columns[16])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In more detail, we see below that removing this sample results in a large reduction in the Gini coefficient for the correponding exposure distribution. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x140fb8970>]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 645.161x324.675 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "H_norm = np.array(H) / np.sum(np.array(X), axis=0)\n",
    "sorted_h, sorted_h_indices = musical.preprocessing.sort_with_indices(H_norm[0, :])\n",
    "l = [musical.preprocessing.gini(sorted_h[::-1][i:][::-1]) for i in range(0, 20)]\n",
    "\n",
    "mpl.rcParams['pdf.fonttype'] = 42\n",
    "fig = plt.figure()\n",
    "sns.set_context('notebook')\n",
    "sns.set_style('ticks')\n",
    "plt.rc('xtick', labelsize=14, color='k')\n",
    "plt.rc('ytick', labelsize=14, color='k')\n",
    "\n",
    "subfig = fig.add_subplot(1, 1, 1)\n",
    "subfig.set_title('', fontsize=14)\n",
    "subfig.spines['right'].set_visible(False)\n",
    "subfig.spines['top'].set_visible(False)\n",
    "subfig.spines['bottom'].set_color('black')\n",
    "subfig.spines['left'].set_color('black')\n",
    "for axis in ['top','bottom','left','right']:\n",
    "    subfig.spines[axis].set_linewidth(1)\n",
    "musical.plot._set_size(5, 2.5, ax=subfig)\n",
    "for tick in subfig.get_xticklabels():\n",
    "    tick.set_fontname(\"Arial\")\n",
    "for tick in subfig.get_yticklabels():\n",
    "    tick.set_fontname(\"Arial\")\n",
    "subfig.set_xlabel('Index of sorted samples', fontsize=14, color='k')\n",
    "subfig.set_ylabel('Remaining gini coefficient', fontsize=14, color='k')\n",
    "\n",
    "subfig.plot(l, '.-', color='k', markersize=15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "python310_musical",
   "language": "python",
   "name": "python310_musical"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.13"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  },
  "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": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}