Tutorial_04_state_sequence_estimation.ipynb

{
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   "source": [
    "# Ermine Tutorial 04\n",
    "## Predict state sequences for single-particle tracking data with ermine\n",
    "\n",
    "by Sebastian Malkusch (c) 2021  \n",
    "malkusch@med.uni-frankfurt.de  \n",
    "Data Science| Klinische Pharmakologie  \n",
    "Institut für Klinische Pharmakologie  \n",
    "Goethe - Universität  \n",
    "Theodor-Stern-Kai 7  \n",
    "60590 Frankfurt am Main"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81715b65",
   "metadata": {},
   "source": [
    "## Abstarct\n",
    "In this tutorial, we will label the temporal sequence of molecular jumps by associating each jump with a mobility mode of our hidden Markov model that was parameterized in tutorial 03."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b01994bb",
   "metadata": {},
   "source": [
    "## Prerequisite\n",
    "* Tutorial 01 must be completed\n",
    "* The file Fab_CS6_cell20_jumps.csv needs to be saved in folder results\n",
    "* Tutorial 02 must be completed\n",
    "* The optimal number of mobility modes must be known\n",
    "* Tutorial 03 must be completed\n",
    "* An HMM needs to be parameterized"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d15e1c7d",
   "metadata": {},
   "source": [
    "## Import libraries\n",
    "You need to install Ermine prior to usage.  \n",
    "Run  \n",
    "python -m pip install pyErmine  \n",
    "from the command line  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "bac6900b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import ermine as em\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3011f9cc",
   "metadata": {},
   "source": [
    "## Import Jump_df\n",
    "Store the path to the jump data set in the variable \"file_name\"\n",
    "The routine imports the jump data to a data frame (data_df)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "4057fe52",
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   "outputs": [
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     "execution_count": 2,
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   ],
   "source": [
    "file_name = \"results/Fab_CS6_cell20_jumps.csv\"\n",
    "data_df = pd.read_csv(filepath_or_buffer = file_name)\n",
    "data_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ca2e9d3",
   "metadata": {},
   "source": [
    "## Define experimental parameters\n",
    "* Define mobility modes for the model: priorModel_components  \n",
    "* Define time interval between two measurements : $\\tau$  \n",
    "* Define degrees of freedom for translational movement: dof (tutorial 02)\n",
    "* define mobility mode weights (tutorial 03)\n",
    "* define transition probabilities (tutorial 03)\n",
    "* define expected mean squared displacements (tutorial 03)\n",
    "* define diffusion coefficients (tutorial 03)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "76b992ff",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "done\n"
     ]
    }
   ],
   "source": [
    "priorModel_components = 3 # estimated in Tutorial 02\n",
    "tau = 0.02\n",
    "dof = 4\n",
    "weights = np.array([0.18397737, 0.28859201, 0.52743061])\n",
    "transition_probabilities = np.array([[9.57170509e-01, 4.28294557e-02, 3.52491759e-08],\n",
    "                                     [2.44333751e-02, 9.48943492e-01, 2.66231325e-02],\n",
    "                                     [4.73471675e-04, 2.08831546e-02, 9.78643374e-01]])\n",
    "mu = np.array([[ 1369.51580774],\n",
    "               [ 5198.55501515],\n",
    "               [14391.12696119]]) \n",
    "diffusion_coefficients = np.array([[ 17118.94759672],\n",
    "                                   [ 64981.93768936],\n",
    "                                   [179889.08701485]])\n",
    "print(\"done\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2063c8e6",
   "metadata": {},
   "source": [
    "## Create observation sequence\n",
    "An observation sequence with multiple trajectories is created for training: x_hmm  \n",
    "The respective trajectory lengths are stored separately: lengths"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "34ba6864",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "done\n"
     ]
    }
   ],
   "source": [
    "x_hmm, lengths = em.create_observation_sequence(data_df)\n",
    "print(\"done\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aba2b2c4",
   "metadata": {},
   "source": [
    "## Estimate state sequence\n",
    "The estimation process is done using the Viterbi algorithm. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "e1b14079",
   "metadata": {},
   "outputs": [
    {
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       "      <th>D</th>\n",
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      "text/plain": [
       "        jump  state             D\n",
       "0  13.285330      0  17118.947597\n",
       "1   7.964923      0  17118.947597\n",
       "2  50.420631      0  17118.947597\n",
       "3  26.654268      0  17118.947597\n",
       "4  57.015437      0  17118.947597"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hmm = em.ErmineHMM(n_components = priorModel_components,\n",
    "                   diffusion_degrees_of_freedom = dof,\n",
    "                   tau = tau,\n",
    "                   algorithm='viterbi')\n",
    "    \n",
    "hmm.startprob_ = weights\n",
    "hmm.transmat_ = transition_probabilities\n",
    "hmm.diffusion_coefficients_ = diffusion_coefficients\n",
    "state_sequence = hmm.predict(x_hmm, lengths)\n",
    "viterbi_df = pd.DataFrame({\"jump\": x_hmm[:,0],\n",
    "                          \"state\": state_sequence,\n",
    "                          \"D\": np.take(diffusion_coefficients, state_sequence)})\n",
    "viterbi_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c86a088c",
   "metadata": {},
   "source": [
    "## Plot mobility state distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "00d3676e",
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "viterbi_df[\"diffusion coefficient\"] = viterbi_df[\"D\"].apply(int).apply(str)\n",
    "sns.histplot(x=\"diffusion coefficient\",\n",
    "             hue=\"state\",\n",
    "             data=viterbi_df\n",
    "            )\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}