notebooks/R2_K-Fold_Box_Plots.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model Fitting comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append('..')\n",
    "from model.patch2self import patch2self\n",
    "\n",
    "import numpy as np\n",
    "np.random.RandomState(seed=2014)\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import dipy.data as dpd\n",
    "import dipy.reconst.cross_validation as xval\n",
    "import dipy.reconst.dti as dti\n",
    "import dipy.reconst.csdeconv as csd\n",
    "from dipy.reconst.shm import CsaOdfModel\n",
    "import scipy.stats as stats\n",
    "from dipy.io.image import load_nifti"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Denoise the data with Patch2Self and load the denoised Marchenko-Pastur denoised data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(160, 1, 652536)\n",
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     "name": "stdout",
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    }
   ],
   "source": [
    "dpd.fetch_stanford_hardi()\n",
    "hardi_fname, hardi_bval_fname, hardi_bvec_fname = dpd.get_fnames('stanford_hardi')\n",
    "img, gtab = dpd.read_stanford_hardi()\n",
    "data, affine = load_nifti(hardi_fname)\n",
    "data_p2s = patch2self(data, model='ridge')\n",
    "data_mppca, _ = load_nifti('dwi_mppca.nii') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Select 1 slice across all DWI volumes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_slice = data[..., 38:39, :]\n",
    "data_slice_p2s = data_p2s[..., 38:39, :]\n",
    "data_slice_mp = data_mppca[..., 38:39, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\shrey\\Anaconda3\\lib\\site-packages\\dask\\config.py:168: YAMLLoadWarning: calling yaml.load() without Loader=... is deprecated, as the default Loader is unsafe. Please read https://msg.pyyaml.org/load for full details.\n",
      "  data = yaml.load(f.read()) or {}\n"
     ]
    }
   ],
   "source": [
    "from dipy.segment.mask import median_otsu\n",
    "_, mask = median_otsu(data, vol_idx=[0, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_slice[mask[..., 38:39]==0] = 0\n",
    "data_slice_p2s[mask[..., 38:39]==0] = 0\n",
    "data_slice_mp[mask[..., 38:39]==0] = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Initialize the models to fit to the data: DTI and CSD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "dti_model = dti.TensorModel(gtab)\n",
    "response, ratio = csd.auto_response(gtab, data, \n",
    "                                    roi_radius=10, fa_thr=0.7)\n",
    "csd_model = csd.ConstrainedSphericalDeconvModel(gtab, response)\n",
    "\n",
    "dti_model = dti.TensorModel(gtab)\n",
    "response_p2s, ratio = csd.auto_response(gtab, data_p2s, \n",
    "                                        roi_radius=10, fa_thr=0.7)\n",
    "csd_model = csd.ConstrainedSphericalDeconvModel(gtab, response)\n",
    "\n",
    "dti_model = dti.TensorModel(gtab)\n",
    "response_mp, ratio = csd.auto_response(gtab, data_mppca, \n",
    "                                       roi_radius=10, fa_thr=0.7)\n",
    "csd_model = csd.ConstrainedSphericalDeconvModel(gtab, response)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Run the 2-Fold Crossvalidation for each model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "dti_slice = xval.kfold_xval(dti_model, data_slice, 2)\n",
    "csd_slice = xval.kfold_xval(csd_model, data_slice, 2, response)\n",
    "\n",
    "dti_slice_P2S = xval.kfold_xval(dti_model, data_slice_p2s, 2)\n",
    "csd_slice_P2S = xval.kfold_xval(csd_model, data_slice_p2s, 2, response_p2s)\n",
    "\n",
    "dti_slice_MP = xval.kfold_xval(dti_model, data_slice_mp, 2)\n",
    "csd_slice_MP = xval.kfold_xval(csd_model, data_slice_mp, 2, response_mp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Append all the scores for each model on each dataset via both models: CSD and DTI"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\shrey\\Anaconda3\\lib\\site-packages\\scipy\\stats\\stats.py:3508: PearsonRConstantInputWarning: An input array is constant; the correlation coefficent is not defined.\n",
      "  warnings.warn(PearsonRConstantInputWarning())\n"
     ]
    }
   ],
   "source": [
    "r2s_dti = []\n",
    "for i in range(0, dti_slice.shape[0]):\n",
    "    for j in range(0, dti_slice.shape[1]):\n",
    "        for k in range(0, dti_slice.shape[2]):\n",
    "            dti_r2 = stats.pearsonr(data_slice[i, j, k, :], dti_slice[i, j, k, :])[0]**2\n",
    "            r2s_dti.append(dti_r2)\n",
    "r2s_dti = np.array(r2s_dti)\n",
    "r2s_dti = r2s_dti[~np.isnan(r2s_dti)]\n",
    "\n",
    "r2s_csd = []\n",
    "for i in range(0, csd_slice.shape[0]):\n",
    "    for j in range(0, csd_slice.shape[1]):\n",
    "        for k in range(0, csd_slice.shape[2]):\n",
    "            csd_r2 = stats.pearsonr(data_slice[i, j, k, :], csd_slice[i, j, k, :])[0]**2\n",
    "            r2s_csd.append(csd_r2)\n",
    "r2s_csd = np.array(r2s_csd)\n",
    "r2s_csd = r2s_csd[~np.isnan(r2s_csd)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "r2s_dti_mp = []\n",
    "for i in range(0, dti_slice.shape[0]):\n",
    "    for j in range(0, dti_slice.shape[1]):\n",
    "        for k in range(0, dti_slice.shape[2]):\n",
    "            dti_r2_mp = stats.pearsonr(data_slice[i, j, k, :], dti_slice_MP[i, j, k, :])[0]**2\n",
    "            r2s_dti_mp.append(dti_r2_mp)\n",
    "r2s_dti_mp = np.array(r2s_dti_mp)\n",
    "r2s_dti_mp = r2s_dti_mp[~np.isnan(r2s_dti_mp)]\n",
    "\n",
    "r2s_csd_mp = []\n",
    "for i in range(0, csd_slice.shape[0]):\n",
    "    for j in range(0, csd_slice.shape[1]):\n",
    "        for k in range(0, csd_slice.shape[2]):\n",
    "            csd_r2_mp = stats.pearsonr(data_slice[i, j, k, :], csd_slice_MP[i, j, k, :])[0]**2\n",
    "            r2s_csd_mp.append(csd_r2_mp)\n",
    "r2s_csd_mp = np.array(r2s_csd_mp)\n",
    "r2s_csd_mp = r2s_csd_mp[~np.isnan(r2s_csd_mp)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "r2s_dti_p2s = []\n",
    "for i in range(0, dti_slice.shape[0]):\n",
    "    for j in range(0, dti_slice.shape[1]):\n",
    "        for k in range(0, dti_slice.shape[2]):\n",
    "            dti_r2_p2s = stats.pearsonr(data_slice[i, j, k, :], dti_slice_P2S[i, j, k, :])[0]**2\n",
    "            r2s_dti_p2s.append(dti_r2_p2s)\n",
    "r2s_dti_p2s = np.array(r2s_dti_p2s)\n",
    "r2s_dti_p2s = r2s_dti_p2s[~np.isnan(r2s_dti_p2s)]\n",
    "\n",
    "r2s_csd_p2s = []\n",
    "for i in range(0, csd_slice.shape[0]):\n",
    "    for j in range(0, csd_slice.shape[1]):\n",
    "        for k in range(0, csd_slice.shape[2]):\n",
    "            csd_r2_p2s = stats.pearsonr(data_slice[i, j, k, :], csd_slice_P2S[i, j, k, :])[0]**2\n",
    "            r2s_csd_p2s.append(csd_r2_p2s)\n",
    "r2s_csd_p2s = np.array(r2s_csd_p2s)\n",
    "r2s_csd_p2s = r2s_csd_p2s[~np.isnan(r2s_csd_p2s)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "df = pd.DataFrame({'Raw DTI':r2s_dti,\n",
    "                   'Raw CSD':r2s_csd,\n",
    "                   'Marchenko-Pastur DTI':r2s_dti_mp,\n",
    "                   'Marchenko-Pastur CSD':r2s_csd_mp,\n",
    "                   'Patch2Self DTI':r2s_dti_p2s,\n",
    "                   'Patch2Self CSD':r2s_csd_p2s})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4606,) (4606,) (4606,)\n"
     ]
    }
   ],
   "source": [
    "print(r2s_csd.shape, r2s_csd_mp.shape, r2s_csd_p2s.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Subtract the $\\mathbf{R}^2$ scores of Noisy Data from both Marchenko-Pastur and Patch2Self"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_diff = pd.DataFrame({'(MP - Noisy) DTI':r2s_dti_mp - r2s_dti,\n",
    "                        '(P2S - Noisy) DTI':r2s_dti_p2s - r2s_dti,\n",
    "                        '(MP - Noisy) CSD':r2s_csd_mp - r2s_csd,\n",
    "                        '(P2S - Noisy) CSD':r2s_csd_p2s - r2s_csd})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Compute the Box-Plots and perform comparison using a 2-sided t-test "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value annotation legend:\n",
      "ns: 5.00e-02 < p <= 1.00e+00\n",
      "*: 1.00e-02 < p <= 5.00e-02\n",
      "**: 1.00e-03 < p <= 1.00e-02\n",
      "***: 1.00e-04 < p <= 1.00e-03\n",
      "****: p <= 1.00e-04\n",
      "\n",
      "(MP - Noisy) DTI v.s. (P2S - Noisy) DTI: t-test independent samples with Bonferroni correction, P_val=6.056e-45 stat=-1.419e+01\n",
      "(MP - Noisy) CSD v.s. (P2S - Noisy) CSD: t-test independent samples with Bonferroni correction, P_val=0.000e+00 stat=-4.059e+01\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(<matplotlib.axes._subplots.AxesSubplot at 0x22fcd1365c8>,\n",
       " [<statannot.StatResult.StatResult at 0x22fca295748>,\n",
       "  <statannot.StatResult.StatResult at 0x22fcd1ed588>])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "sns.set(style=\"whitegrid\")\n",
    "ax = sns.boxplot(x=\"variable\", y=\"value\", data=pd.melt(df_diff), fliersize=0, sym='', palette=\"Set2\")\n",
    "\n",
    "from statannot import add_stat_annotation\n",
    "add_stat_annotation(ax, data=pd.melt(df_diff), x=\"variable\", y=\"value\",\n",
    "                    box_pairs=[('(MP - Noisy) DTI', '(P2S - Noisy) DTI'), \n",
    "                               ('(MP - Noisy) CSD', '(P2S - Noisy) CSD')],\n",
    "                               test='t-test_ind', text_format='star', loc='outside', verbose=2)"
   ]
  }
 ],
 "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}