26_feat_agg_vs_univariate_sel.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparing two dimensionality reduction methods \n",
    "- univariate feature selection with ANOVA \n",
    "- feature agglomeration with Ward hierarchical clustering "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "import matplotlib.pyplot as plt \n",
    "%matplotlib inline \n",
    "\n",
    "from scipy import linalg, ndimage  \n",
    "from joblib import Memory \n",
    "\n",
    "import shutil \n",
    "import tempfile \n",
    "\n",
    "from sklearn.feature_extraction.image import grid_to_graph \n",
    "from sklearn import feature_selection \n",
    "from sklearn.cluster import FeatureAgglomeration \n",
    "from sklearn.pipeline import Pipeline \n",
    "from sklearn.linear_model import BayesianRidge \n",
    "from sklearn.model_selection import GridSearchCV, KFold"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#setting parameters \n",
    "\n",
    "n_samples = 200 \n",
    "size = 40 \n",
    "roi_size = 15 \n",
    "snr = 5.0 \n",
    "np.random.seed(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Generating data \n",
    "\n",
    "coef = np.zeros((size, size))\n",
    "coef[0:roi_size, 0:roi_size] = -1.0 \n",
    "coef[-roi_size, -roi_size] = 1.0 \n",
    "\n",
    "X = np.random.randn(n_samples, size ** 2)\n",
    "for x in X:\n",
    "    x[:] = ndimage.gaussian_filter(x.reshape(size, size), sigma=1.0).ravel()\n",
    "X -= X.mean(axis=0)\n",
    "X /= X.std(axis=0)\n",
    "\n",
    "y = np.dot(X, coef.ravel())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#add noise \n",
    "\n",
    "noise = np.random.randn(y.shape[0])\n",
    "noise_coef = (linalg.norm(y, 2) / np.exp(snr /20.0)) / linalg.norm(noise, 2)\n",
    "y += noise_coef * noise "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#compute the coefs of a Bayesian Ridge with GridSearch \n",
    "\n",
    "cv = KFold(2) \n",
    "ridge = BayesianRidge()\n",
    "cachedir = tempfile.mkdtemp()\n",
    "mem = Memory(location=cachedir, verbose=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "________________________________________________________________________________\n",
      "[Memory] Calling sklearn.cluster._agglomerative.ward_tree...\n",
      "ward_tree(array([[-0.451933, ..., -0.675318],\n",
      "       ...,\n",
      "       [ 0.275706, ..., -1.085711]]), connectivity=<1600x1600 sparse matrix of type '<class 'numpy.int32'>'\n",
      "\twith 7840 stored elements in COOrdinate format>, n_clusters=None, return_distance=False)\n",
      "________________________________________________________ward_tree - 0.0s, 0.0min\n",
      "________________________________________________________________________________\n",
      "[Memory] Calling sklearn.cluster._agglomerative.ward_tree...\n",
      "ward_tree(array([[ 0.905206, ...,  0.161245],\n",
      "       ...,\n",
      "       [-0.849835, ..., -1.091621]]), connectivity=<1600x1600 sparse matrix of type '<class 'numpy.int32'>'\n",
      "\twith 7840 stored elements in COOrdinate format>, n_clusters=None, return_distance=False)\n",
      "________________________________________________________ward_tree - 0.0s, 0.0min\n",
      "________________________________________________________________________________\n",
      "[Memory] Calling sklearn.cluster._agglomerative.ward_tree...\n",
      "ward_tree(array([[ 0.905206, ..., -0.675318],\n",
      "       ...,\n",
      "       [-0.849835, ..., -1.085711]]), connectivity=<1600x1600 sparse matrix of type '<class 'numpy.int32'>'\n",
      "\twith 7840 stored elements in COOrdinate format>, n_clusters=None, return_distance=False)\n",
      "________________________________________________________ward_tree - 0.0s, 0.0min\n"
     ]
    }
   ],
   "source": [
    "#Ward Agglomeration followed by BayesianRidge \n",
    "\n",
    "connectivity = grid_to_graph(n_x=size, n_y=size)\n",
    "ward = FeatureAgglomeration(n_clusters=10, connectivity=connectivity, memory=mem)\n",
    "\n",
    "clf = Pipeline([(\"ward\", ward),(\"ridge\", ridge)])\n",
    "\n",
    "#select the optimal number of parcels with grid search \n",
    "\n",
    "clf = GridSearchCV(clf, {\"ward__n_clusters\":[10,20,30]}, n_jobs=1, cv=cv)\n",
    "clf.fit(X,y)\n",
    "\n",
    "coef_ = clf.best_estimator_.steps[-1][1].coef_\n",
    "coef_ = clf.best_estimator_.steps[0][1].inverse_transform(coef_)\n",
    "coef_agglomeration_ = coef_.reshape(size, size)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ANOVA univariate feature selection followed by BAyesian Ridge \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "________________________________________________________________________________\n",
      "[Memory] Calling sklearn.feature_selection._univariate_selection.f_regression...\n",
      "f_regression(array([[-0.451933, ...,  0.275706],\n",
      "       ...,\n",
      "       [-0.675318, ..., -1.085711]]), \n",
      "array([48.315095, ..., 27.619534]))\n",
      "_____________________________________________________f_regression - 0.0s, 0.0min\n",
      "________________________________________________________________________________\n",
      "[Memory] Calling sklearn.feature_selection._univariate_selection.f_regression...\n",
      "f_regression(array([[ 0.905206, ..., -0.849835],\n",
      "       ...,\n",
      "       [ 0.161245, ..., -1.091621]]), \n",
      "array([-61.330139, ..., -71.427245]))\n",
      "_____________________________________________________f_regression - 0.0s, 0.0min\n",
      "________________________________________________________________________________\n",
      "[Memory] Calling sklearn.feature_selection._univariate_selection.f_regression...\n",
      "f_regression(array([[ 0.905206, ..., -0.849835],\n",
      "       ...,\n",
      "       [-0.675318, ..., -1.085711]]), \n",
      "array([-61.330139, ...,  27.619534]))\n",
      "_____________________________________________________f_regression - 0.0s, 0.0min\n"
     ]
    }
   ],
   "source": [
    "f_regression = mem.cache(feature_selection.f_regression) #caching function \n",
    "\n",
    "anova = feature_selection.SelectPercentile(f_regression)\n",
    "clf = Pipeline([(\"anova\",anova), (\"ridge\",ridge)])\n",
    "\n",
    "clf = GridSearchCV(clf, {\"anova__percentile\":[5, 10, 20]}, cv=cv)\n",
    "clf.fit(X, y)\n",
    "\n",
    "coef_ = clf.best_estimator_.steps[-1][1].coef_ \n",
    "coef_ = clf.best_estimator_.steps[0][1].inverse_transform(coef_.reshape(1,-1))\n",
    "coef_selection_ = coef_.reshape(size, size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 525.6x194.4 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#inversing the transform to plot the results on an image \n",
    "\n",
    "plt.close(\"all\")\n",
    "plt.figure(figsize=(7.3, 2.7))\n",
    "plt.subplot(1,3,1)\n",
    "plt.imshow(coef, interpolation=\"nearest\", cmap=plt.cm.RdBu_r)\n",
    "plt.title(\"True weights\")\n",
    "plt.subplot(1,3,2)\n",
    "plt.imshow(coef_selection_, interpolation=\"nearest\", cmap=plt.cm.RdBu_r)\n",
    "plt.title(\"Feature Selection\")\n",
    "plt.subplot(1, 3, 3)\n",
    "plt.imshow(coef_agglomeration_, interpolation=\"nearest\", cmap=plt.cm.RdBu_r)\n",
    "plt.title(\"Feature Agglomeration\")\n",
    "plt.subplots_adjust(0.04, 0.0, 0.98, 0.94, 0.16, 0.26)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.9.9"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}