CV_discrete.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cross-validation for discrete structural parameter\n",
    "Computation of a cross-validation score for different combinations of the number of features $N_f$ and the number of \n",
    "clusters $N_c$ used in adaptive kernel density estimation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import io\n",
    "from sklearn import manifold\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.decomposition import PCA, KernelPCA\n",
    "from sklearn.cross_decomposition import CCA\n",
    "from adap_ks import adap_ks\n",
    "from adap_ks_out import adap_ks_out\n",
    "import euler_curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# load traveltime data and (inverted) velocity data.\n",
    "ttdata = np.load('ttdata_disc.npy')\n",
    "veldata = np.load('veldata_disc.npy')\n",
    "nsamps = np.size(ttdata, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Insight-driven features\n",
    "\n",
    "# Build arrays (images) of the inverted velocities.\n",
    "velimag = np.zeros((49,24,nsamps))\n",
    "for i in range(nsamps):\n",
    "    velimag[:,:,i] = veldata[i,:].reshape(49,24)\n",
    "\n",
    "# compute traveltime histograms.\n",
    "nbins = 15\n",
    "tthist = np.zeros([150,nbins])\n",
    "rang = (np.min(ttdata), np.max(ttdata))\n",
    "for i in range(len(ttdata)):\n",
    "    tthist[i,:], _ = np.histogram(ttdata[i,:], bins=nbins, range=rang, density=True)\n",
    "\n",
    "# compute Euler characteristic curve from inverted velocities.\n",
    "nthreshold = 100\n",
    "eulchar = euler_curve.euler_curve(velimag, nthreshold)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initialize cross-validation matrix.\n",
    "ndims = 10\n",
    "nclus = 15\n",
    "classdiag = np.zeros((nclus,ndims))\n",
    "pscendiag = np.zeros((nclus,ndims))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "score computed for N_f=1 and N_C=2\n",
      "score computed for N_f=1 and N_C=3\n",
      "score computed for N_f=1 and N_C=4\n",
      "score computed for N_f=1 and N_C=5\n",
      "score computed for N_f=1 and N_C=6\n",
      "score computed for N_f=1 and N_C=7\n",
      "score computed for N_f=1 and N_C=8\n",
      "score computed for N_f=1 and N_C=9\n",
      "score computed for N_f=1 and N_C=10\n",
      "score computed for N_f=1 and N_C=11\n",
      "score computed for N_f=1 and N_C=12\n",
      "score computed for N_f=1 and N_C=13\n",
      "score computed for N_f=1 and N_C=14\n",
      "score computed for N_f=1 and N_C=15\n",
      "score computed for N_f=2 and N_C=2\n",
      "score computed for N_f=2 and N_C=3\n",
      "score computed for N_f=2 and N_C=4\n",
      "score computed for N_f=2 and N_C=5\n",
      "score computed for N_f=2 and N_C=6\n",
      "score computed for N_f=2 and N_C=7\n",
      "score computed for N_f=2 and N_C=8\n",
      "score computed for N_f=2 and N_C=9\n",
      "score computed for N_f=2 and N_C=10\n",
      "score computed for N_f=2 and N_C=11\n",
      "score computed for N_f=2 and N_C=12\n",
      "score computed for N_f=2 and N_C=13\n",
      "score computed for N_f=2 and N_C=14\n",
      "score computed for N_f=2 and N_C=15\n",
      "score computed for N_f=3 and N_C=2\n",
      "score computed for N_f=3 and N_C=3\n",
      "score computed for N_f=3 and N_C=4\n",
      "score computed for N_f=3 and N_C=5\n",
      "score computed for N_f=3 and N_C=6\n",
      "score computed for N_f=3 and N_C=7\n",
      "score computed for N_f=3 and N_C=8\n",
      "score computed for N_f=3 and N_C=9\n",
      "score computed for N_f=3 and N_C=10\n",
      "score computed for N_f=3 and N_C=11\n",
      "score computed for N_f=3 and N_C=12\n",
      "score computed for N_f=3 and N_C=13\n",
      "score computed for N_f=3 and N_C=14\n",
      "score computed for N_f=3 and N_C=15\n",
      "score computed for N_f=4 and N_C=2\n",
      "score computed for N_f=4 and N_C=3\n",
      "score computed for N_f=4 and N_C=4\n",
      "score computed for N_f=4 and N_C=5\n",
      "score computed for N_f=4 and N_C=6\n",
      "score computed for N_f=4 and N_C=7\n",
      "score computed for N_f=4 and N_C=8\n",
      "score computed for N_f=4 and N_C=9\n",
      "score computed for N_f=4 and N_C=10\n",
      "score computed for N_f=4 and N_C=11\n",
      "score computed for N_f=4 and N_C=12\n",
      "score computed for N_f=4 and N_C=13\n",
      "score computed for N_f=4 and N_C=14\n",
      "score computed for N_f=4 and N_C=15\n",
      "score computed for N_f=5 and N_C=2\n",
      "score computed for N_f=5 and N_C=3\n",
      "score computed for N_f=5 and N_C=4\n",
      "score computed for N_f=5 and N_C=5\n",
      "score computed for N_f=5 and N_C=6\n",
      "score computed for N_f=5 and N_C=7\n",
      "score computed for N_f=5 and N_C=8\n",
      "score computed for N_f=5 and N_C=9\n",
      "score computed for N_f=5 and N_C=10\n",
      "score computed for N_f=5 and N_C=11\n",
      "score computed for N_f=5 and N_C=12\n",
      "score computed for N_f=5 and N_C=13\n",
      "score computed for N_f=5 and N_C=14\n",
      "score computed for N_f=5 and N_C=15\n",
      "score computed for N_f=6 and N_C=2\n",
      "score computed for N_f=6 and N_C=3\n",
      "score computed for N_f=6 and N_C=4\n",
      "score computed for N_f=6 and N_C=5\n",
      "score computed for N_f=6 and N_C=6\n",
      "score computed for N_f=6 and N_C=7\n",
      "score computed for N_f=6 and N_C=8\n",
      "score computed for N_f=6 and N_C=9\n",
      "score computed for N_f=6 and N_C=10\n",
      "score computed for N_f=6 and N_C=11\n",
      "score computed for N_f=6 and N_C=12\n",
      "score computed for N_f=6 and N_C=13\n",
      "score computed for N_f=6 and N_C=14\n",
      "score computed for N_f=6 and N_C=15\n",
      "score computed for N_f=7 and N_C=2\n",
      "score computed for N_f=7 and N_C=3\n",
      "score computed for N_f=7 and N_C=4\n",
      "score computed for N_f=7 and N_C=5\n",
      "score computed for N_f=7 and N_C=6\n",
      "score computed for N_f=7 and N_C=7\n",
      "score computed for N_f=7 and N_C=8\n",
      "score computed for N_f=7 and N_C=9\n",
      "score computed for N_f=7 and N_C=10\n",
      "score computed for N_f=7 and N_C=11\n",
      "score computed for N_f=7 and N_C=12\n",
      "score computed for N_f=7 and N_C=13\n",
      "score computed for N_f=7 and N_C=14\n",
      "score computed for N_f=7 and N_C=15\n",
      "score computed for N_f=8 and N_C=2\n",
      "score computed for N_f=8 and N_C=3\n",
      "score computed for N_f=8 and N_C=4\n",
      "score computed for N_f=8 and N_C=5\n",
      "score computed for N_f=8 and N_C=6\n",
      "score computed for N_f=8 and N_C=7\n",
      "score computed for N_f=8 and N_C=8\n",
      "score computed for N_f=8 and N_C=9\n",
      "score computed for N_f=8 and N_C=10\n",
      "score computed for N_f=8 and N_C=11\n",
      "score computed for N_f=8 and N_C=12\n",
      "score computed for N_f=8 and N_C=13\n",
      "score computed for N_f=8 and N_C=14\n",
      "score computed for N_f=8 and N_C=15\n",
      "score computed for N_f=9 and N_C=2\n",
      "score computed for N_f=9 and N_C=3\n",
      "score computed for N_f=9 and N_C=4\n",
      "score computed for N_f=9 and N_C=5\n",
      "score computed for N_f=9 and N_C=6\n",
      "score computed for N_f=9 and N_C=7\n",
      "score computed for N_f=9 and N_C=8\n",
      "score computed for N_f=9 and N_C=9\n",
      "score computed for N_f=9 and N_C=10\n",
      "score computed for N_f=9 and N_C=11\n",
      "score computed for N_f=9 and N_C=12\n",
      "score computed for N_f=9 and N_C=13\n",
      "score computed for N_f=9 and N_C=14\n",
      "score computed for N_f=9 and N_C=15\n",
      "score computed for N_f=10 and N_C=2\n",
      "score computed for N_f=10 and N_C=3\n",
      "score computed for N_f=10 and N_C=4\n",
      "score computed for N_f=10 and N_C=5\n",
      "score computed for N_f=10 and N_C=6\n",
      "score computed for N_f=10 and N_C=7\n",
      "score computed for N_f=10 and N_C=8\n",
      "score computed for N_f=10 and N_C=9\n",
      "score computed for N_f=10 and N_C=10\n",
      "score computed for N_f=10 and N_C=11\n",
      "score computed for N_f=10 and N_C=12\n",
      "score computed for N_f=10 and N_C=13\n",
      "score computed for N_f=10 and N_C=14\n",
      "score computed for N_f=10 and N_C=15\n"
     ]
    }
   ],
   "source": [
    "# iterate over the cross-validation combinations (may take a while).\n",
    "# uncomment/comment each of the 6 'blocks' to compute the CV matrix for the corresponding method.\n",
    "for j in range(ndims):\n",
    "    try:\n",
    "        \n",
    "#        textmeth = 'PCA_t'\n",
    "#        dim = j+1\n",
    "#        mypca = PCA(n_components=dim, random_state=5894)\n",
    "#        lowdim = mypca.fit_transform(ttdata)\n",
    "        \n",
    "#        textmeth = 'MDS_t'\n",
    "#        dim=j+1\n",
    "#        mymds = manifold.MDS(n_components=dim, random_state=5894, n_init=20)\n",
    "#        lowdim = mymds.fit_transform(ttdata)\n",
    "        \n",
    "#        textmeth = 'PCA_h'\n",
    "#        dim = j+1\n",
    "#        mypca = PCA(n_components=dim, random_state=5894)\n",
    "#        lowdim = mypca.fit_transform(tthist)\n",
    "        \n",
    "        textmeth = 'MDS_h'\n",
    "        from scipy.spatial.distance import pdist, squareform\n",
    "        from JSD import JSD\n",
    "        dJS = pdist(tthist, JSD)\n",
    "        dJS = np.sqrt(dJS)\n",
    "        dim=j+1\n",
    "        mymds = manifold.MDS(n_components=dim, random_state=8155, n_init=20, dissimilarity='precomputed')\n",
    "        lowdim = mymds.fit_transform(squareform(dJS))\n",
    "        \n",
    "#        textmeth = 'MDS_v'\n",
    "#        dim=j+1\n",
    "#        mymds = manifold.MDS(n_components=dim, random_state=5894, n_init=20)\n",
    "#        lowdim = mymds.fit_transform(veldata)\n",
    "\n",
    "#        textmeth = 'MDS_c'\n",
    "#        dim=j+1\n",
    "#        mymds = manifold.MDS(n_components=dim, random_state=2358, n_init=20)\n",
    "#        lowdim = mymds.fit_transform(eulchar)\n",
    "        \n",
    "        for l in range(nclus-1):\n",
    "            \n",
    "            K = l+2\n",
    "            obs = lowdim[:,:dim]\n",
    "            prior = np.array([1/3, 1/3, 1/3])\n",
    "            dens1 = np.zeros(len(obs))\n",
    "            dens2 = np.zeros(len(obs))\n",
    "            dens3 = np.zeros(len(obs))\n",
    "            dens1[50:] = adap_ks(lowdim[:50,:], dim, K, obs[50:])\n",
    "            dens2[:50] = adap_ks(lowdim[50:100,:], dim, K, obs[:50])\n",
    "            dens2[100:] = adap_ks(lowdim[50:100,:], dim, K, obs[100:])\n",
    "            dens3[:100] = adap_ks(lowdim[100:150,:], dim, K, obs[:100])\n",
    "            nsims = 50\n",
    "            for i in range(50):\n",
    "                #print(i)\n",
    "                dens1[i] = adap_ks_out(lowdim[:50], dim, K, i, nsims)\n",
    "                dens2[50+i] = adap_ks_out(lowdim[50:100], dim, K, i, nsims)\n",
    "                dens3[100+i] = adap_ks_out(lowdim[100:], dim, K, i, nsims)\n",
    "            \n",
    "               \n",
    "            dens = np.column_stack([dens1, dens2, dens3])\n",
    "            pscen = np.zeros(dens.shape)\n",
    "            classp = np.zeros(dens.shape)\n",
    "            for i in range(len(dens)):\n",
    "               pscen[i] = (prior*dens[i,:])/np.dot(prior,dens[i,:])\n",
    "               classp[i] = 1*(pscen[i] == np.max(pscen[i]))\n",
    "               \n",
    "            # Build classification matrix (confusion matrix) and mean updated probability matrix\n",
    "            nscen = 3\n",
    "            pscen_eff = np.zeros([nscen, nscen])\n",
    "            classp_eff = np.zeros([nscen, nscen])\n",
    "            for i in range(nscen):\n",
    "                classp_eff[i] = sum(classp[i*50:(i+1)*50])\n",
    "                pscen_eff[i] = np.mean(pscen[i*50:(i+1)*50], axis=0)\n",
    "            classdiag[l,j]=np.sum(np.diag(classp_eff))\n",
    "            pscendiag[l,j]=np.sum(np.diag(pscen_eff))\n",
    "            print('score computed for N_f=%i and N_C=%i'%(j+1,K))\n",
    "    except:\n",
    "        pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
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     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 252x252 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the cross-validation matrix\n",
    "\n",
    "# In case the AKDE computes a bandwidth of zero, the KDE estimation is not defined, then to plot we set:\n",
    "classdiag[classdiag==0.0] = np.nan\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "fig.set_size_inches(3.5,3.5)\n",
    "cb = ax.matshow(classdiag, origin='lower')\n",
    "ax.set_xticks(np.arange(0,10,2))\n",
    "ax.set_xticklabels(np.arange(1,11,2))\n",
    "ax.set_yticks(np.arange(0,14,2))\n",
    "ax.set_yticklabels(np.arange(2,16,2))\n",
    "ax.tick_params(labelbottom=True, labeltop=False, axis='x')\n",
    "ax.set_xlabel(r'$N_{dim}$')\n",
    "ax.set_ylabel(r'$N_k$')\n",
    "fig.colorbar(cb, orientation='vertical', fraction=.1)"
   ]
  },
  {
   "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}