pca.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Principal Components Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import Libraries\n",
    "import numpy as np\n",
    "from pylearn_ml191.dimentional_reduction import PCA\n",
    "\n",
    "from sklearn.decomposition import PCA as Sklearn_PCA\n",
    "from sklearn.metrics import classification_report\n",
    "from sklearn import datasets\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.svm import SVC\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib import lines\n",
    "%matplotlib inline\n",
    "\n",
    "# Fixed random seed \n",
    "np.random.seed(21)\n",
    "\n",
    "# Ignore warnings \n",
    "import warnings \n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Data Generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def true_model(x):\n",
    "    return x - 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 10\n",
    "x_min = 0\n",
    "x_max = 2\n",
    "\n",
    "norm_mu = 0\n",
    "norm_scale = 1\n",
    "\n",
    "x = np.random.uniform(x_min, x_max, N)\n",
    "noise = np.random.normal(norm_mu, norm_scale, N)\n",
    "y = (true_model(x) + noise)\n",
    "\n",
    "x = np.reshape(x, (N, 1))\n",
    "y = np.reshape(y, (N, 1))\n",
    "\n",
    "X = np.concatenate([x, y], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# For plot true model \n",
    "step_size = 0.001\n",
    "x_plot = np.arange(x_min, x_max, step_size)\n",
    "y_true_plot = true_model(x_plot)\n",
    "\n",
    "plt.figure(figsize=(7,4))\n",
    "plt.scatter(X[:, 0], X[:,1], s=60, c='blue', alpha=0.5)\n",
    "plt.plot(x_plot, y_true_plot, linewidth=2, c ='g')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Some helper functions\n",
    "def project(X, u):\n",
    "    def project_vec(x, u):\n",
    "        return u * (x @ u) / (u @ u) \n",
    "    u = u.reshape((-1,))\n",
    "    Z = np.zeros(X.shape)\n",
    "    for i, x in enumerate(X):\n",
    "        z = project_vec(x, u)\n",
    "        Z[i] = z\n",
    "    return Z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Principal Component Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "===================================================\n",
      "Nghiệm do thư viện tự hiện thực (pylearn_ml191): \n",
      "[[-0.29442484 -0.95567464]]\n",
      "---------------------------------------------------\n",
      "Nghiệm của PCA trong sklearn: \n",
      "[[0.29442484 0.95567464]]\n",
      "===================================================\n"
     ]
    }
   ],
   "source": [
    "# Visualization \n",
    "step_size = 0.001\n",
    "x_plot = np.arange(x_min, x_max, step_size)\n",
    "y_true_plot = true_model(x_plot)\n",
    "\n",
    "pca = PCA(n_components = 1)\n",
    "Y = pca.fit_transform(X)\n",
    "X_retrival = pca.inverse_transform(Y)\n",
    "print(\"===================================================\")\n",
    "print(\"Nghiệm do thư viện tự hiện thực (pylearn_ml191): \")\n",
    "print(pca.U)\n",
    "print(\"---------------------------------------------------\")\n",
    "sPCA = Sklearn_PCA(n_components=1)\n",
    "sPCA.fit(X)\n",
    "print(\"Nghiệm của PCA trong sklearn: \")\n",
    "print(sPCA.components_)\n",
    "print(\"===================================================\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "custom_point = 4\n",
    "ori = X[custom_point]\n",
    "new = X_retrival[custom_point]\n",
    "\n",
    "pca = PCA(n_components=2)\n",
    "pca.fit(X)\n",
    "vecs = pca.U\n",
    "mean = pca.mean\n",
    "\n",
    "plt.scatter(X[:, 0], X[:,1], s=60, c='r', alpha=1)\n",
    "plt.plot([ori[0], mean[0]], [ori[1], mean[1]] , 'g', alpha=0.6)\n",
    "plt.plot([new[0], mean[0]], [ori[1], mean[1]] , 'b', alpha=0.6)\n",
    "plt.plot([ori[0], new[0]], [ori[1], new[1]] , 'y--')\n",
    "\n",
    "u1, u2 = vecs\n",
    "u1_vec = plt.arrow(*mean, u1[0]*0.5, u1[1]*0.5, head_width=0.05, linewidth=2, color='b', label=\"u1\")\n",
    "plt.arrow(*mean, - u1[0]*0.5, - u1[1]*0.5, head_width=0.05, linewidth=2, color='b', label=\"u1\")\n",
    "u2_vec = plt.arrow(*mean, u2[0] * 0.5, u2[1] * 0.5, head_width=0.05, linewidth=2, color='black', label=\"u2\")\n",
    "plt.arrow(*mean, - u2[0]*0.5, - u2[1]*0.5, head_width=0.05, linewidth=2, color='black', label=\"u2\")\n",
    "plt.legend([u1_vec, u2_vec,], ['$u_{1}$', '$u_{2}$']);\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Using PCA with IRIS dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1 Loading IRIS Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "iris = datasets.load_iris()\n",
    "X = iris.data\n",
    "y = iris.target\n",
    "target_names = iris.target_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PCA from pylearn_ml191: \n",
      "=======================\n",
      "10 samples from X_new: \n",
      "---------------------\n",
      "[[-2.68412563 -0.31939725]\n",
      " [-2.71414169  0.17700123]\n",
      " [-2.88899057  0.14494943]\n",
      " [-2.74534286  0.31829898]\n",
      " [-2.72871654 -0.32675451]\n",
      " [-2.28085963 -0.74133045]\n",
      " [-2.82053775  0.08946138]\n",
      " [-2.62614497 -0.16338496]\n",
      " [-2.88638273  0.57831175]\n",
      " [-2.6727558   0.11377425]]\n",
      "---------------------\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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m4rXV2BSYvXmMwY7gQLCJcNz/S64nWql0HX6zcuVKfvGLX7BlyxZuvvlmrr76an7605/S09MDwNGjR2ltbT3rcSdPnsTn83HTTTfxzW9+k5dffnnE/RdccAEtLS3s2GEd0NLd3Y3H4+EDH/gAGzduBODgwYO88847nH/++SMeG3zNtm3bmDp16lmfIFIhUzn82cCRoJ+b/bcdC71QRFZhfQpg3rx5GRmcyrwWj5tym4M8sTFkDA7ADgwan55opQDr8JvHOqwQUSg2+ozPOvymNLnDby666CK6u7uZPXs2M2fOZObMmezfv5/3vve9ABQXF/Pzn/8cu90+4nFHjx7lzjvvxOez3oS+853vjLjf5XKxadMm7rvvPvr7+ykoKOCZZ57h3nvv5e6772bhwoU4HA7Wr19PXl7eiMeuWbOGO++8k0WLFlFYWJi2Hvopa48sIpXAb40xF4e573fAd4wx2/0//xn4Z2PMrmjPmY32yNqONTPWtDXR4fXgMT4ODw1iQzAYbAgzHK7cPuREJSze9siBBf1jHjczdUH/LLnaHrkZmBv08xygJUOvHbPAoclFRa4RhyavXbtCg36KBWZv+TYb8xx5tHjdDPgMF+QVcEfpdP2lVsAYO/xmDMhUHf5TwG3+ap1lQKcx5qx0Tral49BkFV7w0YVegcX5xTxcUcV3Z5yrv+BKpUlKZvgi8j/AcmCqiDQDDwJOAGPMD4HfA9cCh4A+4M5UvG6qNTZ2MH168Yjbkj00WUWmszelMislAd8Y88lR7jfAZ1PxWulUVVVGa2svJSVnFlSSPTRZKaVyhbZWCFJXt5TeXjddXYP4fIaurkH/oclLsz00pZRKmgb8IDU1laxdu4KKiiJOnOihoqJIF2yVUuOG9tIJoYcmKzWxtLS08LnPfW64AVqs7rrrLr74xS+yYMGCiNf88Ic/pLCwMCWNz1IhZXX46ZCNOnylVPrEW4efTaloR5xu8dbha0pHqQhS3ZpXJeBIAzxVCxuqra9HGpJ6ukjtkS++2Novun79empra/noRz/KihUr8Pl83HvvvVx00UVcd911XHvttcOfBJYvX05gQlpcXMwDDzzAJZdcwrJlyzhx4sTw8//7v/87AIcOHeLKK6/kkksu4dJLL+Wtt96ip6eHD33oQ1x66aUsXLiQX//610n9/UajAV+pMALN3Tq8nhGteTXoZ9CRBti2GvpaoWi69XXb6qSC/sqVK9m0adPwz0888cRwd8uAF154gccff5xnn32WJ598kqamJvbt28dPfvITXnjhhbDP29vby7Jly9izZw8f+MAH+PGPf3zWNbfccguf/exn2bNnD3/729+YOXMm+fn5/OpXv+Lll1/mueeeY/Xq1TE1W0uUBnylwkhHa14Vp1fqwVkEeSUgNuurs8i6PUHh2iOH9uy66qqrmDJlCmC1La6trcVmszFjxgz+4R/+Iezzulyu4eMKL7vsMpqamkbc393dzdGjR/nYxz4GQH5+PoWFhRhj+NrXvsaiRYu48sorOXr06PCng3TI7QSVUlkSaO4WbMx28TzSYAXJzkYorYIldTC3JtujGl1nozWzD+Yqhq7GpJ420B75+PHjrFy58qz7g9sRxzrbdjqdw+2M7XY7Ho9nxP2Rnmfjxo20tbWxa9cunE4nlZWVDAwMxPpXiZvO8JUKI12teTMuDWmRjCmtAnfPyNvcPVBSldTThrZHjuaKK67gl7/8JT6fjxMnTrBt27aEXrOkpIQ5c+awdetWAAYHB+nr66Ozs5OKigqcTifPPfcchw8fTuj5Y6UBX6XVWF34vLG4nAGfj16fF2MMvT6v1Zq3OLnWvBl1pAF+fwt0HIDTb0L/qZSkRTJmSR0M9cJgFxif9XWo17o9CaHtkaO56aabmDNnDhdffDH/9E//xHve8x5KS0sTet0NGzbwve99j0WLFvG+972P48ePc8stt7Bz506qq6vZuHEjF1xwQULPHSsty1RpE3wmaXA/87HS+nhMt+YNzOxPHQBHAeAFnxemXAgFU6DvBHwq879bcZdlBtJRXY3WzD4L6aienh6Ki4tpb2/n8ssv569//SszZszI6BgiydX2yGoCCl74BCgS+/Dt2Q6csRycPqabuw0veE4C7yAE1iO6D4PdlXRaJGPm1mR9veG6667j9OnTuN1uvv71r+dMsE+EBnyVNrm68Bn8ySO45PIeGLsBPlRgwbOkEtpf999oB3d3StIiE0mieftcpDl8lTa5uPC5u7+bb598hyOeQZqHBunyecZnyWVgwbOgHMoXgD0PPP2QVwrL12Z11pzLaeSxJJF/R53hq7RJ15mksQpN21zsLOBPfZ30+ry4RBgyhsNDg8wHSmyOEZ88Ykn55LQldVYOHyC/DGxOa2af5WCfn59Pe3s75eXlw2WMKn7GGNrb28nPz4/rcRrwVdosLpjEPTBy4bM0M4EzXNrm8f5WKuxOCmx2hjA4EDwGjnuGcDhtw588Ek355NSbxNwaK7hnecEz1Jw5c2hubqatrS2r4xgP8vPzmTNnTlyP0YCv0ipbC5/hFoy9xnDa52WGw8XhoQE8AjYM/caM+OSRyGJzTq4L5MCCZyin00lV1RhZMB6HNIevxqUWj5tCGfm/d77Y6Dc+Su0O5jvzcSK4jaFIbCNKRcM9drTFZm3FoMYCDfhqXAq3YFxmd2IHen1eSmx25jjzmOvM54Gp80bMwhNZbE7kTUKpTNOAr8alcDtlHSLcXlJBmd3BKZ+HMrsj7CawRHbZ5mJFklKhNIevxqVoC8bRu6ckttic7YqkMdsgTWWUtlZQE16qqmuy1ooh0EbBWWR1k3T35EQJpsoOba0Qo4aGJurrd9DY2EFVVRl1dUv1fNtxLpXVNVlrxRDcNx7OfH2l/uyAv+tR2PkIDHRY9fnVX4bLPp/Z8aqs0Ry+X0NDE6tXP01ray/TpxfT2trL6tVP09DQlO2hqTQaF9U1nY3WzD5YuL7xux6F7V+z2is4iqyv279m3a4mBJ3h+9XX76CoyEVJSR7A8Nf6+h06yx/HYu33k41NVTG/ZmmV1ec+MLOH8H3jdz5iNVFz+Hdn2vLBM2DdrrP8CUFn+H6NjR0UF4+sqCgudtHY2JGlEalMiKW6Jhvn28b1mrH2jR/oAFveyNtsedbtkPIDw1Xu0YDvV1VVRk/PyFldT4+bqqqyLI1IZUIsJZjZSPvE9ZqBNgqFFVaf+8KK8Au2+WXgGxx5m2/Qun0sn4ylYpaSgC8i14jIARE5JCL3h7n/DhFpE5Hd/j93peJ1w2loaKK2djPV1euord0ccw6+rm4pvb1uuroG8fkMXV2D9Pa6qatbOvqD1Zi1uGAS95TNjFqbH25T1ZDPx67+7rSd5BX3Rq65NXD9ZutQk+s3h6/Oqf4y+DxWGsdn/F891u1pODBc5Z6kc/giYge+D1wFNAM7ROQpY8zrIZduMsaktQl3YOG1qMg1YuF17doVYfPwoVU5t966iO3bjwRV6SzX/P0EMFp1zSyHiw6vZ7inTqd3iEbPAC7S1zcn9DUhBRu5Ann6cFU6r28Y/cBwrfUf81KxaHs5cMgY8zaAiPwCuAEIDfhpF8/Ca7g3hw0b9kZ8c1ATV+imqqMeN2JgjivPSrdEaa6W6GJv2jZyXfb58Au0oy38Btf6B6d8tNZ/TElFSmc2cCTo52b/baFuEpG9IrJFROam4HXPEs/Ca/Cbg80mlJTkUVTkor5+RzqGpsaw0LSP1xgqnfmU2s/MlyJV9iS62BtLqimlRlv41ZTPuJCKGX64UwxCt+/+BvgfY8ygiNwNPA58MOyTiawCVgHMmzcvroFUVZXR2to7PLOHyAuvjY0dTJ8+snZZq3JUJMFpnzVtTXR4PSPuD5duSfZM34xu5Bqtf37gyMRg4Wr9VU5LxQy/GQiesc8BWoIvMMa0G2MC5QE/Bi6L9GTGmHXGmGpjTPW0adPiGkg8C69alaMSFWtztTHXQTPawm/gyMRg4Wr9VU5LRcDfAZwnIlUi4gJWAk8FXyAiM4N+vB7Yn4LXPUtNTSVr166goqKIEyd6qKgoipiT16oclahY0y251EFzd383a9qaEq8qirXWX+W0lDRPE5Frge8CduCnxphvi8hDwE5jzFMi8h2sQO8BTgH3GGPeGO150908TXvnqHQK7tMz5PNx1ONmEB/nOwu4c/KMjKVrgscRvAAc95pAoEonh45MVGeL1jxNu2UqNYpk2irs7u9mfecJ3hjsI99mY5bdhdNmSyzgJiiw5hBYSwDrEJgyu4M10yrT/voqs6IFfN1pq1QUybZVWFwwicl2B+fnFbIgr4jJDmfGG7SNubUElTbaPE2NC+lqbpZspQ3E1qAtnc3ZRt3EpRuqJgyd4asxL53NzVIxOw4s3nZ6hzgw2MfegR72u/vI91c0p7s5W9SqIu2hM6FM2ICfaM8dlXvS2dwstNKm0zvEfncfLUODMVe73FhczinPEG8PDTBkfAjg9vk45fMMz+zT2ZwtalWRbqiaUCZkSifenjsqt8Xa0z4RNxaXs/ZUM03uAQaMFw/WL805zoKYe+gsLphEucNJl9uLF0Oe2JjhdOEQGU7jpGP8MaWJdEPVhDIhA368h51o+WZuS3WjseBAWSg2BrxeRMBrrG3lNmR4Jg6x5fP7jI8FeYWInNmYbozhmD8Yp7pRWsxHN8Z6eIoaFyZkSieenjt69GHui3XnayxC8+mN7gF68DHb4SJfbEwSO06bjeP+2XesM/Fom7BSOf6AmNNEuqFqQpmQAT+etgraZC33pbLRWGig9GJwIhz3DJEnNrxYuwsHjY9Or4fXB2PL50cL6ulolBZusXnBiR189Lm7R55oFevhKWpcmJApnbq6paxe/TRgzex7etz+tgrLz7pWm6yNDalqNBaaT88TG30+D33GhwNrq7jTCA6g0d2PEahy5I+az19cMIl7sN5Qjnnc1sy+9ExOPdWN0kLTRJXH/841u76NL1J7Yw3wE8KEDPiBnjsj8/LhDzuJpwOnyi2J1LaHBspJYqMD66NwvtjoNz7cGHwIBTYbsx0uSu3O4cdHy+dnsvtlaD/9pQceZ8BRyPSCKWeqccCqxtFgP2FMyIAPVtCPZeE18Gng9Ol+Wlv76Olx43AIa9YsT/sYVeJiXrQMERooTxsvTqyZvgcotjmYbHPQ6nVzoWvkImwu7V4N/UQxvaeZouJZI3r451w1jm4AS7sJG/CjCVTl7N17nN7eIQYHh+jsdONw2CgtzaOioogNG/ayePEMrdbJUYnukA0NlF5jOMdZwGTHmVm8MYZWr5s+40vtEYQpNuITRfkFVhoneHy5VI2jJ2plhAb8EIGqnKEhL8eP9wBCX98QTqcNl8tOVVUZ5eWFdHUNRizjVNmXTG37aIedtHrc2AwccPeRh5XWCTRES/oIwnRZUmcFULBm9u6exKpxkp2FR3p88AYw0JRTmkzIKp1oAlU5bW19OBx28vMdGGPwen3Y7Taamk4DZxZudcdubkpVL/rQ6poTQ4Mc9biZ6nDxLkc+IvD20AACGet+mZC5NbDgVuh8C45ss74uuDX+YJ1oG4YjDfCLGnjyWmjeBjbnyMd3NlpvRMFyLeU0DmjADxGo0e/rG8LhsP557HbB6zU4HDb6+oYAaG7u5PDhTq69diPbtjXidNq0Rj+HpKq2PbRkssvnZbYjj+lOF5MdThbkFXF+XiGT7Y7cDfZgBdXXN0DpOTB3ufX19Q3x9cxJtA1D4I2i/XWw51v1/qf2g2/ozOP1RK2M0JROiEBVTmGhk8FBLw6Hjbw8B319Q5w61Ycx8Pzzhxkc9JCXZyc/34nPB/v3n2TBgmnDNfqa6smu0cog432uwONWHTuYtjYOwZLqnhkubZKKlEksbRiivbZvCOwuCCx0dzVBxRLr8TVrU5NyUlFpwA8RqMqZNq2QpqbTeDw+vF6DzQY+H+TlORgYGMJms2b9eXkyXKnR1HSaJUtmao1+jkhHGWQ62iDA2e0c2j1DTHE4Y6swCg6yrmLoboHimSPTLoNdMOW8kY+LN2UyWhuGSAuvQ90w+VxwFoJ3EMRh/RnqO/P40Q5RVymhKZ0ggeqcrq5B2tv7KSnJZ9IkFyJQWlrA0mBtfzwAAB3GSURBVKWz+eAHqygocFJQ4Bx+MwBwOGx0dQ3y0kvNvPXWKc3nj1PpaIMQrp3DSd8QHuMbvXtmaF69/TXoOwZe98i0i7cv+ZTJaG0YIqV8hnqt15o0H3xe8Hn8s33nyMdHO0RdpYQGfL/gnjnnnVfOOedMYfr0IjZu/DgXXDCVyy+fzdSphQAUFjoREX9u34fH46Ovz83AgIeBAQ/nnz9V8/njVDraIERr5xAQMW0UGmS9Q2BzQffhM9e4is8E3sEu6GuDlhfhxE7ob4s9jz9aG4ZIC6+OQuu17S6YcgFgs2b65Rdp2WWG6Zm2frW1m8/aUdvVNUhFRRHAiPveeusUBw9as62Skjy8Xh+9vUMUF7u48MJpw28Mgcdv3lybkb+DGpsC6wKB1OCBwT7cxocBFuUX0+n10Dw0iA/DZQWTRubzN1RbM/tA35wTu8AzYM3w80qstInNCeUL4P0PwV+/YQV6ZyGUnmsF4aHe1ATep2rPTvkMdllvDIFcvqZr0i7ambaaw/eL1jNn7doVw713Wlt7ePPNU/6qHWFgwENenoMZM4q45JKZ2Gxy1uPVxBLvgmvousAMh4tGdz8um43TniGahgYi9+wJzauXVELrbvC5wZNnvRF4BqDvuHV/YQVMrx4ZlCE19e7Rav21X09O0JSOX2gHzZMn+3jppaO89VYH9fU7uPXWRQAcPHgKEZg8OZ+SknxcLjvz5pUAEnMHTjV+JXJcYei6gEOEcoeT+Y48jngGcdlsvMuZH/4A9NC8us0JNruVwjFecOTDtIVQOGPkwm6wVNW7a+fNnKczfL/gDpqDgx5ee60VgIsvrqC1tZcNG/ZSXOyisNBJQYFjRA8VK92TT2+vFfBH68Cpxq9EWjqEKyG9s3Q6iwsmnZXugTP5/N393WzNn0/Rwi9w7Zv/TVVPC4WTz4XCmVZFTnB7ZOOzgnq6DzzRmXxO04DvF9xB85ln3iI/38F555VTXl44fM2ePScoLnbhdntxOKxfQIfDRk+PmyuumE9d3dKYOnCqsS9S2ibRlg6RSkgjlYHmI8PN4QZnvo91M5Yx4PNZC8h/+nTkoJ6qFgtqTNJF27Cvu47p04tH5ON9PsPf/vYO8+aVcvhwJ3a7DbtdGBz0YrMJW7d+QoP7BBHcibNQbPQZ33Cw3drTbgVo25kA3evzUmZ3sGZaZcpeq8Bmw0D41xk4fKYePjioB9Irgbp9XUAdl3TRNk6ReuAvWjSD3l438+eXhrRKrhk12Ou5uONHtLRNaHvlQICOp6la6KeHqwpLeXWof8SO4R+cPhb5k8Rom5hyOe2iLZLTSgN+GJFOxFq7dgVgNVhzOmMP3IEa/6Ii14hzcdeuXaFBfwyKlrZJtqVDuD7+fxrqPKvWf1bgk0SkHb+5HNQj0RbJaacBP4zRTsSKN0gHn4sLDH/Vnjtj02jtFZJp6RDrom8qPknknFj6/egngKSkJOCLyDXAo1jnO//EGPNwyP15wP8BLgPagU8YY5pS8drpEuuJWLHQc3HHl3QG21gXfVPZHC5njNacTT8BJC3pgC8iduD7wFVAM7BDRJ4yxrwedNlngA5jzLkishL4V+ATyb52NsWTk9dzcceXRIJtrJux4mnOlskzcjNitJJRPSQlaanYeHU5cMgY87Yxxg38Argh5JobgMf9328BPiTBhcVjTHDfneCcfKS+OXV1S+ntddPVNYjPZ+jqGvTX6C/N7MBVyiwumMSaaZX8aOa7WTOtctRgH+tmrHQ0ZxszRmvOpoekJC0VAX82cCTo52b/bWGvMcZ4gE4g7P/BIrJKRHaKyM62trYUDC/1gnPyNptQUpI33Ac/nMCaQEVFESdO9FBRUaQLthNIaHO0aN0v09GcLWOONFj9dDZUW1/jOVwFRt+pq4ekJC0VOfxwM/XQ4v5YrrFuNGYdsA6sOvzkhpYeieTkU7kmoMaWeDdjjblUzZEG+NuDcHyH1Rlz8jmJ59ejVRfpprGkpWKG3wzMDfp5DtAS6RoRcQClwKkUvHbKxXJGbWjfHdCcvIosVefrBtvd382atiZWHTvImramqL160mr4+MLXwJ4H+ODUG1a3zliOP4yH9upJWioC/g7gPBGpEhEXsBJ4KuSap4Db/d/fDDxrcnCLb6y5ec3Jq3ikOi+fSIO2lAiXsgkspHqH/I3bHFbztu7D6cmv6yEpSUk64Ptz8nXAH4H9wBPGmNdE5CERud5/2X8B5SJyCPgicH+yr5sOsebmk8nJx/IJQo0vqc7Lx7MmkDKhJ2sFUjate/wHrBSC8VjXin3k8YUqZ6SkDt8Y83vg9yG3fSPo+wEg508BGS03n2x7BN1xO3GlMi+faIO2pEQqiew7Dl3N4BmEwdPW7N6WZ7Vl1vx6ztF++EGi5ebjKcWMNIuPt7pHqXDSsSYwqkglkQicPgDuLsBYZ9V6eqFolubXc9C4DPiJpk2i5eZjDdbR3hgaGzsoLh75S6k7blW8slKrH6kk0jsA2EDESuXYnGDPh4Kys4N9smWbKmnjLuDHuykqWLTcfKzBOtobg1b3qIBkqmyyUqsfaVOUZ8BK3+SXQcEU66sjH9r2jHx8pDUADfoZNe6apyXbqCxSvXxoe4T29j7efLMdj8dHbe3m4Xx+rGfj6qlYE1e4jpgjzqmNQcZr9SO1XP71jZy9zUY4a5uNtkXICeNuhp+utElwuufkyV727TvBwICH88+fOuJTRLRZvO64VZClKptUCFcSOXWRdWC6zwPGWF99buv2YKO1RdB0T0aMuxl+uhqVjTwC8W3y852ce+4Upk49cwRiff2Os87GfeutDvr63CxdOpuGhibdcavCVtkM+Xzscnez6tjBqM3Vcs77H4I//iP0t8KQf+HWng/nfXzkddEao2kXzIwZdzP8dG6KqqmpZPPmWs45p4zLL589ItgHPkUE3hgA9u07ARgWLZqOMcS8lqDGt9Aqm07vEI2eAWxIZjdSpcLcGljyWWvR1p4PBdOs1gqvbxg5S4/WGC043SM262uqd+kqYBwG/EykTUZbfK2pqaSioojq6tksWzaXqVOLtARTDQutsjnqcSMG5jjzxlaKJ+DodiuFM285zKiGknlnB+zAGoAItPwNTu61rgHtgplB4y6lA+lvVBZI25w+3R9ytu3y4Wv00BMVSWg/fa8xVDrzKbWf+XWMtJEq1r76GTXawSXB3D3Wm0Og+dm21We+j9QHX6XMuJvhZ0JNTSW33rqId97poqdnkOJiJ/PmlbJhw97hlI2WYKpogvvpX1YwCadt5K9iuI1UifTQSbj8M55F1FjbFkdK3RgTvQ++ShkN+KOItIlr+/YjLFo0neXLq6iuns28eZNHpGy0wZqKVawbqeKt7onnDSL4jeFn+zbR99wXYq+ZH+3gkoBIqRtPr3bBzFCVkgb8CKyKmvVce+1Gtm1rxOm0xbVrVkswVaxi3UjV4nFTKCN/ZaP10In1DSL0jWHxG+tpxkmnozC2RdRY2xZH+yQQTxfM8VbCmcFNaeMyh5+swG7dw4c7yc934vPB/v0nWbBg2ohds6OVf2oJpopVLBupgs+77fR6OO5x0+/zUmSzs7u/O+wbRCxN1oLfGACm9TRzOr+c4173mXWF0RZRox1cEpCKA0zGYwlnBjel6Qw/jMBu3aEhL3a74HDYsNttNDWdHp7Fa8pGZVog9XNiyE2Tu58B40NEKLHZw6ZqYm2yFvrJoaN4LoWefgZ9QbtlU7GIGu8BJtH674+nEs4MVinpDD+MQIVNYaGTwUEvDocV9Lu6BnnppWZ6etxcc81GPB4vDoedqVMLWbZsDnV1y3VGr1ImXEXOPWUz+fbJdzAiFIiNGQ4npXYnvT4vW3vaR8zybywu57GOY4A1s+8zPmttoHTk2kDwJweAF86/jWt2fosSAFOQ2qMEY/kkAJFn8oNdMOW8kdeO9RLOaJvSUkxn+GEEKmzmz5+M1+ujv3+I9vY+enuHaG/vZ2DAy9CQtcBms8GpU31cccVcDfYqZbacPsHX25p4qb+bds8QR9wDw8G7zOHkkrwizs8rpNTuBMKnamJdGwhdNH6toponltxP6aRZmVlEjWcm7+0bfweZx7ronQKSgycNDquurjY7d+7M+OsGH1TS1tbDwYOn8HoNdrvg9Vr/Xg6HDRGw2YS8PAeTJrlobv5ixseqxp/d/d18va0JH+BC8AI+DNPtTua68gGsGbk/5w7Q6/NSZnewZlplwq8Z2BcwM5P1/cEz+eC8/lA3TD7XCvYBxgenD4Fzkj/4u6HzkHW61vRqq83DWM3jB97kghvTJfh3EZFdxpjqcPdpSieM4L45e/eeoKysgL4+N8XFebS29gLg8/lwOOx4vYa8PDsdHf1ZHrUaL7b2tOM1hjybDUFwAB4Dp31eHB4390yeGVOqJh4Z774ZEO0krXCbsaYusoLh3x60dus6CmHqQuv+WBdvA8G1s9FKpyQRXFMm1lRXkjTgRxCosKmuXsf06cW88soxBge92Gzg81l7RYyxZv29vW58PqiuXpfQ0YdKBWvxuMkXGx7O/ILagX7/gmvoTt2ZDhc3lubAjttoIgXZSLt0HYVW0D/1Onjc4HBB/pQzs/iCadasPvgNAcJXtgS/tqsYulugeOb4qfKJg+bwRxHI51dWWvl8l8v6GG2MNcsXgf5+D7NmFSV89KFSwWY5XJTZnfiMwYPBYHBjsMPwZqzgnbprplXmfrCPVGceqTa/eBb4jNVWP9BeP7hqKNbKltDXbn8N+o5Z6aDxUuUTBw34owiUXzqddi68cCrFxS7sdnC5bDgcdkCoqiplwYLpCR99qFSwG4vLcYgw3e7CYWDQ58MG3F5SkduBPZJopZSRFiyNsWbhs5bBnA9YX4tnngnMibZz8A6BzQXdh89cM9arfOKgAX8UwTtmh4Z8LF9exZ//fDuDg19nYOBfuOiiaVxwQcWIxwRq9YNn9Lfc8iRDQ149wFyNKlBdM9eVxzSni8sLS/jmtEpunjw96uOSOTYxadF2v0abjUeqzR/qjT6DT7Sdg7MQMNZCb8BYr/KJg+bwYxBtx2xVVRkHD56kra2Pvr4hCgudTJtWyOTJBcOVPtOnF3PgwEm6u90UFrqG++hr90wVSbyLqKk4NjFho+1+Ha3OPNyCZSyPCXfk4mjPU1IJbfusc3eNL7V7DMYAneEn6Yor5nLo0Cl6e4dwuez09g5x6NApOjsHRhxmPmmS1YLh8OHTw4/t6XFTVOTSvL5KWlaPTRxt92sideaxPCaW/juhz2NzwqRZUL5gQjZq04CfpO3bj3DuuVMoKnLidnspKrKOPjx8uHNEc7XKysmAobvbPdyK4dixbo4f79a8vkpavI3VUmq0BdR4Wyok+phYn+eqdbCyIbZGbYnI4eZumtJJUmNjB3PmlDJv3uTh23w+wzvvdNLT4x5urlZeXkhl5WTa2/s5caKHqqoyRKy1qcA1ga/19Tu0rFPFddhJaHsECN83Jy1iaQ0Qb515KmvlM1TjDuR8czed4Scp0kEnixbNOKu5mtNpZ+PGj7Nz5yo2b66lp8cdtcWymrjiPewk1p76aZHq1gAZbBeccjne3C2pgC8iU0TkTyLypv9r2OOcRMQrIrv9f55K5jVzTaSumQ89tHzUfvh6KpaKJN6cfKx9c9IiVemXgBwPmlHl+Pm8yaZ07gf+bIx5WETu9//8lTDX9RtjFif5WjmrqMjFrl1Hcbt95OU5uOyymcDo/fADZ+OCNbPv6XH7Wywvz8CoVS6LtZd9sHgqe1J+Nm4q0ybxnJGbazLY+TIRyaZ0bgAe93//OHBjks83pgQ2U50+3Y/dbqegwInNBh0d/TEtvuqpWCqSWHvZJyKRs3EzKtZNVbkog50vE5FUt0wROW2MmRz0c4cx5qx8hIh4gN2AB3jYGLM1ynOuAlYBzJs377LDhw9HujTrams309ray5tvtvv75tvweHzk5dk577xyKiqK2Ly5NtvDVGNQcF19cIO0VKRp1rQ1pbzbZkpF6qCZIwufo0ph58tEJNUtU0SeAWaEueuBOMYwzxjTIiLvAp4VkX3GmLfCXWiMWQesA6s9chyvkXGBg1L6+oaGe+w4HDb6+oZ08VUlJZ0N0hJJF2VUrJuqckW4iqLrN2d7VGGNGvCNMVdGuk9ETojITGPMMRGZCbRGeI4W/9e3RWQbsAQIG/DHksC5tsEnY3k8PgoLnbr4qpKWrpbFWS3hjFUsawK50OY4x8swQyWbw38KuN3//e3Ar0MvEJEyEcnzfz8VeD/wepKvmxMCFToFBXa6ugY5ebKPrq4BCgrser6tyllZLeFMlVwp3RxjFUXJBvyHgatE5E3gKv/PiEi1iPzEf82FwE4R2QM8h5XDHxcBv6amkltvXcSpU4M4nTacTsHptHPq1CC33rpIF19VTspqCWeq5EqgzfEyzFBJlWUaY9qBD4W5fSdwl//7vwELk3mdXNTQ0ER9/Q6eeeYtHA4bF144g/JyqylaV9cg27cf4fOfX5blUSoVXtZOuEqVXCndzPEyzFC60zYBwb3tfT7weg2vv95Ge7vVclUXbJVKs1wp3czxMsxQGvATUF+/Y7gTZlGRExHBbrfR1GR1wtQFW6XSLFcCbap3GaeZNk9LQKAcE2D+/Mns39+G3W6js3OAF188Ql/fENXVs2loaNI8vlLpkEulm5lszpYkneEnILgHztSphVx44TS8Xh+Dg15AWLjQyi1qq2Ol0iiWfvhqBA34CQhtmOZyWQ2uLrpoGsuWzWHatCI9wlAplXM0pZOAQA+c+vodNDZ2UFVVxrRphcyZUzriOl28VdmS8uZoE0EubORKMw34CQrthBnoqxM4xAR08VZlR1bPtx2rxtiO2URpSidFIvXF1922KtOyer7tWJUrG7nSTAN+imirY5Ursnq+7Vg1xnbMJkpTOik02oEnAYFduoH8f13dUn1jUCkzJpqj5ZoxtmM2UTrDz7DgXbrTpxfT2tqr5ZsqpcZFc7RMy5WNXGmmAT/Dgnfp2myi5Zsq5cZFc7RMG2M7ZhOlKZ0MC96lG6DlmyrVxnxztHSJVno5hnbMJkpn+BkWvEs3QMs3lcqAXOmhn0Ua8BPQ0NDE8uXrKSv7V8rKHqamZn3MOXgt31QqSyZI6WU0GvDj1NDQxKpVv2HXrhZEwGaz8fLLLfzjP/4mpqCv5ZtKZckEKb2MRnP4caqv38GpU/24XA4cjsD7pYOOjgHq63fEFLhjLd9USqXQBCm9jEZn+HFqbOzA7fYGBXuw2wW326sLr0rlsglSehmNBvw4VVWV4XLZ8Xh8w7d5vVbHzEQWXhsamqit3Ux19TpqazdrPb5S6TJBSi+j0ZROnOrqlrJ373FaWroxxupV4nZ7mDlzUtwLr4FNWEVFrhGbsDSnr1SaTIDSy2h0hh+nmppK1q37KJddNgtjwOfzcemls/jxjz8ad5DWTVhKqUzSGX4Camoq2bbtjqSfRzdhKaUySWf4WaSbsJRSmaQBP4t0E5ZSKpM04GeRbsJSSmWS5vCzTDdhKaUyRWf4Sik1QWjAV0qpCSKpgC8itSLymoj4RKQ6ynXXiMgBETkkIvcn85pKKaUSk+wM/1Xg48DzkS4QETvwfeDDwALgkyKyIMnXVUopFaekFm2NMfsBRCTaZZcDh4wxb/uv/QVwA/B6Mq+tlFIqPpnI4c8GjgT93Oy/LSwRWSUiO0VkZ1tbW9oHp5RSE8WoM3wReQaYEeauB4wxv47hNcJN/02ki40x64B1ANXV1RGvU0opFZ9RA74x5sokX6MZmBv08xygJcnnVEopFadMpHR2AOeJSJWIuICVwFMZeF2llFJBki3L/JiINAPvBX4nIn/03z5LRH4PYIzxAHXAH4H9wBPGmNeSG3Zu0MNLlFJjiRiTu2ny6upqs3PnzmwPI6zgw0uKi1309Ljp7XVrLxylVFaJyC5jTNh9UbrTNkF6eIlSaqzRgJ+gxsYOiotdI27Tw0uUUrlMA36C9PASpdRYowE/QXp4iVJqrNF++AloaGiivn4HXV2DHD/eQ1GRi0WLplNXt1wXbJWa6I40wCv10NkIpVWwpA7m1mR7VIDO8OMWqM5pbe3lvPPKOeecKUya5KKubqkGe6UmuiMNsG019LVC0XTr67bV1u05QAN+nLQ6RykV0Sv14CyCvBIQm/XVWWTdngM04MdJq3OUUhF1NoKreORtrmLoaszOeEJowI+TVucopSIqrQJ3z8jb3D1QUpWd8YTQgB8nrc5RSkW0pA6GemGwC4zP+jrUa92eAzTgx6mmppK1a1dQUVHEiRM9VFQUaTsFpZRlbg0sXwuFFdB3wvq6fG3OVOloLx2llBpHtJeOUkopDfhKKTVRaMBXSqkJQlsrpFmgDUNjYwdVVWW6I1cplTU6w0+j4DYM06cX09ray+rVT+vJWEqprNCAn0bahkEplUs0pZNGjY0dTJ8+cpu1tmFQagzK4Q6Y8dAZfhppGwalxoEc74AZDw34aaRtGJQaB3K8A2Y8NOCnkbZhUGocyPEOmPHQHH6a1dRUaoBXaiwrrbLSOHklZ27LoQ6Y8dAZvlJKRZPjHTDjoQFfKaWiyfEOmPHQlI5SSo1mbs2YDPChdIavlFITRFIBX0RqReQ1EfGJSNj+y/7rmkRkn4jsFhFtcK+UUlmQbErnVeDjwI9iuPYfjDEnk3w9pZRSCUoq4Btj9gOISGpGo5RSKm0ylcM3wNMisktEVkW7UERWichOEdnZ1taWoeEppdT4N+oMX0SeAWaEuesBY8yvY3yd9xtjWkSkAviTiLxhjHk+3IXGmHXAOrDOtI3x+ZVSSo1i1IBvjLky2RcxxrT4v7aKyK+Ay4GwAV8ppVR6pD2lIyJFIjIp8D2wAmuxVymlVAaJMYlnTUTkY8D/B0wDTgO7jTFXi8gs4CfGmGtF5F3Ar/wPcQD/bYz5dozP3wYcTniAsZkKjJXqIR1reuhY00PHmh6jjXW+MWZauDuSCvjjgYjsNMZE3EOQS3Ss6aFjTQ8da3okM1bdaauUUhOEBnyllJogNOD7S0DHCB1reuhY00PHmh4Jj3XC5/CVUmqi0Bm+UkpNEBrwlVJqgtCAD4jIN0Vkr79989P+fQQ5SUQeEZE3/OP9lYhMzvaYIom1fXa2iMg1InJARA6JyP3ZHk80IvJTEWkVkZzetCgic0XkORHZ7/9v//lsjykaEckXkZdEZI9/vP8722OKRkTsIvKKiPw2kcdrwLc8YoxZZIxZDPwW+Ea2BxTFn4CLjTGLgIPAV7M8nmgC7bNzro2GiNiB7wMfBhYAnxSRBdkdVVTrgWuyPYgYeIDVxpgLgWXAZ3P833UQ+KAx5hJgMXCNiCzL8pii+TywP9EHa8AHjDFdQT8WYXX3zEnGmKeNMR7/jy8Cc7I5nmiMMfuNMQeyPY4ILgcOGWPeNsa4gV8AN2R5TBH5mw2eyvY4RmOMOWaMedn/fTdWcJqd3VFFZiw9/h+d/j85+fsvInOAjwA/SfQ5NOD7ici3ReQIcAu5PcMP9mng/2Z7EGPUbOBI0M/N5HBgGotEpBJYAvw9uyOJzp8m2Q20An8yxuTqeL8L/DPgS/QJJkzAF5FnROTVMH9uADDGPGCMmQtsBOpyeaz+ax7A+vi8MXsjjW2sOSrcqT05ObMbi0SkGPgl8IWQT9A5xxjj9adz5wCXi8jF2R5TKBG5Dmg1xuxK5nmSPeJwzIijzfN/A78DHkzjcKIabawicjtwHfAhk+WNFKlon50lzcDcoJ/nAC1ZGsu4IiJOrGC/0RjzZLbHEytjzGkR2Ya1VpJri+PvB64XkWuBfKBERH5ujPlUPE8yYWb40YjIeUE/Xg+8ka2xjEZErgG+AlxvjOnL9njGsB3AeSJSJSIuYCXwVJbHNOaJdd7pfwH7jTH/ke3xjEZEpgUq3USkALiSHPz9N8Z81RgzxxhTifX/6rPxBnvQgB/wsD8NsRerX38ul5LVA5OwTg7bLSI/zPaAIhGRj4lIM/Be4Hci8sdsjynAv/BdB/wRa2HxCWPMa9kdVWQi8j/AC8D5ItIsIp/J9pgieD9wK/BB//+fu/2z0lw1E3jO/7u/AyuHn1DJ41igrRWUUmqC0Bm+UkpNEBrwlVJqgtCAr5RSE4QGfKWUmiA04Cul1AShAV8ppSYIDfhKKTVB/P/szEL2JaB0VAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"PCA from pylearn_ml191: \")\n",
    "print(\"=======================\")\n",
    "\n",
    "pca = PCA(n_components=2)\n",
    "X_new = pca.fit_transform(X)\n",
    "\n",
    "print(\"10 samples from X_new: \")\n",
    "print(\"---------------------\")\n",
    "print(X_new[:10, :])\n",
    "print(\"---------------------\")\n",
    "\n",
    "plt.figure()\n",
    "colors = ['navy', 'turquoise', 'darkorange']\n",
    "lw = 2\n",
    "\n",
    "plt.figure()\n",
    "for color, i, target_name in zip(colors, [0, 1, 2], target_names):\n",
    "    plt.scatter(X_new[y == i, 0], X_new[y == i, 1], alpha=.7, c=color,\n",
    "                label=target_name)\n",
    "plt.legend(loc='best', shadow=False, scatterpoints=1)\n",
    "plt.title('LDA of IRIS dataset')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PCA from sklearn: \n",
      "=======================\n",
      "10 samples from X_new: \n",
      "---------------------\n",
      "[[-2.68412563  0.31939725]\n",
      " [-2.71414169 -0.17700123]\n",
      " [-2.88899057 -0.14494943]\n",
      " [-2.74534286 -0.31829898]\n",
      " [-2.72871654  0.32675451]\n",
      " [-2.28085963  0.74133045]\n",
      " [-2.82053775 -0.08946138]\n",
      " [-2.62614497  0.16338496]\n",
      " [-2.88638273 -0.57831175]\n",
      " [-2.6727558  -0.11377425]]\n",
      "---------------------\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"PCA from sklearn: \")\n",
    "print(\"=======================\")\n",
    "\n",
    "sklearn_pca = Sklearn_PCA(n_components=2)\n",
    "X_new = sklearn_pca.fit_transform(X)\n",
    "\n",
    "print(\"10 samples from X_new: \")\n",
    "print(\"---------------------\")\n",
    "print(X_new[:10, :])\n",
    "print(\"---------------------\")\n",
    "\n",
    "plt.figure()\n",
    "colors = ['navy', 'turquoise', 'darkorange']\n",
    "lw = 2\n",
    "\n",
    "plt.figure()\n",
    "for color, i, target_name in zip(colors, [0, 1, 2], target_names):\n",
    "    plt.scatter(X_new[y == i, 0], X_new[y == i, 1], alpha=.7, c=color,\n",
    "                label=target_name)\n",
    "plt.legend(loc='best', shadow=False, scatterpoints=1)\n",
    "plt.title('LDA of IRIS dataset')\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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}