K-Means Algortihm.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Import the library and datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "from sklearn.datasets import load_digits\n",
    "digits = load_digits()\n",
    "digits.data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# It has 1797 samples and 64 features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Clustering part"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 64)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kmeans = KMeans(n_clusters=10)\n",
    "cluster = kmeans.fit(digits.data)\n",
    "clusters = kmeans.predict(digits.data)\n",
    "kmeans.cluster_centers_.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# First fitted the cluster then used the predict method on the dataset. The result is 10 clusters in 64 dimensions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Finding out the cluster centers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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1/H6/mXn33XelWQkJCUEfV/cgFGJjY6WccuLIwMCAmWlvb5fWy8zMNDNdXV3SrNbW1qCPj4+PS3NCYWJiQsp99NFHZkY5NWjXrl3SeiUlJWYmPj5emhVpfD6flFOuBRUVFWZGPRlMOTlnampKmhVJPM+Tcsq1JyMjw8xkZWVJ66WmppqZmZkZadZ88E4TAAARpQkAgIjSBABARGkCACCiNAEAEFGaAACIKE0AAESUJgAAIm8uN4N6nnfVOdf29305/xh5MzMz9t39BvZbxn6HH3seXux3eM2633MqTQAA/s349SwAACJKEwAAEaUJAICI0gQAQERpAgAgojQBABBRmgAAiChNAABElCYAAKL/ACVa4L/ZMSWHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x216 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(2,5,figsize = (8,3))\n",
    "centers = kmeans.cluster_centers_.reshape(10,8,8)\n",
    "for axi,center in zip(ax.flat,centers):\n",
    "    axi.set(xticks=[],yticks=[])\n",
    "    axi.imshow(center,interpolation='nearest',cmap = plt.cm.binary)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# without the labels, KMeans can find clusters whose centers are recognizable digits, with the exception of 1 and 8"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# As the identity of the cluster is unknown, the labels maybe permuted. By matching each learned cluster label with the correct names we can fix this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import mode\n",
    "\n",
    "labels = np.zeros_like(clusters)\n",
    "for i in range(10):\n",
    "    mask = (clusters == i)\n",
    "    labels[mask] = mode(digits.target[mask])[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Now we check the accuracy of the clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7929883138564274"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "accuracy_score(digits.target, labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# We can see with just a simple k-means algorithm we correctly discovered 80% of the input digits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Creating the confusion matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(91.68, 0.5, 'predicted label')"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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lupGR+Rnz/Ves/X0ea9bN9ctHMqATg11mnaPHTKRly3Z+6/z0w1TaP/LcZWXffjGKJnc/zL33tGHBnMW89OrzHmm1uuMWvu76oFt5+wbVmdirHRN7tePuW8tdtm/gz0uoc8v1XsdtV72CdXWbkUAzg01OTuG11/vxn6oNqHt3K55/rgM33+S/7sefvM38eYu5/bYm1L6zBdu37/RZK8vEICKbRGRjJp9NIrLR5ytaiF1mncuWreL4iZN+66z6bR0nT5y6rOzM6UuWdWHhYZ6bzFYsRYHwUI+v/euGXZQqGkmFEkU8PicNO01QrarbjASaGeyhQ4eJjd0MwJkzicTF7aBkKf+8JPPnj6B2nVqMGT0RgKSkJE6d8s4mMCPZGbW09FkVEJFagDHGrBGRW4BmQJwxZpY/uhnJzACzVk3/bLivBq+99SJt2rYiIeE0j7bq5JfW+CUbmLl6G7dcV5xXHrqbAuGhnLuQxP/NX8u33R9i9ILfvdYMtHq1K96rUQ/XX1+aqlUrs3r1er90ypYrw7Gjx/nmuwFUrnIzses38/qr/Th79pxPelm2GIwxf6Z9XEWVXNuHgWz9zUSkLzAE+EZEPgK+BCKAXiLyVjbnXVMz2KvFgA+GUKtKY6b89Asdn33CZ51H61ZhZt+nmfB6O4oWyMenU5YCzncP7RpUJzyvb0NpA61eA9EMFiBfvnAmjB9Kz57vcPq0d+uJXElwUDBVq93KiGHjuLv2/Zw9e5aXX3ku5xOzIMd3DCLyLDAJSLNkKw1MzeG0NkAdoB7QDXjQGNMPuBd4LKuTrqUZ7LVg6qRfaH6/++I0nlKkQD6CHA4cDuHh2pXZ/Kfz/75p7yE+n7aM5n1HMm7RekbMXcP4xRs81g20eg1EM9jg4GAmTBjKj+OnMHXabL/19h84yP79h1i71vk9T50SQ9VqlX3W8+TlYzecv+QJAMaYHUBUDuckG2NSjDFngV3GmLRzzwGpPkd7BXaZddpJufLXpW83bd6AXTv2ZHN09hw5dalV9euGnVR0vU8Y9b9HmP1uJ2a/24l29avTuWlN2t5T1WPdQKvXQDODBRj63UDi4nYyePAwS/QO/32U/fEHqVjJ+QK6fv3axMXt8FnPEzPYC8aYi2nNKhEJJudJbxdFJNyVGNKXXxKRSCxMDHaZdY4d+xX31LuLokULs2f3Wvr1G8io/xvvtc6XwwZwV52aFC5SkDWb5/Np/69p2ORuylcsi0k1xO87wBuv9PNIq9eo2azdGc/JM+dp2mcEz993B2t37Gd7/BFEoGThAvRu28jrGDPDrnoF6+r2asRrl27t2jVp374NmzZtY83qOQD0eftjYmJ+9Uv31Z7vMHzk5+TJE8LePX/R9bnXfNbKcdq1iAwATuJ0fn4B6ApsNcZk964grzHmQiblRYESxpgcV2/Vadc67Rp02jXk3mnXvYAjwCbgv8AsoHd2J2SWFFzlRz1JCoqiXFtyfJQwxqSKyGhgFc4Evt3k5lfUiqL4TY6JQURaAN8Cu3C2GMuJyH+NMf6/SlUUJVfiycvHT4EGxpidACJSAfgF0MSgKP9QPHnHcDgtKbjYjXOQk6Io/1CybDGIyMOuzS0iMguYiPMdwyPAmqsQm6Io14gsuytFZFQ25xljjH+D/HMgxIbuSn1j6uTMym8s1yxwlz1dq6n6nttWslq7MssWgzGmo33hKIqSm/GkVyIU6AzcCqTP+7W7xaAoyrXDk5ePY4FonBOgFuOcROX7RG9FUXI9niSGisaYPkCiMWY00AKoYm9YiqJcSzxJDEmuf0+KSGUgEihrW0SKolxzPBngNFRECgF9gOk4DVfetjUqRVGuKTm2GIwxw40xJ4wxi40x5Y0xUcaYb69GcDmhjsP+67797UTq//cdHn514GXlP8Qso9XLA3io50A+GzcTgE07/+LRXoN4tNcgHnl9EAvWeDcfzi53ZMiddXs1Na3WzW4cw8vZnWiMGeTXlXPAk3EMdeveQeKZREaOGkz16jl7EXjSI+5wONi2ZSnN7nuc+PiDrPxtFu2f7Mq2bb6bXuQ23YzjGNZt2014aB7e+no8P3/SE4DVW3YyfOoCvnytM3lCgjl26gxFIiM4d+EiIcFBBAcFceREAo/0GsT8r/sQHBTk0TiG6OgooqOjiI3dTEREPlatnE2bNp3Zlo2hiCfjGHJT3QZarFmNY8iuxZA/h49XiMgYb8/JCXUc9l+3xs3lKRARflnZT/N+o1OrBuQJcT5pFomMACAsbx6Cg4IAuJCUjHjpwmCHOzLk3roN5FizG+D0rq+iIjL9yiKggYgUdGm38lXbbgLNcdgO3T8PHeH3uD18MSGGvCEhvNy+JZUrlAFg486/6PvtRA4ePcEH3dqmJwpvscodGQKrbgMlVk9ePvpCaWArMBxnC16A23HO1MwSEekCdAFwBEXiiSGs1QSa47AduskpqSQknuP7915g8659vDp4LLMGv4GI8J+K1zFlYE927/+b3t9MoG7Vm8ibJ8QrfSvdkSGw6jZQYrVrJarbgXXAW8ApY8wi4JzrBebirE7y1iXaDgLNcdgO3eKFI2lUqwoiQpWK1+EQ4cTpy+38y5cqTljePOzcd8grbavdkSGw6jZQYrUlMRhjUo0xnwEdgbdE5Evsa51YSqA5Dtuh2+D2yqze4pxpv/fgEZKSUyiUPx/xh4+TnJICwIEjJ/jzwBFKFivslbbV7sgQWHUbKLFmN+3a714JY0w88IjLBSrB+/CyRx2H/dd9fcg41m7bxcnTiTTp9j7Pt2nKQw1q8va3E3n41YGEBAfz3vNtERHWb9/DyGkLCQl2IOLgzU4PUaiA5y07u9yRc2vdBnKs2XVX9nVt3gjUxDm4CeB+YIkx5hmfr+oBOu3aPnTatZKGL9Ou3wUQkbnAbcaY066f3wF+siFGRVFyCZ68Y7gOuJjh54voXAlF+UfjyQvBscBqEZmCszX+EGD5YCVFUXIPnqwr8YGIzAbudhV1NMb4PypFUZRci6fdleFAgjFmMBAvIuVsjElRlGtMjonB1TvxOvCGqygE+N7OoBRFubZ48o7hIaA68DuAMeaAiHg9icpb7OikCrSFV+1YIBUg4s7nLddMGNDSck2AAq/NtEXXLkKCrB/HF+LwbT6KP3jyKHHRtValARCRazNWWVGUq4YniWGiiHwHFBSRZ4H5OCdHKYryD8WTXomBItIE55DmG4G3jTHzbI9MUZRrhifrSnxsjHkdmJdJmaIo/0A8eZRokklZc6sDURQl95Dd7Mrnga5ABRHZmGFXfmCF3YEpinLtyK7F8APOmZTTXP+mfWoYY9pdhdg8wg7H3UByn7bLedmfWPM0eYqwLp8Q2v7SKgMhd7UitF0fQtv1Ju9DPZB8ken7pGgp8j72OqFP9nWe40OXXyA4L2fE4XDw22+zmDx5pGWakZH5GfP9V6z9fR5r1s2lVi3frd2ynHadfoDIncCWDLMr8wO3GGNW+XxVDwj2YNq1t864no4KyC3u056MY7DDedmXWDOOY3CUqoS5eJ6893bk/Pf9nIV5QuHieQCCqzVACpcg6dcfQByEPvEWF+aMwhyNh9B8cOEsuGL0ZBxDbnJe9nQcw4svPsNtt/2H/PkjaN06+2VgPR3H8O3QT1ixfA1jRk8kJCSE8PBQTp3KfjXJhMTdXrtEp/ENkNGYL9FV5jEiUldEXhaRpt6clxN2Oe4Gkvu0Hc7L/saaun+H85c7I66kAEBI3vRNx/W3kHp0vzMpAJxPTE8KVyveq61bqlQ0zZo1ZNQo/0yFMpI/fwS169RizOiJACQlJeWYFLLDk8QgJkOzwhiTSg69GSKyOsP2s8CXON9N9BWRXj7G6kZmzrglS/pvR24HVyNWq5yX7Yo1pPYDhHb+iOAba5H0m9P3x1GoOGDI+9CLhD7xFsE1vP/bYVe8dul+8klf3nrrQ1JTU/3WSqNsuTIcO3qcb74bwNIVM/jiq48IDw/zWc+TxLBbRF4UkRDXpwewO4dzMtoGdwGauIxfmgJZvp8QkS4islZE1qamJmZ1WMbj3cqscNy1A7tjtdJ52a5Yk1ZM4/yIN0jevpqQqg1cF3PgKFmRC7NHcH7iAIIqVsdR5qZcEa8dus2bN+Tw4WOsX7/ZL50rCQ4Kpmq1WxkxbBx3176fs2fP8vIrz/ms50lieA6oDewH4oE7cFm8Z6crIoVEpAjOFscRAGNMIpCc1UneukTb5bhrB3bGarXzst31mhK3mqCKzhdj5swJUvf/4XyESE4iZc8mHFHX5Yp47dC9667badmyMXFxyxgz5gvq16/NyJGf+xkp7D9wkP37D7F27QYApk6JoWq1yj7rebJ25WFjTFvXmpXFjTFPGGMO53BaJE77+LVAYRGJBhCRCCycy2SX464d2Bmr1c7LdsQqBaPSt4PKVyX1hNN2PuXPrTiKlobgEBAHQaVvIPXYgaxkrlq8dum+/fYAKla8k5tuqstTT73AokUr6NTpJb9jPfz3UfbHH6RiJacjQv36tYnL5gV0TmQ3juE1Y8wAEfmCTF68G2NezOpcY0zZLHal4pytaQl2Oe4Gkvu0Hc7L/saap3lngkrfCKERhHbuT9LKGQSVrex8n2AM5vRxLi4Y5zz4wlmSfp9P6ONvgjGk7N1M6l7vmtmB4rxsN6/2fIfhIz8nT54Q9u75i67PveazVnYu0fcbY2aISIfM9htjRvt8VQ/wpLvSW3TatRM7nJd12rWTQJt2nVV3ZXYu0TNc/9qaABRFyX1k9ygxg2z+GObmhWkVRfGP7No9A13/PgxEc8nO7XFgr40xKYpyjcnuUWIxgIi8Z4ypl2HXDBFZYntkiqJcMzwZx1BMRMqn/eByiC5mX0iKolxrPJlE1QwYyqXRjmWB/xpj5tgZmB29EoH0lj/QsKvH5+yBpbbohpW8O+eDfMCOe8zO+8vrtSvTMMbEiEglIG2capwx5oKVwSmKkrvwZF2JcOBVoLsxZgNwnYjY02mtKEquwJN3DKNwLmR7l+vneOB92yJSFOWa40liqGCMGQAkARhjzmHfI6WiKLkAjxacEZEwLi04UwHQdwyK8g/Gk4HdfYEYoIyIjAPqAE/bGZSiKNeWnJyYHEAhnKMf78T5CNHDGHP0KsSmKMo1IttHCZeNW3djzDFjzC/GmJm5LSlY7eJrl+syBJaTsV2x+uPA3fvDQdRr0ZYH219yJnqlz0e07tCN1h260bR1B1p3cMY6c86v6eWtO3SjSt37iPtjl9fX/Lc4e1+JJwOc+gDngAk4jWABMMYc9+vKOWCHS/S1cl32JVZPsUPXF027HLgzDnBaG7uJ8LAw3nxvIFO//9bt2E++GEZEvnCe73S5e+Afu/bwYq9+xPw0Kr3MkwFOucXZ2877K6sBTp68fOwEdAOW4HRlSnNmyhIRuUNECri2w0TkXRGZISIfi0hkdud6gx0uvna4LtsVq126dsUK/jlw316tCpEF8me6zxhDzK9LuK9Jfbd9s+Ytpnnje7y+3r/J2ftKPLF2K5fJp3wOp40E0vzDB+O0evvYVTYqq5O8xW7nZatclyGwnIwDyX07jXUbNlOkUCGuL1PKbV/MgsWZJoyc+Dc7e3uyqG0ozqXq6uLsslwKfGuMOZ/NaQ5jTJrp6+3GmNtc28tEJDaba3XBZTQrQZHkZAhrp/Oyla7LEFhOxoHkvp3GrHmLuK+Je6tg45Y4wkJDqVS+rNea/2Znb08eJcYAtwJf4Fwf4hZgbA7nbBaRjq7tDSJyO4CI3IBroFRm5BaXaKtdlyGwnIwDyX0bIDk5hfmLV9CsUT23fbPn+/YYAf9uZ29PEsONxpjOxpiFrk8X4IYcznkGuEdEduFMJL+JyG5gmGufJdjlDmy16zIElpNxILlvA6xcu57y15cmOupyN4DU1FTmLlzqc2L4Nzt7ezLAab2I3GmMWQnOF4vA8uxOMMacAp52rXNZ3nWdeGOMpX927HDxtcN12a5Y7dK10x3ZHwfuV/v2Z836jZw8mUCjB9vTtfOTtL7/XleroL7b8WtjN1O8WFHKlCrhU6z/JmfvK/Gku3IbcCPwl6voOmAbTit4Y4z5j89Xzwb1Ywgs1I/Byb/GjwFoZnEsiqLkcjwxavnzagSiKEruwZOXj4qi/MvQxKAoihuaGBRFccP6hfZyMXa93Q22aW3BsOA8tuhmNkrOXxIunM35IB+wq/fg3D7/up+zolA569/V27l2ZVZoi0FRFDc0MSiK4oYmBkVR3NDEoCiKG5oYFEVxQxODoihuBHxiCBQj1Lx587J06XRWr47h99/n06fPy5boVqxUjiUrpqd//jwQy3Ndn/Zb9/luT7Ni9SyWr/qFYSM/I29ea7pOc6Mhbu/+g6nX6kke7NA9veyVvgNo3akHrTv1oOmjz9C6Uw8A9h/8mxqN26Tve3fg1z7Fu2XbUlatns2Klb+wZNk0nzQyYvV9kOPsymuFHWawnuCLpqfjGPLlCycx8SzBwcH8+utkevZ8J1tLL2/HMTgcDrbuWE6T+q3Zt+9AlsflNI6hRInizJr7I3fVbM758xcYOXow8+Yu5sdxP2d5jifjGHKTIW7GcQxrYzc7TWY//Iypo790O/aTL0cQEZGP559uy/6Df9Ot13uZHgeej2PYsm0p9eq24tixEzke6+04Bk/vA4ATZ3b6bAabawk0I9TEROcvT0hIMCEhwZbbpd1TvzZ7d/+V483gCcHBwYSGhRIUFERYeBiHDh72WzO3GuLeXq0ykQUiMt1njCFm4XLuy8QdKrdixX1gS2IQkRdFpIwd2hkJNCNUh8PBqlWz2bdvPQsWLGPNmlhLdNN4uE0LJk+a6bfOwYN/8+WQEWzcuphtO1eQcOo0C39d5rduIBniprFuwxaKFC7I9WUu2abtP/g3bTr34OkX3mDdhi0+6RpjmDZjDEuXT6djp8ctiTUNK+4Du1oM7wGrRGSpiHQVkWI5noHTDFZE1orI2tTURE+OdyvLzUaoqamp3HFHcypUuIOaNatyyy05OeR5TkhICM1bNGLqlFl+a0UWLEDzFo2oXqUht1SqQ3i+MB55rJXfuoFkiJvGrAVLuK/RpWHZxYoUZt5PI5g0YjCvdu/Ma/0+5Uyi98PBGzdqQ93a9/Pwgx3p0uVJ6tSpZUm8Vt0HdiWG3UBpnAmiBrBVRGJEpIPL7i1TcoMZ7NUwQj11KoElS1bStGl9yzQbN72HDbFbOXL4mN9a9evX5q8/4zl29DjJycnMnD6XWnfclvOJORBIhrjgMpld8hvNGl5KDHnyhFAwsgAAt95YkTKlotm7b7/X2mmPZkeOHGPGjDnUuL2q3/GCdfeBXYnBGGNSjTFzjTGdgZLA1zjdoHZbdZFAMkItWrQwka4bKjQ0Lw0b1mX7du+XTMuKNo+0ZPJPMyzRio8/yO01qxEWFgpAvfp38YcFsQaSIS7AynWxlL+uNNFRRdPLjp88RUpKCgD7Dhzir/gDlPHysSU8PIyIiHzp2w0b3c3Wrdv9jhesuw/sml15WdvOGJMETAemi0iYVRcJJCPU6Ogohg8fRFBQEA6Hg8mTZzJ7tvfrN2ZGWFgo9RvU4X8v9rZEb93aDUyfGsPCZVNJSU5h44atjB41wW/d3GqI++q7n7Bm/WZOnkqgUeuOdO34OK1bNmX2gqU0b3z5S8d1sVv4cuQ4goKCCHI4ePuVrlmujpUVUVFF+XH8dwAEBwcxceJ05s9b4pVGZlh5H9jSXSkiNxhj/PrG7TCDtQuddm3ftGu70GnXTq5qd6W/SUFRlGtLQI9jUBTFHjQxKIrihiYGRVHc0MSgKIobmhgURXEjoGdXesuOm2+xWhKAGrv32qJr13dzLvmi5ZrJqSmWa4J9643axc4qN1quWXGTNYOfMuPihfh/3uxKRVHsQRODoihuaGJQFMUNTQyKorihiUFRFDc0MSiK4kbAJwarXIcLPPEQpSYPpdTPwyjQ7iEA8txQnhJjBlNq0lCKD+mH5Av3K1Y7nJftcom2y9XaDpfo0qVLMHfORDZuWEjs+gV07945V+gWfrsnpeZOInrC8PQyR4H8FPtqACV+Hk2xrwYg+Z1ek47IAkR9+ymll8yk0GsvXPVYrySgxzF46w6c1TiGkIplifr4TQ60ewGTlET01x9x9IMhRH30BscHDeX8uo1EPHgvwaWiOfnVaLfzPRnH4IvzsrffjafuwJ6OY/DG1dqTcQy+uDl7Mo4hOjqK6OgoYmM3ExGRj1UrZ9OmTWe2xfnnPu2LbsZxDHmrVyH17HmK9HudQ489A0DBF7uQeiqBhNHjKdChLY4C+Tn5xTAkNJQ8N1YkpGJZQiqU48SAL9J1PBnH4GsdXNVxDCKSR0SeEpHGrp+fEJEvRaSbiIRYdR2rXIdDyl3HhY1xmPMXICWV8+s2kq9hHULKlub8uo0AnPvtd/I18m9JdjuclzNipUs0WO9qbZdL9KFDh4mN3QzAmTOJxMXtoGQp/81g/dW9sH4TqQkJl5WF3VObMy53qTMz5xJWvw4A5vx5LmzYjLmQdE1ivRK7HiVGAS2AHiIyFngEWAXUBIZnd6I3WOUOnLRzL6E1quCIzI+E5iWsbi2CootxcedewuvfBUC+pvUIjvbI0zZT7HJezohVLtFpWO1qbaebcxrXX1+aqlUrZ7tex7XUDSpciNRjxwFIPXacoEIFLYjucqyI1a7EUMUY8xjwENAUaGOMGQt0BKpnddK1colO2vMXJ0dNIPq7j4n++kMu/rEbklM42vdTCrR9gJI/foUjPAyTlOy1dhp2OS+nYaVLdBpWu1rb6eYMzkefCeOH0rPnO5w+fSbX69qBVbHalRgcIpIHyA+EA5Gu8rxAlo8S19Il+syUGA607crBTq+Qeuo0SX/tJ2nvPg4914sDj3fjTMxCkuN9b6Lb5bychpUu0Vdilau1nQ7cwcHBTJgwlB/HT2HqtNmWaNqhm3L8BI4ihQFwFClMyomTfmumYWWsdiWGEUAcEAu8BfwkIsOANcB4qy5ipTuwo3BBAIKiixHeqA6JsxemlyFCwWfbkfCT7810u5yX07DSJRrscbW2y80ZYOh3A4mL28ngwcMs0bNL99ziFUS0bApARMumnFu8whJdsDZW23olRKQkgDHmgIgUBBoDfxljVntyvqezK5s3a8inn76b7g78Uf8hWR6b3ezKEqMG4YgsgElO5vjA7zi/ej0FnniIAm2dzf3EBcs4MXhEpud6Oruy15sv8mDr+9Kdl3t0f4uLF7PuIfD0uwkLC2Vz3FKqV2lAQkLOzUdPeiUqV77JzdX6ww8HZ3m8p7Mrvfm+wLNeidq1a7Jo4RQ2bdpGamoqAH3e/piYGP8MX33RzdgrUeSDtwitURVHwUhSjp3g1NDRnFu0nKIf9SEoOoqUQ4c52qsfqQmnASg5fRySLxwJCSH19BkOd3+d5D1/etQr4WsdZNUrEdDdld6i066d6LRr+9Bp14qi/GPRxKAoihuaGBRFcUMTg6IobmhiUBTFDU0MiqK4Yddq17mSStu22qJrV5daVL6CtuievnjOcs22Je6wXBNg/MFVtujaxZCjUZZrnhxc2XLNnNAWg6IobmhiUBTFDU0MiqK4oYlBURQ3NDEoiuKGJgZFUdwI+MRgh+twbncyHvjFe8RuX8z85VPSy3q+2Z15S39mzuJJjJs8lOJ+2NCB9XUgDgfvzxrIKyPfBODxN59iwIIhfBgziJe+e53wAv45cNvxnVmp++ayIbwS8zH/m/URPaZ/AEDLN57gtQUDeXn2x3T47mVCPaiDd+ZuouG3v9JmzCVbwK9W7ODRsct47PvlPD95DYfPnAcgKSWVvnM28ciYZTw6djlr93lu4hPQ0659cR22Q9MuJ+OsxjHccVcNEhPP8vk3H9K4jtPqPiJ/Ps6cdtrhderSjko3VuCNV/plev6hMyeyjdWXOshpHEPzZ+6n3H8qEBYRzqedPqTy3VXZumITqSmpPNbrSQAm9B/rdp4n4xjsuA981X2pZL1My99cNoTP73+LsydOp5fdcHcVdq7YQmpKKi16PQ7AL/1/dDu3X69LYyPWxR8nPCSIPnM2MempugCcuZBMRF7nkKQf1u9l97FEeje+lQmxf7L17wTevbcKx89eoPuUdXz/xF2X3a/hzw2+utOuRaSCiPQUkcEi8qmIPCcikTmf6Tl2uA4HgpPxqt/WcfLEqcvK0pICQFh4mF9eDlbXQeHoIlRrWINF4+enl21euoHUFKehyK71f1C4RJFcE6/dumn8sXRTeh38uX4HkdGFczynRunCRIZe7o6YlhQAziWlkPZ7v/t4IrWuc9Zr4fC85M8bzNa/L79vssIu+/gXgW+BUJzO0GFAGeA3Ealv1XXscB0OZCfj1956kdWb5vPQIy0Y+NGXPutYXQft+3bixw/HYFIzT1b1Hm3IxkW/+6xv13dmqa4xdBn7Bi/N+IA7Hm/otrvWI/WJW7TB11D5cvkfNBu2iNlxB3n+rkoA3FA0P4t2/U1yair7T51l6+EEDp0+75GeXS2GZ4Fmxpj3cVq63WKMeQtoBnyW1UnXyiXabs2M2Ok4POCDIdSq0pgpP/1Cx2ef8FnHyjqo1rAGCcdOsXfz7kz3t+remtTkVJZPWeKTPtj3nVmp+2Xrd/i85ZsMf/pj6jzVlPK1bkrf16jbg6SkpPL7VN+XE+he5wZinq1P85tKMCH2TwAeqFyK4hGhtPvhNz5ZFEfVEgUJcng2fN/Ol49p7Zu8ON2iMcb8RS51ibZTMw27nIyvZOqkX2h+f2Ofz7eyDm64/SZua1yTz5Z9S7cvXuaW2lV4/vMeANzduj7VG93O1z2y/Ftx1eO1SzfhsPO9zpljCWyes4YyVSsAcHvretzcqDo/9PC9hZeR5jeVZMFOZ4zBDgc969/MhPZ1+PyB2zh9IZnrCub8ewX2JYbhwBoRGQr8BnwJICLFgONWXcQO1+FAdDIGKFf+uvTtps0bsGvHHp+1rKyDiQPG8eKdz/K/us/x1QuD2LpiE9+8NJj/3FOdls8/xKDOH3HxvH8elHZ9Z1bp5gnLS958oenbN9z9Hw79Ec+N91SlwXP3M+qZgST5UQd/nrjUul686zBlCzl/+c8lpXDOtRbKyj+PEuQQKhSJ8EjTltmVxpjBIjIfuBkYZIyJc5UfATJ/besDKSkp9HipN7N++SHddXjr1j9ynSY4XXzbt2/Dpk3bWLN6DuC7k/GXwwZwV52aFC5SkDWb5/Np/69p2ORuylcsi0k1xO87kGWPhCfYVQcZ6dDvGYLzhNDr+74A7Fz/B6Pe+s4nLbvitUo3omgkTw91LgrsCApi/bTlbF+8gV6LPiM4Twhdvnd24f61fieT38rciTyNXrNiWbfvBCfPX+TeYQt57q5KLNtzhD9PJOIQKJE/jLca3wrAibMX6DplLQ4RiuUL5f1m//E45oDurswtBNq065y6K31Bp107yaq70h8ydldazVXvrlQUJXDRxKAoihuaGBRFcUMTg6IobmhiUBTFDU0MiqK4Y4wJ+A/Q5d+uG0ixBppuIMVqle4/pcXQRXUDKtZA0w2kWC3R/ackBkVRLEQTg6IobvxTEsNQ1Q2oWANNN5BitUQ3186VUBTl2vFPaTEoimIhmhgURXEj4BODiDQTke0islNEelmkOVJEDovIZiv0XJplRGShiGwTkS0i0sMi3VARWS0iG1y671qh69IOEpH1IjLTQs29IrJJRGJFZK2FugVFZJKIxLnq+C4LNG90xZn2SRCRlyzQ/Z/ru9osIj+KSKi/mi7dHi7NLX7HaccAi6v1AYKAXUB5IA+wAae/pL+69YDbgM0WxloCuM21nR/4w6JYBYhwbYcAq4A7LYr5ZeAHYKaF9bAXKGrDvTAaeMa1nQcoaMO9dgi43k+dUsAeIMz180TgaQviqwxsBsJxGjDNByr5qhfoLYZawE5jzG5jzEVgPPCAv6LGmCVYaEHn0jxojPndtX0a2IbzJvFX1xhj0lxlQ1wfv98oi0hpoAVOm75cjYgUwJnMRwAYYy4aY05afJlGwC5jzJ8WaAUDYSISjPMX+UAOx3vCzcBKY8xZY0wysBh4yFexQE8MpYB9GX6Ox4JfNrsRkbJAdZx/3a3QCxKRWOAwMM8YY4Xu58BrQKoFWhkxwFwRWSciVo38Kw8cAUa5Hn2Gi4hnrqee0xZwXw3GS4wx+4GBwF/AQeCUMcYKU9HNQD0RKSIi4cB9OJds8IlATwyZ2VLl6v5XEYkAJgMvGWMSrNA0xqQYY6oBpYFaIlLZHz0RaQkcNsassyK+K6hjjLkNaA50ExErvNCCcT76fWOMqQ4kApa8bwIQkTxAK+AnC7QK4WzVlgNKAvlEpL2/usaYbcDHwDwgBudjdbKveoGeGOK5PCuWxppmmS2ISAjOpDDOGPOz1fqu5vMinOt3+EMdoJWI7MX5eNZQRL73UxMAY8wB17+HgSk4Hwf9JR6Iz9BSmoQzUVhFc+B3Y4wV6wg0BvYYY44YY5KAn4HaFuhijBlhjLnNGFMP56Owz2v0BXpiWANUEpFyrqzeFph+jWPKFHGuXjIC2GaMGWShbjERKejaDsN548X5o2mMecMYU9oYUxZnnf5qjPH7r5qI5BOR/GnbQFOcTWC/MMYcAvaJyI2uokbAVn91M/A4FjxGuPgLuFNEwl33RCOc75v8RkSiXP9eBzyMHzHbYh9/tTDGJItId2AOzrfGI40xW/zVFZEfgfpAURGJB/oaY7L39c6ZOsCTwCbX+wCAN40xs/zULQGMFpEgnIl+ojHGsu5FiykOTHGt8BQM/GCMibFI+wVgnOsPxG6goxWiruf1JsB/rdAzxqwSkUnA7zib+uuxbmj0ZBEpAiQB3YwxPtuB65BoRVHcCPRHCUVRbEATg6IobmhiUBTFDU0MiqK4oYlBURQ3NDH8i3DNQOxqo/7TIvJlDse8IyI9vdQ9k/NRipVoYvh3URDINDG4xkEoCqCJ4d9Gf6CCy1vgExGp7/KI+AHnwKuyGT0oRKSniLzj2q4gIjGuyU9LReSm7C4kIveLyCrXpKb5IlI8w+6qIvKriOwQkWcznPOqiKwRkY1W+koo3hPQIx8Vr+kFVHZNuEJE6uOcq1DZGLPHNeszK4YCzxljdojIHcDXQMNsjl+G0xfCiMgzOGdqvuLa9x/gTiAfsF5EfsHpJ1DJFY8A00WknmsKvHKV0cSgrDbG7MnuANeM0NrAT67hzAB5c9AtDUwQkRI4jVMyXmOaMeYccE5EFuJMBnVxzp1Y7zomAmei0MRwDdDEoCRm2E7m8sfLNMsxB3AyraXhIV8Ag4wx010tk3cy7LtyHL7B2Ur4yBjznRfXUGxC3zH8uziN01YuK/4GolxmH3mBlgAu34g9IvIIOGeKikjVHK4VCex3bXe4Yt8D4vSqLIJzstoanBPhOrlaJ4hIqbTZgsrVR1sM/yKMMcdEZLnrBeNs4Jcr9ieJSD+czlJ7uHz6djvgGxHpjdM+bjxOM5CseAfno8d+YCVOY5I0VruufR3wnsuj4YCI3Az85npcOQO0x+lKpVxldHaloihu6KOEoihuaGJQFMUNTQyKorihiUFRFDc0MSiK4oYmBkVR3NDEoCiKG/8PoSaOKtg6TZcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "mat = confusion_matrix(digits.target, labels)\n",
    "sns.heatmap(mat.T, square=True, annot=True,fmt='d',cbar=False, \n",
    "             xticklabels = digits.target_names,\n",
    "              yticklabels = digits.target_names)\n",
    "\n",
    "plt.xlabel('true label')\n",
    "plt.ylabel('predicted label')"
   ]
  },
  {
   "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}