perceptron.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Perceptron"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Perceptron is a single layer neural network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(88)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_training_examples():\n",
    "    X1 = np.array([[8, 7], [4, 10], [9, 7], [7, 10], [9, 6], [4, 8], [10, 10]])\n",
    "    y1 = np.ones(len(X1))\n",
    "    X2 = np.array([[2, 7], [8, 3], [7, 5], [4, 4],  [4, 6], [1, 3], [2, 5]])\n",
    "    y2 = np.ones(len(X2)) * -1\n",
    "    return X1, y1, X2, y2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "X1, y1, X2, y2= get_training_examples()\n",
    "X = np.vstack((X1, X2))\n",
    "y = np.hstack((y1, y2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8 , 7 , 1.0\n",
      "4 , 10 , 1.0\n",
      "9 , 7 , 1.0\n",
      "7 , 10 , 1.0\n",
      "9 , 6 , 1.0\n",
      "4 , 8 , 1.0\n",
      "10 , 10 , 1.0\n",
      "2 , 7 , -1.0\n",
      "8 , 3 , -1.0\n",
      "7 , 5 , -1.0\n",
      "4 , 4 , -1.0\n",
      "4 , 6 , -1.0\n",
      "1 , 3 , -1.0\n",
      "2 , 5 , -1.0\n"
     ]
    }
   ],
   "source": [
    "# print(X)\n",
    "# print(y)\n",
    "# print( len(X), len(y))\n",
    "\n",
    "for ix,iy in zip(X,y):\n",
    "    print(ix[0],',',ix[1] ,',',iy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.  1.  1.  1.  1.  1.  1. -1. -1. -1. -1. -1. -1. -1.]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "14"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(y)\n",
    "len(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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": [
    "plt.scatter(X[:,0],X[:,1],marker='o', c=y) \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  8.  7.]\n",
      " [ 1.  4. 10.]\n",
      " [ 1.  9.  7.]\n",
      " [ 1.  7. 10.]\n",
      " [ 1.  9.  6.]\n",
      " [ 1.  4.  8.]\n",
      " [ 1. 10. 10.]\n",
      " [ 1.  2.  7.]\n",
      " [ 1.  8.  3.]\n",
      " [ 1.  7.  5.]\n",
      " [ 1.  4.  4.]\n",
      " [ 1.  4.  6.]\n",
      " [ 1.  1.  3.]\n",
      " [ 1.  2.  5.]]\n"
     ]
    }
   ],
   "source": [
    "# add a column with value 1 at the first position.\n",
    "Xa= np.c_[np.ones(X.shape[0]), X]\n",
    "print(Xa)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Hypothesis <br>\n",
    "We have two class {+1, -1}. we need a function that predict either of the class for following criteria, <br>\n",
    "h(x<sub>i</sub>)=+1 for w.x<sub>i</sub>>0 <br>\n",
    "h(x<sub>i</sub>=-1 for w.x<sub>i</sub><0  <br>\n",
    "\n",
    "we can calculate this nature using sign (or signum, not sin) function. which looks like the following\n",
    "\n",
    "h(x<sub>i</sub>)=sign(w.x<sub>i</sub>)\n",
    "<img src='imgs/sign.png' width=15%>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Perceptron\n",
    "<img src='imgs/perceptron.png' width=50%>\n",
    "The figure above looks like a neuron."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#calculate weighted sum\n",
    "def linear_regression(x,w):\n",
    "    val=0\n",
    "    for ix,iy in zip(x,w):\n",
    "        val+=ix*iy\n",
    "    return val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#decide -1 or 1\n",
    "def activate(val):\n",
    "    return np.sign(val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(X, w):\n",
    "    hp=[]\n",
    "    for x in X: \n",
    "        lr=linear_regression(x,w)\n",
    "        h=activate(lr)\n",
    "        hp.append(h)\n",
    "    return hp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.64755105 0.50714969 0.52834138]\n",
      "[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]\n"
     ]
    }
   ],
   "source": [
    "w = np.random.rand(3)\n",
    "print(w)\n",
    "py=predict(Xa,w)\n",
    "print(py)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_miss_indexes(py, y):\n",
    "    miss=[]\n",
    "    for i in range(len(y)):\n",
    "        if py[i]!=y[i]:\n",
    "            miss.append(i)\n",
    "    return miss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[7, 8, 9, 10, 11, 12, 13]\n",
      "total miss classification= 7 total= 14\n"
     ]
    }
   ],
   "source": [
    "miss=get_miss_indexes(py,y)\n",
    "print(miss)\n",
    "print('total miss classification=', len(miss), 'total=',len(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12\n",
      "[1. 1. 3.]\n",
      "-1.0\n"
     ]
    }
   ],
   "source": [
    "#choose randomly.\n",
    "rnd=np.random.choice(miss)\n",
    "print(rnd)\n",
    "rx=Xa[rnd]\n",
    "ry=y[rnd]\n",
    "print(rx)\n",
    "print(ry)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Perceptron Learning Algorithm\n",
    "1. choose random hyperplane, classify training data\n",
    "2. get the data missclassified\n",
    "3. pick one from the missclassified randomly, say rx, ry\n",
    "4. update hyperplane (weights, using update rule: w=w+eta \\* (rx \\* ry) , here, eta=learning rate )\n",
    "5. classify training data using this updated hyperplane\n",
    "5. repeate step 2-5 until all data are correctly classified\n",
    "\n",
    "#### \\*** Why it converge?\n",
    "\n",
    "1. vector dot product, effect of theta.\n",
    "2. vector add, sub"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def perceptron_train(X, y):\n",
    "    w = np.random.rand(3)\n",
    "    py=predict(X,w)\n",
    "    miss=get_miss_indexes(py,y) \n",
    "    while len(miss)>0:\n",
    "        rnd=np.random.choice(miss)\n",
    "        rx=X[rnd]\n",
    "        ry=y[rnd]\n",
    "        w=w+rx*ry\n",
    "        \n",
    "        py=predict(X,w)\n",
    "        miss=get_miss_indexes(py,y)\n",
    "        \n",
    "    return w    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "#a variation. using epoch and learning rate\n",
    "def perceptron_train2(X, y):\n",
    "    w = np.random.rand(3)\n",
    "    py=predict(X,w)\n",
    "    miss=get_miss_indexes(py,y) \n",
    "    eta=0.1\n",
    "    epoch=50000\n",
    "    for i in range(epoch):\n",
    "        if len(miss)==0: #all data are classified.\n",
    "            break\n",
    "        rnd=np.random.choice(miss)\n",
    "        rx=X[rnd]\n",
    "        ry=y[rnd]\n",
    "        w=w+eta*rx*ry\n",
    "        \n",
    "        py=predict(X,w)\n",
    "        miss=get_miss_indexes(py,y)\n",
    "        \n",
    "    return w   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-63.27777635   3.23140505   7.13012829]\n"
     ]
    }
   ],
   "source": [
    "w=perceptron_train(Xa,y)\n",
    "print(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-4.90738273  0.28251107  0.50397976]\n"
     ]
    }
   ],
   "source": [
    "w=perceptron_train2(Xa,y)\n",
    "print(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0]\n"
     ]
    }
   ],
   "source": [
    "py=predict(Xa,w)\n",
    "print(py)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-1.0]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xt=[1,4,4]\n",
    "predict([xt],w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.0]"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xt=[1,8,9]\n",
    "predict([xt],w)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plotting the hyperplane.\n",
    "hyperplane equation: ax<sub>1</sub>+bx<sub>2</sub>+c=0 (0 means hyperplane goes between two class -1 and 1) <br>\n",
    "setting, x<sub>1</sub>=0, x<sub>2</sub>= -c/b <br>\n",
    "setting, x<sub>2</sub>=0, x<sub>1</sub>= -c/a  <br>\n",
    "so, hyperplane_x<sub>1</sub>=[0, -c/a] <br>\n",
    "    hyperplane_x<sub>2</sub>=[-c/b, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 17.37058560559841]\n",
      "[9.737261555882277, 0]\n"
     ]
    }
   ],
   "source": [
    "#calculating decision boundary line.\n",
    "#from ax+by+c=0, setting x=0 and y=0 we get.\n",
    "px=[0, -w[0]/w[1] ] #x=0, and x=value for y=0\n",
    "print(px)\n",
    "px2=[ -w[0]/w[2], 0 ] #y= value for x=0, 0\n",
    "print(px2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "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": [
    "plt.scatter(X[:,0],X[:,1],marker='o', c=y)  \n",
    "plt.plot(px, px2 )  \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w= [-6919.31101688   561.91476573   591.47126942]\n",
      "[0, 12.313808852938962]\n",
      "[11.698473576942657, 0]\n"
     ]
    },
    {
     "data": {
      "image/png": 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05VBNK5fkpxfaM7JjbRZuPUmn0bH8uOm4DvtSqghooSuH8/a0MbJjHea/0IHKpf0ZMWsTg6bHcfJCys0/WSmVb1roqtDUva0Ec4e25fXu9Vi5/wydo2KZsfYIdrvurStVGLTQVaHysAmDOtRgychwGlYM5m/fb6X/1DUcOnPZ6mhKuR0tdFUkqpYJYMbgVrzXpxHbj1+k69hYpsQeIEv31pVyGC30IrB/8yHe6PUeD1cYzPA2f+P3RRutjmQJEaFfyyosjYygfa0Q/rVwJ30mrmT3qSSro7kUY7+A/eI72OPDsSd0xH5pCtnjlBy4jozd2M8NxR7fDvvZBzGpvzr0+VXh0CtFC9m+jQcZ1eEN0lLSuPKl9vH3ZvjEwXR+/E5Ls1nJGMP8LSd5a952LqZm8NydtXjurpr4eOpsmBsxJg1zpgdknQCulLgv+LTFVupjx6wjYzcm8WEwKcCVfvCFoDew+T/okHWoW6NXijqJqa9+TWry/8ocIC05ncl//RK73W5dMIuJCD2bVGBpZATdG5Vn7M976Tl+BRuPnLM6mnNLXQD2BP5X5gCpkLYKk+GY2XgmKeqqMs9ZR9L7GJPpkHWowqGFXsj2xO3PdXlyUgoXzuihhtIB3ozp14zPnggjKTWTPpNW8c/5O0hO1+LIjUlfByY5l48IZGx1zEoyt/DnMr+y8jSwn3HMOlSh0EIvZCEVS+e63CZCQLB/EadxXnffXo7oUeE82qoKn644SNcxy1m1T8vjGh5VAZ9rl4sNPCo4Zh22267zAQO2YMesQxUKLfRC9ujrffHx//MPoI+/N90Gd8Tbx8uiVM6phK8Xb9/XiFlDWmMT6D91La/M2cKFFB32dYX49QW5+nUGG9hKgncbx6wj8DnA76qlvuB3PyJXL1fORAu9kEU82IZB7/UnINgfH38fvH296fLkXQz5YIDV0ZxW6xplWDwynGciavBt3FE6j45h6Q4d9gUgHiFIqek5e+regBd4NUVKz0CuKfp8rsO3E5R4GaQE2cXuA369kaDXHfL8qvDoWS5FJDMjk8ST5wgKCcLXP5dfmVWuthw7z0uzt7DrVBI9GpfnrV4NCAnUr58xBuzxIF6ILffDegVfR0bOOkohNj08aKW8nuWiha6cXnqmnU9i9jP+l334+3jwZs/63Ne0Itl3PlTK/elpi8pteHvaeOGe2iwY3p7qIQGM+mYzT01bx4nzOuxLqT/SQlcuo3a5Esx+ti3/16M+aw4k0nl0LF+uOazDvpTKoYWuXIqHTXiqfXWiR4XTtHJJ3vhhG/2mrOGgDvtSSgtduabKpf358umWvP9AY3aevEjXMbF8HLOfzKzie/WtUlroymWJCA/dUZllkRFE1AnlvUW7uG/iSnacuGh1NKUsoYWuXF65IF8+GdCCiY8259SFVHp9tIIPo3eTlplldTSlipQWunILIkK3RuVZOiqCXk0rMP6XfXQft4L1h3XYlyo+tNCVWykV4E3UQ02Z9uQdpKRn0ffjVfz9p+1cTtNhX8r9FajQRaSkiMwWkV0islNEHDNMQjmdS+cv8+HgSfQKHkDPwMd497GxnDt93upY13Vn3bIsGRXOgNZV+XzlIbqMiWX53gSrY7kMk7YW+5n7sJ9qgD0+AvvlmRTlRYgqfwp0paiITAeWG2Omiog34G+Mue5PuV4p6prsdjvPNP0Lx/acJDNnrK2HpwdlKpbi813jnH7I2O8HE3llzhYOnLnMQ2GVeK1bfYL9nTuzlUz6BkziE0DqH5b6QeDz2AKHWJSqeCv0K0VFJAgIBz4FMMak36jMletaH72Z04cT/lvmAFmZWSSdvcSKOWssTJY3LauXZuGIDgy9syZzNhyn4+gYFm87ZXUsp2UujebPZQ6QApcnYUy6FZFUHhXkkEsNIAH4XEQ2ishUEQlwUC7lRA5tP0ZG2rUjbFMupXJgy2ELEt06Xy8PXu56Oz8+347QQB+e/Wo9z329nvikq4tLkbkv9+UmC+yJRZtF3ZKCFLon0ByYZIxpBlwGXrn6QSIyRETiRCQuIUGPYbqiSnXK45XLYRXfQF8q317RgkT517BiMD8Oa8dfu9Rl2c54OkXFMmf9MT0+/EceVXNfLgKFNNlROUZBCv0YcMwYszbn/dlkF/yfGGMmG2PCjDFhoaGhBVidskrLe5tRMjQYjz/cwNnmYcMvwJeIh9pamCx/vDxsPH9XLRYO70CtsoG8+N1mBn6+jmPncru1W/EjgSMA36uW+oH/QLJfKlPOKt+Fbow5BRwVkbo5i+4BdjgklXIqHp4ejF35Nq17tMDD0wObh43m9zRi/Jp3XHq2e62ygXz3TBv+3qsBcYcS6TI6li9WHyr2w77Epw2UHA0elQEBCYLAZ5HAkVZHUzdR0LNcmgJTyb51ygHgSWPMda/k0LNcXJ/dbscYg4eHY+6O4yyOJibzt++3snzvGcKqluLffRtTMzTQ6liWMyYD8NTZ8xbTG1wodYuMMczZcJx/zt9BSkYWI+6pzZDwGnh56PV3ylp6gwulbpGI0LdFJZZGhtOxXlk+WLKb+yasZNvxC1ZHUypPtNCVukrZEr5MfLQFHz/WnNMX0+g9YSXvL95FaoYO+1LOTQtdqevo2rA8P0dG0KdZRSb+tp9u45YTd0jPw1bOSwtdqRsI9vfigweb8MVTLUnLsPPgJ6t588dtXNJhX8oJaaErlQfhdUKJHhXOwDbV+GLNYbqMjiVmj14op5yLFrpSeRTg48lbvRow+9k2+HrZGPjZ70R+u4nzyTrfRDkHLXSlblGLqqVZMLwDw+6qxbxNJ+gYFcPCrSetjqWUFnpRMcZw+cJlsrL0TAl34OvlwV+61OXHYe24LdiX577ewLNfrif+Yvawr4z0DJKTUixOqYobvbCoCPw8YzmT//IFF88m4eXrxQMjezDgzQex2fT/U3eQmWVnyvKDjF62B19PG81PnuD09GiM3VCpbgUipzxL/dZ1rI6pXJheWOQk1sxfz+ghH5N46jyZGVmkJKXy3Yc/Me2NWVZHUw7i6WFj6J01WTyiA97xifxWqiyHe99FaoAfh7cf5eVO/+DkgdNWx1TFgBZ6IZv+1jekXfWiWVpyGt+PW0hG+rUzxpXr8kg4R7np8wmNXk1KxbIcfrI355vXIyMji+/HLbQ6nioGPK0O4O5OH8r91DZ7lp1L55MpVTa4iBOpwnLyQDyeXp6U3LSbgP3HiO/choSOrUiqV52tB85YHU8VA7qHXsiqN6qS63JvP2+Cyug0P3dSrWFlMnN+6/JKukyFOcsoNz+WjNLBRNevx0e/7CUjy25xSuXOtNAL2dPv9MfH/883BfDx9+HJf/ZzuxG0xd1t1crS7v5W//33FqDkroPUnxPNPXVC+E/0HnqOX8HWYzrsSxUOLfRCVr9NXd5b8gYN2tXFL9CXynUr8OLUofR6rqvV0VQheHn6MPq/9gBlKpTGP8iPdve3ZHLs35n8VGs+GdCCxMvp3DdxJe8t0mFfyvH0tEWlitCFlAzeWbCTb+KOUj0kgPf6NKJVjTJWx1JOTk9bVMoJBft58e++jfl6UCsy7XYenryG13/YSlKqnvGkCk4LXSkLtKsVwpKR4Tzdvjpfrz1Cl9Gx/Lor3upYysVpoStlEX9vT97oUZ85Q9sS4OPJk9PWMeqbTSRe1mFfKn+00JWyWPMqpZg/vD3D76nNT5tP0CkqhvlbTlCUr28p96CFrpQT8PH0ILJTHX56oT0VS/kxbMZGhny5ntM5w76UygstdKWcSL3yQcwd2pa/dbud2D0JdIyKYdbvR3RvXeWJFrpSTsbTw8aQ8JosGRlO/fJBvDJ3K49OXcuRs8lWR1NOTgtdKSdVLSSAmYNb8879jdhy7AKdx8QwdfkBsuy6t65yp4WubsnpwwmcPHBaDwEUEZtN6N+qCksjw2lbM4S3F+zkgUmr2HM6yepoygkVuNBFxENENorIfEcEUs7p8I6jDGo4iqfqjWBwo0gG1nmB3XH7rY5VbJQP9uPTgWGM7deUI4nJdB+3nLHL9pKeqcO+1P8U+NJ/EYkEwoAgY0yPGz1WL/13TWkpafSvOpSks0n88dvFP8iPLw9MIKh0CevCFUNnL6Xx9592MG/zCeqWK8H7fRvTpHJJq2OpQlQkl/6LSCWgOzC1IM+jnNuqH+PISM3g6v/7szKz+HXmSmtCFWNlAn0Y90gzpj4exoWUDO6fuJJ/LdhBSroO+yruCnrIZQzwEnDd3/tEZIiIxIlIXEJC7jd7UM7t7InEXO+ulJaczpljZy1IpAA61i9HdGQ4/VpWYcryg3QdG8vq/frvUZzlu9BFpAcQb4xZf6PHGWMmG2PCjDFhoaGh+V2dslC91nXw9Lr25lZ+gb7Ub1vXgkTqiiBfL965vxEzBrcC4JEpa3h17lYu6rCvYqkge+jtgF4icgiYBdwtIl85JJVyKvXb1KFB27p/ulGHt58XVepVpGW3ZhYmU1e0rRnC4hHhDAmvwTfrjtA5Kpafd+qNqYsbh8xDF5E7gb/oi6LuKyM9gx8/Wsziz37BnmWn44Bw+ozsga+/j9XR1FU2HT3Py7O3sPt0Er2aVODNnvUpE6j/Tq4sry+KaqEr5YbSM+1M+m0/H/26lxK+XrzZsz69mlRARKyOpvKhSG9wYYz57WZlrpQqOt6eNkZ0rM2C4R2oUtqfEbM2MWh6HCcvpFgdTRUivVJUKTdWp1wJ5gxty+vd67Fy/xk6RcXy9drD2HV8gFvSQlfKzXnYhEEdahA9MoLGlYJ57ftt9J+6hkNnLlsdTTmYFrpSxUSVMv58PagV7/VpxPbjF+kyJpbJsfvJzNLxAe5CC12pYkRE6NeyCksjI+hQO5R3Fu7igUmr2HXqotXRlANooStVDN0W7MuUx1vwUf9mHDuXQo9xK4hauoe0TB0f4Mq00JUqpkSEHo0rsCwygp5NKjDu5730GLeCDUfOWR1N5ZMWulLFXKkAb0Y/3JTPn7iDS2mZPDBpFf+cv4Pk9Eyro6lbpIUOpKemszlmO7vX7cNu1xeIlPNLT01nS+wOdq7d67Dv2btuL0v0qHAebVWFT1ccpMuYWFbuO+OQ51ZFwyFXiuaVM14pGvPdaj4cNBERwdgNgSUD+NeCV6neqKrV0ZTK1Yrv1/LBExNAwBiDfwl/3p7/CrWaVnfYOtYeOMsrc7dy8Mxl+t1RmVe71SPYz8thz69uTZFe+p9XzlboR3cfZ2jzl0hLSf/T8uDQIGYd+yTXCYNKWenkgdMMbhxJWvKfv2dLlA5k1vHJePs4rnRTM7IYvWwPU2IPEBLow9v3NaRzg9sc9vwq74r00n9XtejTn8nMuPZV/Yy0DNZHb7YgkVI3tuizX8jKuPYQS1ZGFusWbXTouny9PHj13nr88Hw7Sgd4M+TL9Tw/YwMJSWkOXY9ynGJd6OfiL5KVy2ladrvhYuIlCxIpdWPn4y+QmXHti5V2u52LZwvnxtGNK5Xkpxfa85fOdVi6/TSdRsfw/cZjeqNwJ1SsC711t+b4Blw7VtSemUWTiPoWJFLqxlp1a45voO81y+1Zdpre1bDQ1uvlYWPY3bVZOKI9NUICGPXNZp6cto7j53XYlzMp1oXe7v6WVG9UFZ8/zPT2DfCh1/NdKVtF766knE/rni2o3az6Nd+z3QZ3pHyNcoW+/lplS/Dds215s2d91h5IpHNUDF+u0WFfzqJYvygKkJ6WQfS03/h11gr8An3p8UxnWnVvrnOjldPKSM9g6Rex/DJjOT7+3nQf3Ik2vcKK/Hv2aGIyr87dyop9Z2hZrTTvPdCIGqGBRZqhuNCzXJRShc4Yw3frj/H2/B2kZdoZ1akOg9pXx9OjWP/y73B6lotSqtCJCA+FVWZZZAR31g3lvUW7uG/iSnac0GFfVtBCV0oVWNkgXz4ZEMakR5tz6kIavT5awX+W7CY1l9OCVeHRQldKOcy9jcqzLDKc3k0r8tGv++g+bjnrDydaHavY0EJXSjlUSX9vPnyoCdOfaklqhp2+H6/mrXnbuZymw74Kmxa6UqpQRNQJZcmocB5vXZVpqw7RZUwsy/cmWB3LrWmhK6UKTaCPJ3/v3ZDvnm2Dt6eNAZ/+zl+/28yF5Ayro7klLXSZeccUAAAKB0lEQVSlVKG7o1ppFg7vwHN31mTuxuN0HB3D4m0nrY7ldrTQlVJFwtfLg5e63s6Pz7cjNNCHZ7/awNCv1hOflGp1NLeR70IXkcoi8quI7BSR7SIywpHBlFLuqWHFYH4c1o6/dqnLz7vi6RQVy+z1OuzLEQqyh54JvGiMqQe0Bp4XEZ1opZS6KS8PG8/fVYuFwztQu2wgf/luMwM/X8exc8lWR3Np+S50Y8xJY8yGnLeTgJ1ARUcFU0q5v1plA/n2mTb8o3cD1h9KpPPoWKavOqTDvvLJIcfQRaQa0AxY64jnU0oVHzab8HibaiwZFU5YtdK8OW87D32ymn3xek+CW1XgQheRQGAOMNIYc80ABxEZIiJxIhKXkKDnoCqlcleplD/Tn7yDDx9swt74S3Qbu5wJv+4jI0tv3J5XBZq2KCJewHxgiTEm6maP12mLSqm8SEhK481521i49RT1ywfxft/GNKwYbHUsyxT6tEXJHr78KbAzL2WulFJ5FVrCh4mPtuDjx5qTcCmN3hNW8u/Fu3TY100U5JBLO2AAcLeIbMr5081BuZRSiq4Ny7NsVAR9mlVk0m/76TZ2OesO6bCv69EbXCilXMLyvQm8Oncrx86l8HibqrzU9XYCfTytjlUk9AYXSim30qF2KEtGhvNku2p8ueYwXUbH8tvueKtjORUtdKWUywjw8eTNng2Y/Wxb/Lw9eOLzdUR+u4lzl9OtjuYUtNCVUi6nRdVSLBjenhfursW8TSfoNDqGhVtPFvvxAVroSimX5OPpwYud6zJvWHvKB/vx3NcbePar9cRfLL7DvrTQlVIurX6FIL5/ri2v3Hs7v+1OoGNUDN/GHS2We+ta6Eopl+fpYePZiJosGtGB28sH8dLsLQz49HeOJhavYV9a6Eopt1EjNJBZg1vz9n0N2XT0PJ1Hx/LZioNkFZNhX1roSim3YrMJj7WuSvSocFrVKM0/5u/gwY9Xsfd0ktXRCp0WulLKLVUo6cfnT9zBmIebcvDMZbqPW8H4n/e69bAvLXSllNsSEe5rVpGlkRF0blCOD5fuoef4FWw9dsHqaIVCC10p5fZCAn34qH9zJg9owbnkdHpPWMG7i3a63bAvLXSlVLHRucFtRI+K4OE7KvNJzAHuHbucNQfOWh3LYbTQlVLFSrCfF+/2acyMQa3Ishv6TV7Da99vJSk1w+poBaaFrpQqltrWCmHxyA4Mal+dmb8fofPoWH7d5drDvrTQlVLFlr+3J6/3qM+coW0J9PHkyWnrGDlrI4kuOuxLC10pVew1q1KK+cPbM+Ke2szfcpJOUTH8tPmEy40P0EJXSimyh32N6lSH+cPbU6mUHy/M3MjgL9Zz6oLrDPvSQldKqT+4/bYg5j7Xjte61WPFvgQ6RcUw8/cjLrG3roWulFJX8bAJg8NrsHhEOA0qBvHq3K30n7KWw2cvWx3thrTQlVLqOqqFBDBjUGveub8R245foMuYWKYuP+C0w7600JVS6gZsNqF/qypER4bTrmYIby/YSZ9Jq9h9yvmGfWmhK6VUHpQP9mPqwDDGPdKMo4nJ9Bi/nDHL9pCe6TzDvrTQlVIqj0SEXk0qsCwygm6NyjNm2V56jl/BpqPnrY4GaKErpdQtKx3gzdh+zfh0YBgXUjLoM3El/1qwg5R0a4d9aaErpVQ+3VOvHNGR4fRrWYUpyw/SZUwsq/afsSxPgQpdRLqKyG4R2ScirzgqlFJKuYogXy/eub8RMwe3RgT6T1nLq3O3ctGCYV/5LnQR8QAmAPcC9YFHRKS+o4IppZQraVOzDItHhDMkvAbfrDtCp6gYlu04XaQZCrKH3hLYZ4w5YIxJB2YBvR0TSymlXI+ftwd/61aP759rRyl/bwZ9EcfwmRs5eymtSNZfkEKvCBz9w/vHcpYppVSx1qRySeYNa09kpzos2naSjlExrN5f+DfSKEihSy7Lrrl8SkSGiEiciMQlJCQUYHVKKeU6vD1tDL+nNguGd6BhxWCqhfgX+joLUujHgMp/eL8ScOLqBxljJhtjwowxYaGhoQVYnVJKuZ465Urw5dOtKB/sV+jrKkihrwNqi0h1EfEG+gHzHBNLKaXUrfLM7ycaYzJFZBiwBPAAPjPGbHdYMqWUUrck34UOYIxZCCx0UBallFIFoFeKKqWUm9BCV0opN6GFrpRSbkILXSml3IQWulJKuQkpyjtZi0gCcDifnx4CWDeX0nHcYTt0G5yHO2yHO2wDFO52VDXG3PTKzCIt9IIQkThjTJjVOQrKHbZDt8F5uMN2uMM2gHNshx5yUUopN6GFrpRSbsKVCn2y1QEcxB22Q7fBebjDdrjDNoATbIfLHENXSil1Y660h66UUuoGXKLQXf1m1CJSWUR+FZGdIrJdREZYnSm/RMRDRDaKyHyrs+SXiJQUkdkisivn36SN1ZlulYiMyvle2iYiM0XE1+pMeSEin4lIvIhs+8Oy0iKyVET25vxdysqMeXGd7fgg53tqi4h8LyIlizqX0xe6m9yMOhN40RhTD2gNPO+C23DFCGCn1SEKaCyw2BhzO9AEF9seEakIDAfCjDENyR5f3c/aVHk2Deh61bJXgJ+NMbWBn3Ped3bTuHY7lgINjTGNgT3Aq0UdyukLHTe4GbUx5qQxZkPO20lkF4jL3X9VRCoB3YGpVmfJLxEJAsKBTwGMMenGmPPWpsoXT8BPRDwBf3K5W5gzMsbEAolXLe4NTM95ezpwX5GGyofctsMYE22Mycx5dw3Zd3ErUq5Q6G51M2oRqQY0A9ZamyRfxgAvAXargxRADSAB+Dzn0NFUEQmwOtStMMYcB/4DHAFOAheMMdHWpiqQcsaYk5C98wOUtTiPIzwFLCrqlbpCoefpZtSuQEQCgTnASGPMRavz3AoR6QHEG2PWW52lgDyB5sAkY0wz4DKu8Sv+f+UcY+4NVAcqAAEi8pi1qdQVIvIa2YdZvy7qdbtCoefpZtTOTkS8yC7zr40xc63Okw/tgF4icojsw153i8hX1kbKl2PAMWPMld+QZpNd8K6kI3DQGJNgjMkA5gJtLc5UEKdFpDxAzt/xFufJNxEZCPQAHjUWnBPuCoXu8jejFhEh+5jtTmNMlNV58sMY86oxppIxphrZ/wa/GGNcbq/QGHMKOCoidXMW3QPssDBSfhwBWouIf8731j242Au7V5kHDMx5eyDwo4VZ8k1EugIvA72MMclWZHD6Qs95keHKzah3At+64M2o2wEDyN6r3ZTzp5vVoYqxF4CvRWQL0BR4x+I8tyTnt4vZwAZgK9k/x5ZfpZgXIjITWA3UFZFjIvI08B7QSUT2Ap1y3ndq19mOj4ASwNKcn/GPizyXXimqlFLuwen30JVSSuWNFrpSSrkJLXSllHITWuhKKeUmtNCVUspNaKErpZSb0EJXSik3oYWulFJu4v8BlaiGYlMZFz0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#experiment with scaled hyperplane.\n",
    "#calculating decision boundary line.\n",
    "#from ax+by+c=0, setting x=0 and y=0 we get.\n",
    "# w=w*4\n",
    "print('w=',w)\n",
    "px=[0, -w[0]/w[1] ] #x=0, and x=value for y=0\n",
    "print(px)\n",
    "px2=[ -w[0]/w[2], 0 ] #y= value for x=0, 0\n",
    "print(px2)\n",
    "plt.scatter(X[:,0],X[:,1],marker='o', c=y)  \n",
    "plt.plot(px, px2 )  \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w= [-15.52214818   0.84753321   1.51193928]\n",
      "[0, 18.31450141978161]\n",
      "[10.266383335546005, 0]\n"
     ]
    },
    {
     "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": [
    "#changing C\n",
    "w[0]-=0.1\n",
    "print('w=',w)\n",
    "px=[0, -w[0]/w[1] ] #x=0, and x=value for y=0\n",
    "print(px)\n",
    "px2=[ -w[0]/w[2], 0 ] #y= value for x=0, 0\n",
    "print(px2)\n",
    "plt.scatter(X[:,0],X[:,1],marker='o', c=y)  \n",
    "plt.plot(px, px2 )  \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-40.82877848545206 -1.0\n"
     ]
    }
   ],
   "source": [
    "#scaling experience two.\n",
    "x=[3,5]\n",
    "w=w*3\n",
    "lr=linear_regression(x,w)\n",
    "h=activate(lr)\n",
    "print(lr,h)    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Refs.\n",
    "1. https://zahidhasan.github.io/2017-09-10-perceptron/\n",
    "2. svm-succinctly book\n",
    "3. https://towardsdatascience.com/perceptron-learning-algorithm-d5db0deab975"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    " 1.  4.  8.]\n",
    " [ 1. 10. 10.]\n",
    " [ 1.  2.  7.]\n",
    " [ 1.  8.  3.]\n",
    " [ 1.  7.  5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "X1=[1, 3,4]\n",
    "y1=1\n",
    "X2=[1, 8,9]\n",
    "y2=-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "X=[ \n",
    "      [1, 10,10], \n",
    "     [ 1. , 7. , 5]\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [],
   "source": [
    "X=np.array(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-3.   0.2  0.4]\n"
     ]
    }
   ],
   "source": [
    "w=np.array([-3, 0.2, 0.4])\n",
    "print(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.0, 1.0]\n"
     ]
    }
   ],
   "source": [
    "py=predict(X,w)\n",
    "print(py)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-4.  -6.8 -4.6]\n"
     ]
    }
   ],
   "source": [
    "w=w+X[1]*y2\n",
    "print(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.0, -1.0]\n"
     ]
    }
   ],
   "source": [
    "py=predict(X,w)\n",
    "print(py)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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