SVM.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pip install cvxopt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from cvxopt import matrix\n",
    "from cvxopt import solvers\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X.shape: (10000, 3)\n",
      "Diag.shape: (10000, 10000)\n",
      "G.shape: (10000, 3)\n"
     ]
    }
   ],
   "source": [
    "(a,b,c) = (1,1,1) # ax+by+c = 0\n",
    "Npoints = 10000\n",
    "offset_negative = 5+10*np.random.random((Npoints//2,1))\n",
    "offset_positive = 5+10*np.random.random((Npoints//2,1))\n",
    "x_negative = -20*np.random.random((Npoints//2,1)) # Negative class\n",
    "x_positive = 20*np.random.random((Npoints//2,1))  # Positive class\n",
    "y_negative = -(a/b)*x_negative-(c/b) - offset_negative\n",
    "y_positive = -(a/b)*x_positive-(c/b) + offset_positive\n",
    "labels_negative = -1*np.ones((Npoints//2,1))\n",
    "labels_positive = np.ones((Npoints//2,1))\n",
    "\n",
    "x_all = np.r_[x_negative,x_positive]\n",
    "y_all = np.r_[y_negative,y_positive]\n",
    "y_all_line = -(a/b)*x_all-(c/b)\n",
    "labels_all = np.r_[labels_negative,labels_positive]\n",
    "\n",
    "X = np.c_[x_all,y_all,np.ones((Npoints,1))]\n",
    "print(f'X.shape: {X.shape}')\n",
    "\n",
    "Diag = np.zeros((Npoints,Npoints))\n",
    "np.fill_diagonal(Diag, labels_all)\n",
    "print(f'Diag.shape: {Diag.shape}')\n",
    "\n",
    "G_array = np.dot(Diag,X)\n",
    "print(f'G.shape: {G_array.shape}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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.plot(x_all,y_all_line)\n",
    "plt.scatter(x_all,y_all)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "P_array = np.array([[1,0,0],[0,1,0],[0,0,0]])\n",
    "P = matrix(P_array,tc='d')\n",
    "G = matrix(G_array,tc='d')\n",
    "q = matrix(np.array([0,0,0]),tc='d')\n",
    "h = matrix(-1*np.ones((Npoints,1)), tc='d')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     pcost       dcost       gap    pres   dres\n",
      " 0:  7.2313e-03  1.5275e+03  2e+04  2e+00  1e+05\n",
      " 1:  5.4132e-02 -1.9222e+03  2e+03  2e-01  1e+04\n",
      " 2:  6.4590e-02 -3.4158e+01  3e+01  2e-03  2e+02\n",
      " 3:  6.4461e-02 -3.5992e-01  4e-01  3e-05  2e+00\n",
      " 4:  4.9962e-02  1.5122e-02  3e-02  4e-07  3e-02\n",
      " 5:  4.9635e-02  1.7300e-02  3e-02  3e-07  3e-02\n",
      " 6:  4.1731e-02  2.8898e-02  1e-02  1e-07  9e-03\n",
      " 7:  3.9934e-02  3.5488e-02  4e-03  2e-08  2e-03\n",
      " 8:  4.0017e-02  3.5597e-02  4e-03  2e-08  2e-03\n",
      " 9:  4.0148e-02  3.6863e-02  3e-03  1e-08  9e-04\n",
      "10:  3.9944e-02  3.8773e-02  1e-03  7e-10  7e-05\n",
      "11:  3.9881e-02  3.9680e-02  2e-04  9e-11  8e-06\n",
      "12:  3.9875e-02  3.9851e-02  2e-05  9e-12  8e-07\n",
      "13:  3.9874e-02  3.9874e-02  3e-07  1e-13  9e-09\n",
      "14:  3.9874e-02  3.9874e-02  3e-09  1e-15  9e-11\n",
      "Optimal solution found.\n"
     ]
    }
   ],
   "source": [
    "sol = solvers.qp(P,q,G,h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(sol['x'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.20014437798505913 -0.1992235455253532 -0.19982147117133378\n",
      "0.06543264522849063\n"
     ]
    }
   ],
   "source": [
    "print(sol['x'][0],sol['x'][1],sol['x'][2])\n",
    "print(np.square(sol['x'][0])+np.square(sol['x'][1]+np.square(sol['x'][2])))"
   ]
  },
  {
   "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": [
    "y_all_line_after = -(sol['x'][0]/sol['x'][1])*x_all-(sol['x'][2]/sol['x'][1])\n",
    "plt.plot(x_all,y_all_line_after)\n",
    "plt.scatter(x_all,y_all)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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.plot(x_all,y_all_line)\n",
    "plt.scatter(x_all,y_all)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(None, 1)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LogRegModel = tf.keras.Sequential()\n",
    "LogRegModel.add(tf.keras.layers.Input(shape=(Npoints,)))\n",
    "LogRegModel.add(tf.keras.layers.Dense(1, activation='sigmoid'))\n",
    "LogRegModel.output_shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_Train.shape: (10000, 2)\n",
      "y_Train.shape: (10000, 1)\n",
      "X_Test.shape: (5000, 2)\n",
      "y_Test.shape: (5000, 1)\n"
     ]
    }
   ],
   "source": [
    "X_Train = np.c_[x_all,y_all]\n",
    "y_Train = np.r_[labels_negative,labels_positive]\n",
    "print(f'X_Train.shape: {X_Train.shape}')\n",
    "print(f'y_Train.shape: {y_Train.shape}')\n",
    "\n",
    "Npoints_test = 5000\n",
    "offset_negative = 5+10*np.random.random((Npoints_test//2,1))\n",
    "offset_positive = 5+10*np.random.random((Npoints_test//2,1))\n",
    "x_negative_test = -20*np.random.random((Npoints_test//2,1)) # Negative class\n",
    "x_positive_test = 20*np.random.random((Npoints_test//2,1))  # Positive class\n",
    "y_negative_test = -(a/b)*x_negative_test-(c/b) - offset_negative\n",
    "y_positive_test = -(a/b)*x_positive_test-(c/b) + offset_positive\n",
    "labels_negative_test = -1*np.ones((Npoints_test//2,1))\n",
    "labels_positive_test = np.ones((Npoints_test//2,1))\n",
    "\n",
    "x_all_test = np.r_[x_negative_test,x_positive_test]\n",
    "y_all_test = np.r_[y_negative_test,y_positive_test]\n",
    "X_Test = np.c_[x_all_test,y_all_test]\n",
    "y_Test = np.r_[labels_negative_test,labels_positive_test]\n",
    "print(f'X_Test.shape: {X_Test.shape}')\n",
    "print(f'y_Test.shape: {y_Test.shape}')\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### WITH INPUT LAYER"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "313/313 [==============================] - 0s 1ms/step - loss: -45.9610 - accuracy: 0.5000\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<tensorflow.python.keras.callbacks.History at 0x2557fc00088>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model1 = tf.keras.Sequential([\n",
    "  tf.keras.layers.InputLayer(input_shape=(2,)),\n",
    "  tf.keras.layers.Dense(1,activation='sigmoid')])\n",
    "model1.compile(loss=tf.keras.losses.BinaryCrossentropy(from_logits=False),\n",
    "optimizer='sgd',metrics=['accuracy'])\n",
    "    \n",
    "model1.fit(X_Train,y_Train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From <ipython-input-14-a53c30428250>:1: Sequential.predict_classes (from tensorflow.python.keras.engine.sequential) is deprecated and will be removed after 2021-01-01.\n",
      "Instructions for updating:\n",
      "Please use instead:* `np.argmax(model.predict(x), axis=-1)`,   if your model does multi-class classification   (e.g. if it uses a `softmax` last-layer activation).* `(model.predict(x) > 0.5).astype(\"int32\")`,   if your model does binary classification   (e.g. if it uses a `sigmoid` last-layer activation).\n",
      "1\n",
      "1\n"
     ]
    }
   ],
   "source": [
    "pred1 = model1.predict_classes(X_Test)\n",
    "# print(pred1.shape)\n",
    "print(np.max(pred1))\n",
    "print(np.min(pred1[Npoints_test//2:,0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "157/157 [==============================] - 0s 2ms/step - loss: -85.3300 - accuracy: 0.5000\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[-85.32997131347656, 0.5]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model1.evaluate(X_Test,y_Test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### WIHTOUT INPUT LAYER"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model1.evaluate(X_Test,Y_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model2 = tf.keras.Sequential([  \n",
    "  tf.keras.layers.Dense(1,input_shape=(2,),activation='sigmoid')])\n",
    "model2.compile(optimizer='sgd', loss=tf.keras.losses.BinaryCrossentropy())\n",
    "model2.fit(X_Train,y_Train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model2.predict(X_Test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model2.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "wts1 = model1.get_weights()\n",
    "wts2 = model2.get_weights()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a_hat1 = wts1[0][0]\n",
    "b_hat1 = wts1[0][1]\n",
    "c_hat1 = wts1[1]\n",
    "\n",
    "a_hat2 = wts2[0][0]\n",
    "b_hat2 = wts2[0][1]\n",
    "c_hat2 = wts2[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_all_line_NN1 = -(a_hat1/b_hat1)*x_all-(c_hat1/b_hat1)\n",
    "plt.plot(x_all,y_all_line_NN1)\n",
    "plt.scatter(x_all,y_all)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_all_line_NN2 = -(a_hat2/b_hat2)*x_all-(c_hat2/b_hat2)\n",
    "plt.plot(x_all,y_all_line_NN2)\n",
    "plt.scatter(x_all,y_all)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(a_hat1,b_hat1,c_hat1)\n",
    "print(a_hat2,b_hat2,c_hat2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(x_all,y_all_line_NN1,'-b')\n",
    "plt.plot(x_all,y_all_line_after,'-k')\n",
    "plt.legend(['LogReg','SVM'])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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