Breast_cancer_LogisticRegression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sklearn\n",
    "import warnings\n",
    "import numpy as np\n",
    "from sklearn.datasets import load_breast_cancer\n",
    "from sklearn.utils import shuffle\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = load_breast_cancer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "feature_names = data['feature_names']\n",
    "features = data['data']\n",
    "label_names = data['target_names']\n",
    "labels = data['target']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['mean radius' 'mean texture' 'mean perimeter' 'mean area'\n",
      " 'mean smoothness' 'mean compactness' 'mean concavity'\n",
      " 'mean concave points' 'mean symmetry' 'mean fractal dimension'\n",
      " 'radius error' 'texture error' 'perimeter error' 'area error'\n",
      " 'smoothness error' 'compactness error' 'concavity error'\n",
      " 'concave points error' 'symmetry error' 'fractal dimension error'\n",
      " 'worst radius' 'worst texture' 'worst perimeter' 'worst area'\n",
      " 'worst smoothness' 'worst compactness' 'worst concavity'\n",
      " 'worst concave points' 'worst symmetry' 'worst fractal dimension']\n"
     ]
    }
   ],
   "source": [
    "print(feature_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  1.79900000e+01   1.03800000e+01   1.22800000e+02   1.00100000e+03\n",
      "   1.18400000e-01   2.77600000e-01   3.00100000e-01   1.47100000e-01\n",
      "   2.41900000e-01   7.87100000e-02   1.09500000e+00   9.05300000e-01\n",
      "   8.58900000e+00   1.53400000e+02   6.39900000e-03   4.90400000e-02\n",
      "   5.37300000e-02   1.58700000e-02   3.00300000e-02   6.19300000e-03\n",
      "   2.53800000e+01   1.73300000e+01   1.84600000e+02   2.01900000e+03\n",
      "   1.62200000e-01   6.65600000e-01   7.11900000e-01   2.65400000e-01\n",
      "   4.60100000e-01   1.18900000e-01]\n"
     ]
    }
   ],
   "source": [
    "print(features[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['malignant' 'benign']\n"
     ]
    }
   ],
   "source": [
    "print(label_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
      " 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 0 1 1 1 1 0 1 0 0 1 1 1 1 0 1 0 0\n",
      " 1 0 1 0 0 1 1 1 0 0 1 0 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 0 1 1\n",
      " 1 1 1 1 1 1 0 0 0 1 0 0 1 1 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 0 1 1 1 1 0 1\n",
      " 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 0 1 1 0 0 1 1 1 1 0 1 1 0 0 0 1 0\n",
      " 1 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 1 1\n",
      " 1 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 1 0 1 1 1 1 0 1 1 1 1 1 0 1 0 0 0 0 0 0 0\n",
      " 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1\n",
      " 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 0 0 1 1\n",
      " 1 1 0 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0\n",
      " 0 1 0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1\n",
      " 1 0 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 0 1 1\n",
      " 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1\n",
      " 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 1 0 1 1 1 1 1 0 1 1 0 1 0 1 0 0\n",
      " 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
      " 1 1 1 1 1 1 1 0 0 0 0 0 0 1]\n"
     ]
    }
   ],
   "source": [
    "print(labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(398,)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train, test, train_labels, test_labels = train_test_split(features, labels, test_size=0.30, random_state=42, shuffle = True)\n",
    "train_labels.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 398)\n"
     ]
    }
   ],
   "source": [
    "train_set_x = np.array(train.T)\n",
    "train_set_y = np.array(train_labels)\n",
    "train_set_y = np.reshape(train_set_y,(1,398))\n",
    "test_set_x = np.array(test.T)\n",
    "test_set_y = np.array(test_labels)\n",
    "test_set_y = np.reshape(test_set_y,(1,171))\n",
    "print(train_set_y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    s = 1/(1+np.exp(-z))\n",
    "    return s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def initialize_with_zeros(dim):\n",
    "    w = np.zeros((dim,1),dtype=float)\n",
    "    b = 0\n",
    "    assert(w.shape == (dim, 1))\n",
    "    assert(isinstance(b, float) or isinstance(b, int))\n",
    "    \n",
    "    return w, b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w = [[ 0.]\n",
      " [ 0.]\n",
      " [ 0.]]\n",
      "b = 0\n"
     ]
    }
   ],
   "source": [
    "dim = 3\n",
    "w, b = initialize_with_zeros(dim)\n",
    "print (\"w = \" + str(w))\n",
    "print (\"b = \" + str(b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def propagate(w, b, X, Y):\n",
    "    m = X.shape[1]\n",
    "    A = 1 / (1 + np.exp(-(np.dot(np.transpose(w), X) + b)))\n",
    "    cost = -((np.sum(Y*np.log(A) + (1 - Y) * np.log(1 - A)))/m)\n",
    "    \n",
    "    dw = (np.dot(X,np.transpose(A-Y)))/m\n",
    "    db = np.sum(A-Y)/m\n",
    "    \n",
    "    assert(dw.shape == w.shape)\n",
    "    assert(db.dtype == float)\n",
    "    cost = np.squeeze(cost)\n",
    "    assert(cost.shape == ())\n",
    "    \n",
    "    grads = {\"dw\": dw,\n",
    "             \"db\": db}\n",
    "    \n",
    "    return grads, cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dw = [[ 0.99845601]\n",
      " [ 2.39507239]]\n",
      "db = 0.00145557813678\n",
      "cost = 5.80154531939\n"
     ]
    }
   ],
   "source": [
    "w, b, X, Y = np.array([[1.],[2.]]), 2., np.array([[1.,2.,-1.],[3.,4.,-3.2]]), np.array([[1,0,1]])\n",
    "grads, cost = propagate(w, b, X, Y)\n",
    "print (\"dw = \" + str(grads[\"dw\"]))\n",
    "print (\"db = \" + str(grads[\"db\"]))\n",
    "print (\"cost = \" + str(cost))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def optimize(w, b, X, Y, num_iterations, learning_rate, print_cost = False):\n",
    "    costs = []\n",
    "    \n",
    "    for i in range(num_iterations):\n",
    "        \n",
    "        \n",
    "        grads, cost = propagate(w,b,X,Y)\n",
    "        \n",
    "        dw = grads[\"dw\"]\n",
    "        db = grads[\"db\"]\n",
    "        \n",
    "        w = w-learning_rate*dw\n",
    "        b = b-learning_rate*db\n",
    "        \n",
    "        if i % 100 == 0:\n",
    "            costs.append(cost)\n",
    "        \n",
    "        if print_cost and i % 100 == 0:\n",
    "            print (\"Cost after iteration %i: %f\" %(i, cost))\n",
    "    \n",
    "    params = {\"w\": w,\n",
    "              \"b\": b}\n",
    "    \n",
    "    grads = {\"dw\": dw,\n",
    "             \"db\": db}\n",
    "    \n",
    "    return params, grads, costs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w = [[ 0.19033591]\n",
      " [ 0.12259159]]\n",
      "b = 1.92535983008\n",
      "dw = [[ 0.67752042]\n",
      " [ 1.41625495]]\n",
      "db = 0.219194504541\n"
     ]
    }
   ],
   "source": [
    "params, grads, costs = optimize(w, b, X, Y, num_iterations= 100, learning_rate = 0.009, print_cost = False)\n",
    "\n",
    "print (\"w = \" + str(params[\"w\"]))\n",
    "print (\"b = \" + str(params[\"b\"]))\n",
    "print (\"dw = \" + str(grads[\"dw\"]))\n",
    "print (\"db = \" + str(grads[\"db\"]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(w, b, X):\n",
    "    m = X.shape[1]\n",
    "    Y_prediction = np.zeros((1,m))\n",
    "    w = w.reshape(X.shape[0], 1)\n",
    "    \n",
    "    A = 1/(1+np.exp(-(np.dot(np.transpose(w),X)+b)))    \n",
    "    \n",
    "    for i in range(A.shape[1]):\n",
    "        \n",
    "        if (A[0][i] > 0.5):\n",
    "            Y_prediction[0][i]=1\n",
    "        else:\n",
    "            Y_prediction[0][i]=0\n",
    "        \n",
    "    assert(Y_prediction.shape == (1, m))\n",
    "    \n",
    "    return Y_prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predictions = [[ 1.  1.  0.]]\n"
     ]
    }
   ],
   "source": [
    "w = np.array([[0.1124579],[0.23106775]])\n",
    "b = -0.3\n",
    "X = np.array([[1.,-1.1,-3.2],[1.2,2.,0.1]])\n",
    "print (\"predictions = \" + str(predict(w, b, X)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model(X_train, Y_train, X_test, Y_test, num_iterations, learning_rate, print_cost = True):\n",
    "    w, b = np.zeros((X_train.shape[0],1), dtype=float), 0\n",
    "\n",
    "    # Gradient descent (≈ 1 line of code)\n",
    "    parameters, grads, costs = optimize(w, b, X_train, Y_train, num_iterations, learning_rate, print_cost=True)\n",
    "    \n",
    "    # Retrieve parameters w and b from dictionary \"parameters\"\n",
    "    w = parameters[\"w\"]\n",
    "    b = parameters[\"b\"]\n",
    "    \n",
    "    # Predict test/train set examples (≈ 2 lines of code)\n",
    "    Y_prediction_test = predict(w, b, X_test)\n",
    "    Y_prediction_train = predict(w, b, X_train)\n",
    "\n",
    "    ### END CODE HERE ###\n",
    "\n",
    "    # Print train/test Errors\n",
    "    print(\"train accuracy: {} %\".format(100 - np.mean(np.abs(Y_prediction_train - Y_train)) * 100))\n",
    "    print(\"test accuracy: {} %\".format(100 - np.mean(np.abs(Y_prediction_test - Y_test)) * 100))\n",
    "\n",
    "    \n",
    "    d = {\"costs\": costs,\n",
    "         \"Y_prediction_test\": Y_prediction_test, \n",
    "         \"Y_prediction_train\" : Y_prediction_train, \n",
    "         \"w\" : w, \n",
    "         \"b\" : b,\n",
    "         \"learning_rate\" : learning_rate,\n",
    "         \"num_iterations\": num_iterations}\n",
    "    \n",
    "    return d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after iteration 0: 0.693147\n",
      "Cost after iteration 100: 0.541033\n",
      "Cost after iteration 200: 0.381645\n",
      "Cost after iteration 300: 0.351470\n",
      "Cost after iteration 400: 0.330675\n",
      "Cost after iteration 500: 0.315753\n",
      "Cost after iteration 600: 0.304558\n",
      "Cost after iteration 700: 0.295833\n",
      "Cost after iteration 800: 0.288826\n",
      "Cost after iteration 900: 0.283068\n",
      "Cost after iteration 1000: 0.278248\n",
      "Cost after iteration 1100: 0.274152\n",
      "Cost after iteration 1200: 0.270629\n",
      "Cost after iteration 1300: 0.267568\n",
      "Cost after iteration 1400: 0.264884\n",
      "Cost after iteration 1500: 0.262515\n",
      "Cost after iteration 1600: 0.260408\n",
      "Cost after iteration 1700: 0.258524\n",
      "Cost after iteration 1800: 0.256831\n",
      "Cost after iteration 1900: 0.255301\n",
      "train accuracy: 90.9547738693 %\n",
      "test accuracy: 95.3216374269 %\n"
     ]
    }
   ],
   "source": [
    "d = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 2000, learning_rate = 0.00001, print_cost = True)\n",
    "#warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Tqr6mgjVb2+ntH0h1KSIiEybKUJgPbI67vyWcNty7zOxpM/uVmS1MtCAzu8zMGs2ssaWl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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xf146a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "costs = np.squeeze(d['costs'])\n",
    "plt.plot(costs)\n",
    "plt.ylabel('cost')\n",
    "plt.xlabel('iterations (per hundreds)')\n",
    "plt.title(\"Learning rate =\" + str(d[\"learning_rate\"]))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}