Softmax-Regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from tqdm.auto import tqdm\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_df = pd.read_csv('train.csv', header=None)\n",
    "test_df = pd.read_csv('test.csv', header=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "columns = [f'Pixel-{index}' for index in range(1, 193)]\n",
    "columns.append('Class-Label')\n",
    "\n",
    "train_df.columns = columns\n",
    "test_df.columns = columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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     "execution_count": 4,
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   "source": [
    "train_df.head()"
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     "execution_count": 5,
     "metadata": {},
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   ],
   "source": [
    "test_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of the train data : (6669, 192)\n",
      "Shape of train labels : (6669,)\n",
      "Shape of the test data : (3332, 192)\n",
      "Shape of test labels : (3332,)\n"
     ]
    }
   ],
   "source": [
    "X_train, y_train = train_df.iloc[:, :-1].values, train_df.iloc[:, -1].values\n",
    "X_test, y_test = test_df.iloc[:, :-1].values, test_df.iloc[:, -1].values\n",
    "\n",
    "print(f'Shape of the train data : {X_train.shape}\\nShape of train labels : {y_train.shape}')\n",
    "print(f'Shape of the test data : {X_test.shape}\\nShape of test labels : {y_test.shape}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Softmax Regression\n",
    "\n",
    "## Instead of training K One-Vs-All logistic regression classifiers, we do the same implicitly.\n",
    "\n",
    "### This can be achieved because the weight vector(array in this case) can be thought of using K vectors that are each weights trained from One-Vs-All logistic regression classification\n",
    "\n",
    "#### So in a general logistic regression the weight vector is of shape : `(n, 1)` or simply `(n, )`\n",
    "#### But incase of softmax regression the weight vector(array in this case) is of shape : `(n, k)` k=> number of classes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.utils import to_categorical\n",
    "\n",
    "\n",
    "def softmax(array: np.ndarray):\n",
    "    softmax_out = np.exp(array)\n",
    "    softmax_out = softmax_out / np.sum(softmax_out, axis=1, keepdims=True)\n",
    "    assert np.allclose(np.sum(softmax_out), array.shape[0])\n",
    "    return softmax_out\n",
    "\n",
    "\n",
    "\n",
    "class SoftmaxRegression:\n",
    "    def __init__(self):\n",
    "        self.X = None  # Feature vectors [shape = (m, n)]\n",
    "        self.y = None  # Class labels [shape = (m, 1) => (m, k)]\n",
    "        self.W = None  # Weights [shape = (n, k)]\n",
    "        self.biases = None  # Biases [shape = (k, 1)]\n",
    "        self.lr = None  # Learning rate\n",
    "        self.m = None\n",
    "        self.n = None\n",
    "        self.epochs = None\n",
    "        print('Softmax Regression initialized')\n",
    "\n",
    "    def fit(self, X: np.ndarray, y: np.ndarray, epochs: int = 50,\n",
    "            use_bias: bool = True, lr: float = 0.02, verbose: bool = True):\n",
    "        self.X = X\n",
    "        (self.m, self.n) = X.shape  # Getting the dimensions X\n",
    "        assert y.shape == (self.m, 1) or y.shape == (1, self.m) or y.shape == (self.m,)\n",
    "        self.y = to_categorical(y)  # Converting labels to one-hot vectors / categorical vectors\n",
    "        num_classes = np.unique(y).size  # Inferring the number of classes\n",
    "        assert self.y.shape == (self.m, num_classes)\n",
    "        self.W = np.random.randn(self.n, num_classes) * 0.01  # Initialising weights\n",
    "        if use_bias:  # If configured to use bias\n",
    "            self.biases = np.zeros((1, num_classes))  # Initialising biases\n",
    "            print('Using Biases')\n",
    "        self.epochs = epochs\n",
    "        self.lr = lr\n",
    "        return self.minimize(verbose)  # Gradient Descent to optimize for loss\n",
    "\n",
    "    def minimize(self, verbose: bool):\n",
    "        loss_hist = []\n",
    "        accuracy_hist = []\n",
    "        for num_epoch in tqdm(range(self.epochs)):  \n",
    "            # Logits sure is an overloaded term but it seemed to fit best here\n",
    "            logits = np.dot(self.X, self.W)  # Z = X · W\n",
    "            if self.biases is not None:  # If configured to use biases\n",
    "                logits = logits + self.biases  # Adding the biases to the logits\n",
    "            predictions = softmax(logits)  # Softmax activation on the logits\n",
    "            assert predictions.shape == self.y.shape\n",
    "            # CrossEntropyLoss = (-1/m) * (y * log(predictions))\n",
    "            loss = (-1 / self.m) * np.sum(self.y * np.log(predictions))\n",
    "            # Gradient of `W` wrt the cost function\n",
    "            grad_W = np.dot(self.X.T, (predictions - self.y)) / self.m\n",
    "            if self.biases is not None:\n",
    "                grad_b = np.sum((predictions - self.y), axis=0, keepdims=True) / self.m  # Gradient of biases\n",
    "                assert self.biases.shape == grad_b.shape\n",
    "                self.biases = self.biases - (self.lr) * grad_b  # Updating the biases\n",
    "            assert self.W.shape == grad_W.shape\n",
    "            self.W = self.W - (self.lr) * grad_W  # Updating the weights\n",
    "            accuracy = self.get_accuracy(predictions, self.y)  # Computing the accuracy\n",
    "            if verbose:  # If verbose is set tot True\n",
    "                print(f'Epoch : {num_epoch+1}/{self.epochs}\\tAccuracy : {accuracy}\\tLoss Values : {loss:.4f}')\n",
    "            loss_hist.append(loss)\n",
    "            accuracy_hist.append(accuracy)\n",
    "        return dict(loss=loss_hist, acc=accuracy_hist)\n",
    "            \n",
    "    def predict(self, X: np.ndarray):\n",
    "        logits = np.dot(X, self.W)\n",
    "        if self.biases is not None:\n",
    "            logits = logits + self.biases\n",
    "        return softmax(logits)\n",
    "    \n",
    "    def get_accuracy(self, predictions: np.ndarray, y_sample: np.ndarray):\n",
    "        flattened_labels = np.argmax(y_sample, axis=1)\n",
    "        flattened_predictions = np.argmax(predictions, axis=1)\n",
    "        assert flattened_labels.shape == flattened_predictions.shape\n",
    "        return np.mean(flattened_labels == flattened_predictions)\n",
    "    \n",
    "    def evaluate(self, X_sample: np.ndarray, y_sample:np.ndarray):\n",
    "        predictions = self.predict(X_sample)\n",
    "        y_sample = to_categorical(y_sample)\n",
    "        loss = (-1 / self.m) * np.sum(y_sample * np.log(predictions))\n",
    "        accuracy = self.get_accuracy(predictions, y_sample)\n",
    "        return accuracy, loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Softmax Regression initialized\n",
      "Using Biases\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f0c9025e710e41e2a64f1594ffa21b7a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=150.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "softmax_regression = SoftmaxRegression()\n",
    "history = softmax_regression.fit(X_train, y_train, 150, True, 0.1, False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = pd.DataFrame(history)\n",
    "fig = df.plot(y=['loss', 'acc'], figsize=(8, 8), lw=4, title='Softmax Regression Loss Vs. Accuracy').get_figure()\n",
    "\n",
    "# fig.savefig('Plots/SoftmaxRegressionLoss.jpeg', dpi=100, quality=95, bbox_inches = 'tight', pad_inches = 0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9018607442977191, 0.17874681733329342)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "softmax_regression.evaluate(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_predictions = softmax_regression.predict(X_test)\n",
    "test_predictions = np.argmax(test_predictions, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3332,)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_predictions.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x800 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 8), dpi=100)\n",
    "start_index = 50\n",
    "\n",
    "for i in range(16):\n",
    "    plt.subplot(4, 4, i+1)\n",
    "    plt.grid(False)\n",
    "    plt.xticks([])\n",
    "    plt.yticks([])\n",
    "    \n",
    "    prediction = test_predictions[start_index + i]\n",
    "    true_label = y_test[start_index + i]\n",
    "    col = 'g' if prediction == true_label else 'r'\n",
    "    plt.xlabel(f'Ind:{i} Pred:{prediction} True:{true_label}', color=col)\n",
    "    plt.imshow(np.reshape(X_test[start_index + i], (16, 12)), cmap='gray')\n",
    "\n",
    "plt.tight_layout()\n",
    "# plt.savefig('Plots/SoftmaxRegressionPredictions.jpeg', dpi=100, quality=95)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted : 3, TrueLabel : 5\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x25f4d329850>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPsAAAFGCAYAAACsUem5AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAPYQAAD2EBqD+naQAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+j8jraAAAEvklEQVR4nO3WwW1aWxhG0csTxTCFCkwbbsBl2NW4jluBmVKCuzgZZJgosh83Odh7rTH69UmwddiNMcYCfHv/zR4A/BtihwixQ4TYIULsECF2iBA7RIgdIsQOEftbDzw+Pi7X63WLLXzC09PTXd25Z6fTafaEv+ZwOCyvr68f+uzNsV+v1+Vyudx6hk96f3+fPeHL8Pv8yd94iBA7RIgdIsQOEWKHCLFDhNghQuwQIXaIEDtEiB0ixA4RYocIsUOE2CFC7BAhdogQO0SIHSLEDhFihwixQ4TYIULsECF2iBA7RIgdIsQOEWKHCLFDhNghQuwQIXaIEDtEiB0i9rMHlLy8vGx26/n5eZM75/N5kzvLsizrum52i+152SFC7BAhdogQO0SIHSLEDhFihwixQ4TYIULsECF2iBA7RIgdIsQOEWKHCLFDhNghQuwQIXaIEDtEiB0ixA4RYocIsUOE2CFC7BAhdogQO0SIHSLEDhFihwixQ4TYIULsECF2iBA7ROxnD2CudV1nT+Af8bJDhNghQuwQIXaIEDtEiB0ixA4RYocIsUOE2CFC7BAhdogQO0SIHSLEDhFihwixQ4TYIULsECF2iBA7RIgdIsQOEWKHCLFDhNghQuwQIXaIEDtEiB0ixA4RYocIsUOE2CFC7BAhdogQO0TsxhjjlgOn02m5XC5b7eGDbvza7t75fN7s1rqum926N8fjcXl7e/vQZ73sECF2iBA7RIgdIsQOEWKHCLFDhNghQuwQIXaIEDtEiB0ixA4RYocIsUOE2CFC7BAhdogQO0SIHSLEDhFihwixQ4TYIULsECF2iBA7RIgdIsQOEWKHCLFDhNghQuwQIXaIEDtEiB0ixA4R+9kD+H92u93sCb8YY2x26+HhYbNb67pudusr87JDhNghQuwQIXaIEDtEiB0ixA4RYocIsUOE2CFC7BAhdogQO0SIHSLEDhFihwixQ4TYIULsECF2iBA7RIgdIsQOEWKHCLFDhNghQuwQIXaIEDtEiB0ixA4RYocIsUOE2CFC7BAhdogQO0TsZw+A31nXdfaEb8fLDhFihwixQ4TYIULsECF2iBA7RIgdIsQOEWKHCLFDhNghQuwQIXaIEDtEiB0ixA4RYocIsUOE2CFC7BAhdogQO0SIHSLEDhFihwixQ4TYIULsECF2iBA7RIgdIsQOEWKHCLFDhNghYj97AHONMWZP+K11XWdP+Ha87BAhdogQO0SIHSLEDhFihwixQ4TYIULsECF2iBA7RIgdIsQOEWKHCLFDhNghQuwQIXaIEDtEiB0ixA4RYocIsUOE2CFC7BAhdogQO0SIHSLEDhFihwixQ4TYIULsECF2iBA7RIgdIsQOEfvZA+7dGGP2hC9jt9vNnsAfeNkhQuwQIXaIEDtEiB0ixA4RYocIsUOE2CFC7BAhdogQO0SIHSLEDhFihwixQ4TYIULsECF2iBA7RIgdIsQOEWKHCLFDhNghQuwQIXaIEDtEiB0ixA4RYocIsUOE2CFC7BAhdogQO0Tsbz1wOBy22ME3cDweZ0/I+Ux/uzHG+ItbgDvhbzxEiB0ixA4RYocIsUOE2CFC7BAhdogQO0SIHSLEDhFihwixQ4TYIeIH3JtH6oSzFJMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "index = 65\n",
    "sample_image = X_test[index][..., np.newaxis].T\n",
    "prediction = softmax_regression.predict(sample_image)\n",
    "true_label = y_test[index]\n",
    "\n",
    "print(f'Predicted : {np.argmax(prediction)}, TrueLabel : {true_label}')\n",
    "\n",
    "plt.figure(figsize=(6, 4), dpi=100)\n",
    "plt.grid(False)\n",
    "plt.xticks([])\n",
    "plt.yticks([])\n",
    "plt.imshow(np.reshape(sample_image, (16, 12)), cmap='gray')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(1.8, -0.2, 'True label : 5, Predicted : 3')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6), dpi=100)\n",
    "bars = plt.bar(list(range(10)), np.squeeze(prediction), color='#4682b4')\n",
    "\n",
    "bars[np.argmax(prediction)].set_color('#bb3f3f')\n",
    "\n",
    "plt.title('Model Predictions(Probabilities) - Softmax')\n",
    "plt.xlabel('Class')\n",
    "plt.ylabel('Probabilities')\n",
    "plt.text(1.8, -0.2, f'True label : {true_label}, Predicted : {np.argmax(prediction)}', fontsize=12)\n",
    "\n",
    "# plt.savefig('Plots/SoftmaxSinglePrediction.jpeg', dpi=100, quality=95)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      2.308969\n",
       "1      1.838934\n",
       "2      1.579710\n",
       "3      1.532744\n",
       "4      1.633748\n",
       "         ...   \n",
       "145    0.322808\n",
       "146    0.322291\n",
       "147    0.321780\n",
       "148    0.321273\n",
       "149    0.320771\n",
       "Name: loss, Length: 150, dtype: float64"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['loss']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      0.079022\n",
       "1      0.417754\n",
       "2      0.599040\n",
       "3      0.485680\n",
       "4      0.625281\n",
       "         ...   \n",
       "145    0.914380\n",
       "146    0.914380\n",
       "147    0.914680\n",
       "148    0.914830\n",
       "149    0.915130\n",
       "Name: acc, Length: 150, dtype: float64"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['acc']"
   ]
  }
 ],
 "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": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}