Centralized Emnist Resnet18.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "973f5e6d-a8ea-4178-afcb-c0dca451f609",
   "metadata": {},
   "source": [
    "# EMNIST DATASET \n",
    "# Test on classes imbalance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b3f43b91-d778-4357-a798-381d027de110",
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow.keras as keras\n",
    "from tensorflow.keras.datasets import mnist\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ca81bb3b-1d56-4d00-887b-b72de2dd4aa4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# the data, split between train and validation sets\n",
    "train = pd.read_csv('./Emnist/emnist-digits-train.csv')\n",
    "test = pd.read_csv('./Emnist/emnist-digits-test.csv')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "50354c75-30f0-417c-9ab5-5dbd4f138484",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train = train.iloc[:,0]\n",
    "y_test = test.iloc[:,0]\n",
    "set(y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c9c94149-3b86-41ce-bf99-7f2bca977607",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train = train.iloc[: , 1:]\n",
    "x_test = test.iloc[:,1:]\n",
    "set(y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6135585f-98a4-4ac1-bdcf-219d3176b57f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(239999, 784)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "30a90107-9e54-49b9-b076-92adba1e2c21",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "255"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.max().max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "db60e990-88ac-409d-aeea-dc98044b1950",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.min().min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "132687dd-91d8-4034-9742-31c56721555c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(239999, 784)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0205a30-ece6-4cb9-947d-d2f0f0ab8daf",
   "metadata": {},
   "source": [
    "Normalization and shape for model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ca0033e0-fb91-4a3c-916c-11ea522ec6a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train = x_train.to_numpy().reshape(-1,28,28,1)/255\n",
    "x_train.shape\n",
    "x_valid = x_valid.to_numpy().reshape(-1,28,28,1)/255\n",
    "y_train =  y_train.to_numpy()\n",
    "y_valid = y_valid.to_numpy()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f14f98a1-6bb4-43c7-9953-21c997c47511",
   "metadata": {},
   "source": [
    "Emnist Dataset : Here we see the difference from the Mnist dataset, numbers are harder to decifer. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b5396596-e802-4243-9d48-6807e2465006",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 18 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "figure, axis = plt.subplots(3, 6)\n",
    "for i in range(6):\n",
    "    for j in range(3): \n",
    "        image = x_train[3*j+i]\n",
    "        axis[j,i].imshow(image, cmap='gray')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a43e5a3e-ee07-4251-a948-694437f77f4d",
   "metadata": {},
   "source": [
    "Here were are interested to study classes imbalance, so we are focusing our work on binary classes 0 and 1 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "f601f0ea-adf6-4b54-9f0e-43d8cd84dea6",
   "metadata": {},
   "outputs": [],
   "source": [
    "train_index= y_train[:] <= 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "56214cf7-cce8-48e3-ae96-7124fdc7103a",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train= x_train[train_index]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a3782604-a441-4481-b1af-498f3ebdd8ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train = y_train[train_index]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "e59955c1-5d8a-427f-a5bc-8f5541164645",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(48000, 28, 28, 1)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ad503f9d-17c8-4358-855b-0d6b00ecea05",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(48000,)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "896e207a-b972-4bce-b579-a637420e0dd1",
   "metadata": {},
   "outputs": [],
   "source": [
    "valid_index = y_valid[:] <= 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "8cd405aa-6140-4919-81e9-e30d5db0dd7b",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_valid = x_valid[valid_index]\n",
    "y_valid = y_valid[valid_index]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "ac9dd562-5f51-4904-b0ff-41340ef7dcfe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7999, 28, 28, 1)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_valid.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "29fe0755-8a06-44a9-a134-5135950a8ca4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7999,)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_valid.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "e6930249-8b38-4c4c-9054-f02c64c1cc6e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x2299cef66d0>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "image = x_train[0]\n",
    "plt.imshow(image, cmap='gray')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "c86b0443-6c5e-4560-9e77-a351d2484c4a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x2299cf5d3a0>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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e2oK773H3T4vvj0o6u8x4ra9doq9+UUfYx0v6U4+fd6q91nt3Sb8xs0/MbFHdzfRi7NlltorbMTX3c67sMt796ZxlxtvmtWtk+fNm1RH23pamaafxvxnufpukeyQ9Xhyuom9+Lul6da8BuEfST+tsplhm/HVJP3L3I3X20lMvffXL61ZH2HdKmtDj52sl7a6hj165++7idp+k5ep+29FOus6uoFvc7qu5n//j7l3uftrdz0j6hWp87Yplxl+X9LK7v1HcXftr11tf/fW61RH2jyVNMrPvmNkQST+UtKKGPr7FzC4rPjiRmV0m6Xtqv6WoV0haWHy/UNKbNfbyZ9plGe+yZcZV82tX+/Ln7t7vX5LuVfcn8v8j6Z/q6KGkr7+Q9Lvia0vdvUl6Rd2Hdd+o+4joEUlXSnpX0mfF7ag26u3f1b2090Z1B2tcTb3NVPdbw42SNhRf99b92iX66pfXjdNlgSA4gw4IgrADQRB2IAjCDgRB2IEgCDsQBGEHgvhfpdT23Z//X0IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "image = x_train[1]\n",
    "plt.imshow(image, cmap='gray')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "94e2ce8c-b58f-423d-90cd-36bc0bc3cb88",
   "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": [
    "sns.histplot(y_train)\n",
    "plt.title('Histogram of number of class')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d52fa8f-56c5-44e4-a538-c95a434cda53",
   "metadata": {},
   "source": [
    "We can see that classes are balanced here. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5866b2b-daa9-44e9-85d9-65ee25b63dde",
   "metadata": {},
   "source": [
    "Data preprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "d8a9e7aa-2def-4c0b-8b51-703eaf4fd417",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "train_split, test_split, train_labels_split, test_labels_split = train_test_split(x_train, y_train, random_state=0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "7d147572-885e-4624-8b2b-b650da4148b8",
   "metadata": {},
   "outputs": [],
   "source": [
    "validation_split = x_valid\n",
    "validation_labels_split = y_valid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "94c933e4-48c2-433b-9678-875cb8e5aa61",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(train_labels_split)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "083a4a54-0690-4cc5-a3f9-13019e8a87b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.optim as optim\n",
    "from torch.optim import lr_scheduler\n",
    "from torchvision import models, transforms\n",
    "import time\n",
    "import copy\n",
    "from torch.utils.data import DataLoader, Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "26a0e797-023c-4cf4-8d5f-1d13852ea834",
   "metadata": {},
   "outputs": [],
   "source": [
    "# define custom dataset\n",
    "class MyDataset(Dataset):\n",
    "    def __init__(self, feature, target=None, transform=None):\n",
    "\n",
    "        self.X = feature\n",
    "        self.Y = target\n",
    "        self.transform = transform\n",
    "\n",
    "    def __len__(self):\n",
    "        return len(self.X)\n",
    "\n",
    "    def __getitem__(self, idx):\n",
    "        if self.transform is not None:\n",
    "            return self.transform(self.X[idx]), self.Y[idx]\n",
    "        elif self.Y is None:\n",
    "            return [self.X[idx]]\n",
    "        return self.X[idx], self.Y[idx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "8ce36dbe-a30c-4f1f-a98b-812511045d7f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# data reshape\n",
    "test_data = torch.from_numpy(test_split.reshape((-1,1,28,28)))\n",
    "train_data = torch.from_numpy(train_split.reshape((-1,1,28,28)))\n",
    "train_labels_data =  torch.from_numpy(train_labels_split)\n",
    "validation_data = torch.from_numpy(validation_split.reshape((-1,1,28,28)))\n",
    "validation_labels_data =  torch.from_numpy(validation_labels_split)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "63cb11b5-3fbb-4878-8d35-1101b404452e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(36000,)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_labels_split.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "8a57fda8-44ad-42b2-80c4-9121b1cbd2d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "train_set = MyDataset(train_data.float(), train_labels_data)\n",
    "valid_set = MyDataset(validation_data.float(), validation_labels_data)\n",
    "test_set = MyDataset(test_data.float())\n",
    "batch_size = 128\n",
    "train_loader = torch.utils.data.DataLoader(train_set, batch_size = batch_size, shuffle = True)\n",
    "valid_loader = torch.utils.data.DataLoader(valid_set, batch_size = batch_size, shuffle = False)\n",
    "test_loader = torch.utils.data.DataLoader(test_set, batch_size = batch_size, shuffle = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "6c1b1d8c-ed3a-4b68-8259-03452e249461",
   "metadata": {},
   "outputs": [],
   "source": [
    "# calculate mean and std of train_set for normalize\n",
    "data = next(iter(train_loader))\n",
    "mean = data[0].mean()\n",
    "std = data[0].std()\n",
    "\n",
    "# set transformation option\n",
    "transform = transforms.Compose([\n",
    "        transforms.ToPILImage(),\n",
    "        transforms.RandomAffine(degrees = 30),\n",
    "        transforms.RandomPerspective(),\n",
    "        transforms.ToTensor(),\n",
    "        transforms.Normalize(mean, std)])\n",
    "\n",
    "# augmented train_set\n",
    "augmented_train_set = MyDataset(train_data.float(), train_labels_data, transform=transform)\n",
    "\n",
    "# combine original set with augmented set\n",
    "datasets = []\n",
    "datasets.append(train_set)\n",
    "datasets.append(augmented_train_set)\n",
    "train_set = torch.utils.data.ConcatDataset(datasets)\n",
    "\n",
    "# redefine train_loader\n",
    "train_loader = torch.utils.data.DataLoader(train_set, batch_size = batch_size, shuffle = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "d8a6dc33-e501-4ab9-a52b-183108123a18",
   "metadata": {},
   "outputs": [],
   "source": [
    "from tqdm import tqdm\n",
    "from time import sleep\n",
    "from tqdm import trange\n",
    "\n",
    "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
    "dataloaders = {'train': train_loader, 'val': valid_loader}\n",
    "dataset_sizes= {'train': len(train_set), 'val': len(valid_set)}\n",
    "\n",
    "def train_model(model, criterion, optimizer, scheduler, dataloaders, dataset_sizes, num_epochs=25):\n",
    "    since = time.time()\n",
    "\n",
    "    best_model_wts = copy.deepcopy(model.state_dict())\n",
    "    best_acc = 0.0\n",
    "    pbar = trange(num_epochs, unit=\"carrots\")\n",
    "    for epoch in pbar:\n",
    "        sleep(0.5)\n",
    "        #print('Epoch {}/{}'.format(epoch, num_epochs - 1))\n",
    "        #print('-' * 10)\n",
    "\n",
    "        # Each epoch has a training and validation phase\n",
    "        pbar.set_description(f\"Epoch {epoch}\")\n",
    "        for phase in ['train', 'val']:\n",
    "            if phase == 'train':\n",
    "                model.train()  # Set model to training mode\n",
    "            else:\n",
    "                model.eval()   # Set model to evaluate mode\n",
    "\n",
    "            running_loss = 0.0\n",
    "            running_corrects = 0\n",
    "\n",
    "            # Iterate over data.\n",
    "            for inputs, labels in dataloaders[phase]:\n",
    "                inputs = inputs.to(device)\n",
    "                labels = labels.to(device)\n",
    "\n",
    "                # zero the parameter gradients\n",
    "                optimizer.zero_grad()\n",
    "\n",
    "                # forward\n",
    "                # track history if only in train\n",
    "                with torch.set_grad_enabled(phase == 'train'):\n",
    "                    outputs = model(inputs)\n",
    "                    _, preds = torch.max(outputs, 1)\n",
    "                    loss = criterion(outputs, labels)\n",
    "\n",
    "                    # backward + optimize only if in training phase\n",
    "                    if phase == 'train':\n",
    "                        loss.backward()\n",
    "                        optimizer.step()\n",
    "\n",
    "                # statistics\n",
    "                running_loss += loss.item() * inputs.size(0)\n",
    "                running_corrects += torch.sum(preds == labels.data)\n",
    "            if phase == 'train':\n",
    "                scheduler.step()\n",
    "\n",
    "            epoch_loss = running_loss / dataset_sizes[phase]\n",
    "            epoch_acc = running_corrects.double() / dataset_sizes[phase]\n",
    "\n",
    "            #print('{} Loss: {:.4f} Acc: {:.4f}'.format(\n",
    "            #    phase, epoch_loss, epoch_acc))\n",
    "\n",
    "            # deep copy the model\n",
    "            if phase == 'val' and epoch_acc > best_acc:\n",
    "                best_acc = epoch_acc\n",
    "                best_model_wts = copy.deepcopy(model.state_dict())\n",
    "\n",
    "        #print()\n",
    "\n",
    "    time_elapsed = time.time() - since\n",
    "    print('Training complete in {:.0f}m {:.0f}s'.format(\n",
    "        time_elapsed // 60, time_elapsed % 60))\n",
    "    print('Best val Acc: {:4f}'.format(best_acc))\n",
    "\n",
    "    # load best model weights\n",
    "    model.load_state_dict(best_model_wts)\n",
    "    pbar.close()\n",
    "    return model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "90f0209d-aa48-4e4c-a0bf-ab72734bdae6",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch 4: 100%|██████████| 5/5 [52:52<00:00, 634.48s/carrots]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training complete in 52m 52s\n",
      "Best val Acc: 0.999750\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "epochs = 5\n",
    "\n",
    "# make resnet 18 model\n",
    "model_ft = models.resnet18(weights='DEFAULT')\n",
    "\n",
    "# change input layer\n",
    "# the default number of input channel in the resnet is 3, but our images are 1 channel. So we have to change 3 to 1.\n",
    "# nn.Conv2d(3, 64, kernel_size=(7, 7), stride=(2, 2), padding=(3, 3), bias=False) <- default\n",
    "model_ft.conv1 = nn.Conv2d(1, 64, kernel_size=(7, 7), stride=(2, 2), padding=(3, 3), bias=False) \n",
    "\n",
    "# change fc layer\n",
    "# the number of classes in our dataset is 10. default is 1000.\n",
    "num_ftrs = model_ft.fc.in_features\n",
    "model_ft.fc = nn.Linear(num_ftrs, 2)\n",
    "\n",
    "model_ft = model_ft.to(device)\n",
    "\n",
    "criterion = nn.CrossEntropyLoss()\n",
    "optimizer_ft = optim.Adam(model_ft.parameters(), lr=0.001)\n",
    "\n",
    "# decay LR by a factor of 0.1 every 5 epochs\n",
    "exp_lr_scheduler = lr_scheduler.StepLR(optimizer_ft, step_size=5, gamma=0.1)\n",
    "\n",
    "# train model\n",
    "model_ft = train_model(model_ft, criterion, optimizer_ft, exp_lr_scheduler, dataloaders, dataset_sizes,\n",
    "                       num_epochs=epochs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdfdf4fb-4c5a-493f-94f1-b42cab84867a",
   "metadata": {},
   "source": [
    "Focal Loss Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "df34b527-b93a-4777-8f55-0d2f98cc1674",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting kornia\n",
      "  Downloading kornia-0.6.7-py2.py3-none-any.whl (565 kB)\n",
      "Requirement already satisfied: torch>=1.8.1 in c:\\users\\coteste\\anaconda3\\lib\\site-packages (from kornia) (1.12.1)\n",
      "Requirement already satisfied: packaging in c:\\users\\coteste\\anaconda3\\lib\\site-packages (from kornia) (21.3)\n",
      "Requirement already satisfied: typing_extensions in c:\\users\\coteste\\anaconda3\\lib\\site-packages (from torch>=1.8.1->kornia) (4.1.1)\n",
      "Requirement already satisfied: pyparsing!=3.0.5,>=2.0.2 in c:\\users\\coteste\\anaconda3\\lib\\site-packages (from packaging->kornia) (3.0.4)\n",
      "Installing collected packages: kornia\n",
      "Successfully installed kornia-0.6.7\n"
     ]
    }
   ],
   "source": [
    "!pip install kornia"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "ac6bcde4-1371-4020-922f-f853eb6824fb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function kornia.losses.focal.focal_loss(input: torch.Tensor, target: torch.Tensor, alpha: float, gamma: float = 2.0, reduction: str = 'none', eps: Optional[float] = None) -> torch.Tensor>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import kornia\n",
    "focal_loss = kornia.losses.focal_loss()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "d4e96f14-0e0d-45ff-b4b3-7e7c2456d477",
   "metadata": {},
   "outputs": [],
   "source": [
    "test_pred = torch.LongTensor()\n",
    "\n",
    "with torch.no_grad():\n",
    "    for images in test_loader:\n",
    "        images = torch.autograd.Variable(images[0])\n",
    "        if torch.cuda.is_available():\n",
    "            images = images.to(device)\n",
    "\n",
    "        outputs = model_ft(images)\n",
    "        predicted = outputs.cpu().data.max(1, keepdim=True)[1]\n",
    "        test_pred = torch.cat((test_pred, predicted), dim=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "f602ec1b-5899-4fee-89ed-d0cf8fefc546",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import accuracy_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "c763e7b2-9da4-44f5-a0b3-784040684871",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3167"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(test_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "16c8059d-2679-4036-b6c7-494c036a6ea4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3167"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(test_labels_split)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "3cb1883d-ec84-46b5-bada-c71b719eac39",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9996842437638144"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(test_pred,test_labels_split)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f3ebb402-77e0-4415-bd25-ac2830a16517",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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