PyTorch_NN_Sample.ipynb

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        "## CPSC: 5616EL - Using PyTorch for NN\n",
        "\n",
        "## PyTorch: The Basics\n",
        "\n",
        "**Arrays are called tensors** in frameworks like TensorFlow and PyTorch, let's break down the terms:\n",
        "\n",
        "**Scalar**: This is just a single number. In tensor terms, this is a 0-dimensional tensor.\n",
        "\n",
        "**Vector**: An array of numbers. This is a 1-dimensional tensor.\n",
        "\n",
        "**Matrix**: A 2D array of numbers. This is a 2-dimensional tensor.\n",
        "\n",
        "Tensor (in the general sense): An N-dimensional array of numbers. When N=0, it's a scalar. When N=1, it's a vector. When N=2, it's a matrix.\n",
        "\n",
        "PyTorch allows you to dynamically define computational graphs. This is done by operating on PyTorch Tensor objects.\n",
        "\n",
        "https://pytorch.org/get-started/pytorch-2.0/\n",
        "\n"
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      "source": [
        "# PyTorch library, which provides tensor computation and deep neural networks\n",
        "import torch\n",
        "# torchvision consists of popular datasets, model architectures, and common image transformations for computer vision tasks\n",
        "import torchvision\n",
        "import torch.nn as nn\n",
        "import torch.optim as optim\n",
        "import torchvision.transforms as transforms\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.metrics import classification_report\n",
        "import numpy as np\n",
        "# Import tqdm, a library to show progress bars in Jupyter Notebooks\n",
        "from tqdm.notebook import tqdm\n",
        "print(torch.__version__)"
      ],
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          "text": [
            "2.1.0+cu118\n"
          ]
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    {
      "cell_type": "markdown",
      "source": [
        "A few other useful imports for debugging and visualizations."
      ],
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    {
      "cell_type": "code",
      "source": [
        "!pip install ipdb\n",
        "!pip install torchviz\n",
        "!apt install graphviz\n",
        "import ipdb\n",
        "from torchviz import make_dot"
      ],
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      "source": [
        "Here is an example, where we work with the function\n",
        "\n",
        "$$f(x) = x^2 + 2x + 6$$\n",
        "\n",
        "Note how there is nothing special about this function in terms of PyTorch specific syntax, i.e. you could apply this to any object that implements the `**`, `*` and `+` operators.\n",
        "\n"
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      "source": [
        "We need to set `requires_grad` property to true. By default, during the forward pass, i.e. when evaluating f(x), an operation is recorded in the backward graph, only if at least one of its input tensors requires a gradient."
      ]
    },
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      "cell_type": "code",
      "source": [
        "def f(x):\n",
        "    return x ** 2 + 2 * x + 6"
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      "source": [
        "Now let's compute the derivative $$\\frac{d}{dx}\\bigg\\rvert_{x=4} f(x) = 2(4) + 2 = 10$$"
      ],
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      "source": [
        "np_x = np.array([4.0])\n",
        "x = torch.from_numpy(np_x).requires_grad_(True) # Need to set requires_grad to True\n",
        "y = f(x)\n",
        "\n",
        "y.backward()\n",
        "\n",
        "print(x.grad)  # This will print the gradient dy/dx at x = 4.0"
      ],
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            "tensor([10.], dtype=torch.float64)\n"
          ]
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      "source": [
        "We can visualize the computation graph by calling the `make_dot` function from `torchviz`. There are\n",
        "\n",
        "* 2 Addition Operations\n",
        "* 1 Power Operation\n",
        "* 1 Multiply Operation\n",
        "* 1 Accumulate Operation"
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      "source": [
        "make_dot(y)"
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      "source": [
        "If we instead evaluate $$\\frac{d}{dx}\\bigg\\rvert_{x=5} f(x) = 2(5) + 2 = 12$$"
      ],
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      "source": [
        "np_x = np.array([5.0])\n",
        "x = torch.from_numpy(np_x).requires_grad_(True) # Need to set requires_grad to True\n",
        "y = f(x)\n",
        "\n",
        "y.backward()\n",
        "\n",
        "print(x.grad)  # This will print the gradient dy/dx at x = 5.0"
      ],
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        "colab": {
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          "text": [
            "tensor([12.], dtype=torch.float64)\n"
          ]
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    {
      "cell_type": "markdown",
      "source": [
        "## MNIST dataset classification using Neural Networks\n",
        "\n",
        "This program will download the MNIST dataset, create a simple feedforward neural network with one hidden layer, train it for 5 epochs, and then test its accuracy on the test set. The neural network architecture used here is just a basic example, and many enhancements can be made for improving the performance.\n",
        "\n",
        "Input layer: 28x28 = 784 neurons (matching the size of a flattened MNIST image)\n",
        "\n",
        "One hidden layer: 500 neurons (as specified by the hidden_size variable)\n",
        "\n",
        "Output layer: 10 neurons (one for each digit from 0 to 9)\n",
        "\n",
        "MNIST training dataset, which consists of 60,000 images. When a batch_size of 100 is used, meaning each batch will contain 100 images.\n",
        "\n",
        "When using torchvision.datasets.MNIST, the training set is split into 60,000 samples, and the test set is split into 10,000 samples by default based on the train argument. If train=True, it fetches the training data, and if train=False, it fetches the test data."
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          "text": [
            "Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz\n",
            "Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz to ./data/MNIST/raw/train-images-idx3-ubyte.gz\n"
          ]
        },
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          "name": "stderr",
          "text": [
            "100%|██████████| 9912422/9912422 [00:00<00:00, 87834030.31it/s]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Extracting ./data/MNIST/raw/train-images-idx3-ubyte.gz to ./data/MNIST/raw\n"
          ]
        },
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          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\n"
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          "text": [
            "\n",
            "Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz\n",
            "Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz to ./data/MNIST/raw/train-labels-idx1-ubyte.gz\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 28881/28881 [00:00<00:00, 39807983.51it/s]\n"
          ]
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          "name": "stdout",
          "text": [
            "Extracting ./data/MNIST/raw/train-labels-idx1-ubyte.gz to ./data/MNIST/raw\n",
            "\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz to ./data/MNIST/raw/t10k-images-idx3-ubyte.gz\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 1648877/1648877 [00:00<00:00, 30760125.95it/s]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Extracting ./data/MNIST/raw/t10k-images-idx3-ubyte.gz to ./data/MNIST/raw\n",
            "\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz to ./data/MNIST/raw/t10k-labels-idx1-ubyte.gz\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 4542/4542 [00:00<00:00, 6401387.35it/s]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Extracting ./data/MNIST/raw/t10k-labels-idx1-ubyte.gz to ./data/MNIST/raw\n",
            "\n",
            "Dataset MNIST\n",
            "    Number of datapoints: 60000\n",
            "    Root location: ./data\n",
            "    Split: Train\n",
            "    StandardTransform\n",
            "Transform: Compose(\n",
            "               ToTensor()\n",
            "               Normalize(mean=(0.5,), std=(0.5,))\n",
            "           )\n"
          ]
        }
      ],
      "source": [
        "# Define hyperparameters\n",
        "input_size = 28*28  # Size of image (28x28 pixels for MNIST)\n",
        "hidden_size = 500   # Size of hidden layer ( a single hidden layer with 500 neurons)\n",
        "num_classes = 10    # Number of output classes (0-9 for MNIST)\n",
        "num_epochs = 5      # Number of times the entire dataset is processed\n",
        "batch_size = 100    # Number of samples per gradient update\n",
        "learning_rate = 0.001\n",
        "\n",
        "# Download the MNIST dataset for training, store it in the 'data' directory, and apply a transform that\n",
        "# converts images into tensors.\n",
        "\n",
        "# Define data transformations and normalization for MNIST dataset\n",
        "transform = transforms.Compose([transforms.ToTensor(), transforms.Normalize((0.5,), (0.5,))])\n",
        "\n",
        "# Load the MNIST dataset\n",
        "train_dataset = torchvision.datasets.MNIST(root='./data', train=True, transform=transform, download=True)\n",
        "test_dataset = torchvision.datasets.MNIST(root='./data', train=False, transform=transform)\n",
        "\n",
        "# Create data loaders for batching and shuffling the datasets\n",
        "train_loader = torch.utils.data.DataLoader(dataset=train_dataset, batch_size=batch_size, shuffle=True)\n",
        "test_loader = torch.utils.data.DataLoader(dataset=test_dataset, batch_size=batch_size, shuffle=False)\n",
        "\n",
        "print(train_dataset) # Print the representation of the train_loader object\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can easily visualize the images and their corresponding label as below. See how index 0 for a given sample corresponds to the image, and index 1 is the label. Each image is represented as a vector of 28 × 28 = 784 pixel values."
      ],
      "metadata": {
        "id": "Nwlc-E6MbvCY"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Define a list of indices for which we want to visualize the corresponding MNIST images.\n",
        "indices = [1, 12000, 344] # label: 0, 7, 9\n",
        "\n",
        "# for showing the figure with a specified size\n",
        "fig = plt.figure(figsize=(len(indices) * 3, 3))\n",
        "\n",
        "# Loop over each index in the 'indices' list.\n",
        "for i, index in enumerate(indices):\n",
        "    # For each index, add a new subplot to the figure.\n",
        "    ax = fig.add_subplot(1, len(indices), i + 1)\n",
        "\n",
        "    # Fetch the MNIST example (image and label) for the given index.\n",
        "    example = train_dataset[index]\n",
        "\n",
        "    # Display the image in the current subplot.\n",
        "    # 'example[0]' is the image which we reshape from its tensor form to a 28x28 numpy array.\n",
        "    # And specify the colormap to be grayscale.\n",
        "    ax.imshow(example[0].reshape(28, 28), cmap=plt.cm.gray)\n",
        "\n",
        "    # Set the title of the current subplot to the label of the image.\n",
        "    ax.set_title(\"Label: {}\".format(example[1]))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 288
        },
        "id": "5b2Ak9bGbw40",
        "outputId": "6e73232d-997a-41ea-cfc7-4b0910ed5015"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 900x300 with 3 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Training"
      ],
      "metadata": {
        "id": "o8HMb565cBvM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "# Check if a GPU is available and set the device accordingly.\n",
        "if torch.cuda.is_available():\n",
        "    print(\"Using cuda\")\n",
        "    use_cuda = True\n",
        "    device = torch.device(\"cuda\")\n",
        "else:\n",
        "    device = \"cpu\"\n",
        "\n",
        "# Define the neural network architecture\n",
        "class Net(nn.Module):\n",
        "    def __init__(self, input_size, hidden_size, num_classes):\n",
        "        super(Net, self).__init__()\n",
        "        # Fully connected layer from input to hidden layer\n",
        "        self.fc1 = nn.Linear(input_size, hidden_size)\n",
        "        # Activation function\n",
        "        self.relu = nn.ReLU()\n",
        "        # Fully connected layer from hidden layer to output\n",
        "        self.fc2 = nn.Linear(hidden_size, num_classes)\n",
        "\n",
        "    def forward(self, x):\n",
        "        # Pass input through first fully connected layer and then apply ReLU activation\n",
        "        out = self.fc1(x)\n",
        "        out = self.relu(out)\n",
        "        # Pass the result through the second fully connected layer\n",
        "        out = self.fc2(out)\n",
        "        return out\n",
        "\n",
        "# Create an instance of the neural network model\n",
        "model = Net(input_size, hidden_size, num_classes)\n",
        "\n",
        "# Define the loss function (Cross Entropy Loss for classification problems)\n",
        "criterion = nn.CrossEntropyLoss()\n",
        "# Define the optimizer (Stochastic Gradient Descent with momentum)\n",
        "optimizer = optim.SGD(model.parameters(), lr=learning_rate, momentum=0.9)\n",
        "\n",
        "# Lists to track progress\n",
        "train_losses = []\n",
        "test_losses = []\n",
        "test_accuracies = []\n",
        "\n",
        "# Train the model\n",
        "for epoch in range(num_epochs):\n",
        "\n",
        "    for i, (images, labels) in enumerate(train_loader):\n",
        "        # Flatten the images into vectors\n",
        "        images = images.view(-1, 28*28)\n",
        "\n",
        "        # Clear gradients, forward propagate, compute loss, backpropagate, and update weights\n",
        "        optimizer.zero_grad()\n",
        "        outputs = model(images)\n",
        "        loss = criterion(outputs, labels)\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "\n",
        "        # Print loss statistics every 100 batches\n",
        "        if (i+1) % 100 == 0:\n",
        "            print ('Epoch: [{}/{}], Step: [{}/{}], Loss: {:.4f}'.format(epoch+1, num_epochs, i+1, len(train_loader), loss.item()))\n",
        "\n",
        "    # Track training loss after each epoch\n",
        "    train_losses.append(loss.item())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UqeBB7z8brG8",
        "outputId": "ad01c78f-1883-4dcb-e4ad-0c3a0b371d62"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Using cuda\n",
            "Epoch: [1/5], Step: [100/600], Loss: 1.4692\n",
            "Epoch: [1/5], Step: [200/600], Loss: 0.8713\n",
            "Epoch: [1/5], Step: [300/600], Loss: 0.7824\n",
            "Epoch: [1/5], Step: [400/600], Loss: 0.5451\n",
            "Epoch: [1/5], Step: [500/600], Loss: 0.5584\n",
            "Epoch: [1/5], Step: [600/600], Loss: 0.4036\n",
            "Epoch: [2/5], Step: [100/600], Loss: 0.4039\n",
            "Epoch: [2/5], Step: [200/600], Loss: 0.5249\n",
            "Epoch: [2/5], Step: [300/600], Loss: 0.3536\n",
            "Epoch: [2/5], Step: [400/600], Loss: 0.3321\n",
            "Epoch: [2/5], Step: [500/600], Loss: 0.3535\n",
            "Epoch: [2/5], Step: [600/600], Loss: 0.2947\n",
            "Epoch: [3/5], Step: [100/600], Loss: 0.4119\n",
            "Epoch: [3/5], Step: [200/600], Loss: 0.2517\n",
            "Epoch: [3/5], Step: [300/600], Loss: 0.3310\n",
            "Epoch: [3/5], Step: [400/600], Loss: 0.3828\n",
            "Epoch: [3/5], Step: [500/600], Loss: 0.5345\n",
            "Epoch: [3/5], Step: [600/600], Loss: 0.2530\n",
            "Epoch: [4/5], Step: [100/600], Loss: 0.2576\n",
            "Epoch: [4/5], Step: [200/600], Loss: 0.4453\n",
            "Epoch: [4/5], Step: [300/600], Loss: 0.4671\n",
            "Epoch: [4/5], Step: [400/600], Loss: 0.2608\n",
            "Epoch: [4/5], Step: [500/600], Loss: 0.2803\n",
            "Epoch: [4/5], Step: [600/600], Loss: 0.3912\n",
            "Epoch: [5/5], Step: [100/600], Loss: 0.2409\n",
            "Epoch: [5/5], Step: [200/600], Loss: 0.2736\n",
            "Epoch: [5/5], Step: [300/600], Loss: 0.2944\n",
            "Epoch: [5/5], Step: [400/600], Loss: 0.2740\n",
            "Epoch: [5/5], Step: [500/600], Loss: 0.2588\n",
            "Epoch: [5/5], Step: [600/600], Loss: 0.3035\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Evaluate the trained model on test data"
      ],
      "metadata": {
        "id": "-7-h1sU5cGsH"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "# Begin evaluation phase for the trained model on test data\n",
        "correct = 0   # Initialize counter for correct predictions\n",
        "total = 0     # Initialize counter for total number of images tested\n",
        "\n",
        "# Lists to store true labels and model predictions for all test images\n",
        "all_labels = []\n",
        "all_predictions = []\n",
        "\n",
        "# torch.no_grad() ensures that operations inside this context won't track gradients.\n",
        "# This is useful when evaluating a model because we don't need gradients computation during inference.\n",
        "with torch.no_grad():\n",
        "\n",
        "    for images, labels in test_loader:\n",
        "        # Reshape the images into a 1D vector to be compatible with the model input\n",
        "        images = images.view(-1, 28*28)\n",
        "\n",
        "        # Pass images through the model to get predicted outputs\n",
        "        outputs = model(images)\n",
        "\n",
        "        # Determine the class with the highest predicted score\n",
        "        _, predicted = torch.max(outputs.data, 1)\n",
        "\n",
        "        # Update the total count and the count of correct predictions\n",
        "        total += labels.size(0)\n",
        "        correct += (predicted == labels).sum().item()\n",
        "\n",
        "        # Store true labels and predicted labels for this batch\n",
        "        all_labels.extend(labels.numpy())\n",
        "        all_predictions.extend(predicted.numpy())\n",
        "\n",
        "# Print overall accuracy of the model on test data\n",
        "print('\\nAccuracy of the network on the 10000 test images: {} %\\n'.format(100 * correct / total))\n",
        "\n",
        "# Use scikit-learn's classification report to get detailed metrics like precision, recall, etc.\n",
        "# The report provides these metrics for each class and averages.\n",
        "print(classification_report(all_labels, all_predictions, target_names=[str(i) for i in range(10)]))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dwzKDdKLQEez",
        "outputId": "a452a132-776a-41d3-932e-9ec71d4355b4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Accuracy of the network on the 10000 test images: 92.14 %\n",
            "\n",
            "              precision    recall  f1-score   support\n",
            "\n",
            "           0       0.94      0.98      0.96       980\n",
            "           1       0.97      0.97      0.97      1135\n",
            "           2       0.93      0.89      0.91      1032\n",
            "           3       0.91      0.90      0.91      1010\n",
            "           4       0.91      0.93      0.92       982\n",
            "           5       0.90      0.87      0.89       892\n",
            "           6       0.93      0.94      0.94       958\n",
            "           7       0.93      0.92      0.93      1028\n",
            "           8       0.87      0.90      0.89       974\n",
            "           9       0.90      0.90      0.90      1009\n",
            "\n",
            "    accuracy                           0.92     10000\n",
            "   macro avg       0.92      0.92      0.92     10000\n",
            "weighted avg       0.92      0.92      0.92     10000\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "udsWvHxxLpef"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Visualize the classification weights after training"
      ],
      "metadata": {
        "id": "pP-8fPcFQPRc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Get the weights of the first fully connected layer (from input to hidden layer)\n",
        "weights = model.fc1.weight.data\n",
        "\n",
        "# Create a 2x5 grid of subplots for visualizing the weights for each class (0 to 9)\n",
        "fig, axarr = plt.subplots(2, 5, figsize=(8, 6))\n",
        "\n",
        "# Iterate over all classes (from 0 to 9)\n",
        "for idx in range(10):\n",
        "    # Select the appropriate subplot for the current class\n",
        "    ax = axarr[idx // 5, idx % 5]\n",
        "\n",
        "    # Combine the weights from the first layer with the weights connecting the hidden layer to the current class\n",
        "    # This provides a higher-level view of the learned patterns for the current class\n",
        "    class_weights = torch.matmul(model.fc2.weight[idx], weights)\n",
        "\n",
        "    # Visualize the computed weights for the current class as a 28x28 image\n",
        "    ax.imshow(class_weights.view(28, 28).detach().numpy(), cmap=\"gray\")\n",
        "\n",
        "    # Turn off axis to have a cleaner visualization\n",
        "    ax.axis('off')\n",
        "\n",
        "    # Set title to indicate which class is being visualized\n",
        "    ax.set_title(f'Class {idx}')\n",
        "\n",
        "# Adjust spacing between subplots for better visualization\n",
        "plt.tight_layout()\n",
        "\n",
        "# Display the visualizations\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 453
        },
        "id": "ggcp24xzLRSw",
        "outputId": "1b23e211-36f6-4326-9ad4-b41b7f313ab3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 10 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}