HammingNetwork+PCA.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "gpuType": "T4"
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "code",
      "source": [
        "import cv2\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "from skimage import io\n",
        "import seaborn as sns\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import stats\n",
        "import matplotlib.image as mpimg\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from tensorflow.keras.datasets import mnist"
      ],
      "metadata": {
        "id": "VFqs4c3KQBFE"
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def power_iteration(A, num_iterations=100):\n",
        "    # Initialize a random vector as the starting point\n",
        "    v = np.random.rand(A.shape[0])\n",
        "\n",
        "    for _ in range(num_iterations):\n",
        "        # Power Iteration step\n",
        "        Av = np.dot(A, v)\n",
        "        # Compute the eigenvalue\n",
        "        eigenvalue = np.dot(v, Av)\n",
        "        # Normalize the eigenvector\n",
        "        v = Av / np.linalg.norm(Av)\n",
        "\n",
        "    return eigenvalue, v\n",
        "\n",
        "def eigen_decomposition(A, num_components=None):\n",
        "    n = A.shape[0]\n",
        "\n",
        "    if num_components is None:\n",
        "        num_components = n\n",
        "\n",
        "    eigenvalues = np.zeros(num_components)\n",
        "    eigenvectors = np.zeros((n, num_components))\n",
        "\n",
        "    for i in range(num_components):\n",
        "        # Get the dominant eigenvalue and corresponding eigenvector\n",
        "        eigenvalue, eigenvector = power_iteration(A)\n",
        "\n",
        "        # Store the results\n",
        "        eigenvalues[i] = eigenvalue\n",
        "        eigenvectors[:, i] = eigenvector\n",
        "\n",
        "        # Deflate A by subtracting the outer product\n",
        "        A = A - eigenvalue * np.outer(eigenvector, eigenvector)\n",
        "\n",
        "    return eigenvalues, eigenvectors\n"
      ],
      "metadata": {
        "id": "K26GmbVzQA8x"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "class PCA:\n",
        "    def __init__(self, n_components=None,start=None):\n",
        "        self.n_components = n_components\n",
        "        self.mean = None\n",
        "        self.explained_variance_ = None\n",
        "        self.explained_variance_ratio_ = None\n",
        "        self.eigenvalues=None\n",
        "        self.Q_matrix=None\n",
        "        self.start=None\n",
        "\n",
        "    def my_mean(self, X):\n",
        "        return np.sum(X, axis=0) / X.shape[0]\n",
        "\n",
        "    def my_cov(self, X, rowvar=False):\n",
        "        if rowvar:\n",
        "            X = X.T\n",
        "        n = X.shape[1]\n",
        "        covariance_matrix = (X.T @ X) / (n - 1)\n",
        "        return covariance_matrix\n",
        "\n",
        "    def my_eigh(self, A):\n",
        "        self.eigenvalues, eigenvectors= eigen_decomposition(A)\n",
        "        return self.eigenvalues, eigenvectors\n",
        "\n",
        "    def my_argsort(self, arr):\n",
        "        n = len(arr)\n",
        "        indices = list(range(n))\n",
        "        for i in range(1, n):\n",
        "            key = arr[i]\n",
        "            j = i - 1\n",
        "            while j >= 0 and key > arr[j]:\n",
        "                arr[j + 1] = arr[j]\n",
        "                indices[j + 1] = indices[j]\n",
        "                j -= 1\n",
        "            arr[j + 1] = key\n",
        "            indices[j + 1] = i\n",
        "        return indices\n",
        "    def fit(self, X):\n",
        "        self.mean = self.my_mean(X)\n",
        "        centered_data = X - self.mean\n",
        "\n",
        "        cov_matrix = self.my_cov(centered_data, rowvar=False)\n",
        "        eigenvalues, eigenvectors = self.my_eigh(cov_matrix)\n",
        "\n",
        "        sorted_indices = self.my_argsort(eigenvalues)\n",
        "        eigenvalues = eigenvalues[sorted_indices]\n",
        "        eigenvectors = eigenvectors[:, sorted_indices]\n",
        "\n",
        "        self.explained_variance_ = eigenvalues\n",
        "\n",
        "        self.Q_matrix = eigenvectors\n",
        "\n",
        "        if self.n_components is not None :\n",
        "          if  self.start is None:\n",
        "                self.Q_matrix = self.Q_matrix[:, :self.n_components]\n",
        "                self.explained_variance_ = eigenvalues[:self.n_components]\n",
        "\n",
        "          if  self.start is not None:\n",
        "                self.Q_matrix = self.Q_matrix[:, self.start : self.n_components]\n",
        "                self.explained_variance_ = eigenvalues[:self.n_components]\n",
        "\n",
        "\n",
        "        total_variance = np.sum(eigenvalues)\n",
        "        self.explained_variance_ratio_ = self.explained_variance_ / total_variance\n",
        "\n",
        "    def transform(self, X):\n",
        "        centered_data = X - self.mean\n",
        "        reduced_data = centered_data @ self.Q_matrix\n",
        "        return reduced_data\n",
        "\n",
        "    def inverse_transform(self, compressed_image):\n",
        "        return compressed_image @ self.Q_matrix.T + self.mean"
      ],
      "metadata": {
        "id": "XTRVpmw9QA6T"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Load the MNIST dataset\n",
        "(x_train, y_train), (x_test, y_test) = mnist.load_data()\n",
        "\n",
        "# Normalize the pixel values to the range [0, 1]\n",
        "x_train_normalized = x_train / 255.0\n",
        "x_test_normalized = x_test / 255.0\n",
        "\n",
        "#preprocessing to make data 1 and 0 to apply hamming network later\n",
        "\n",
        "# Threshold the normalized values to 1 if >= 0.5\n",
        "x_train_thresholded = np.round(np.where(x_train_normalized >= 0.5, 1.0, 0.0))\n",
        "x_test_thresholded = np.round(np.where(x_test_normalized >= 0.5, 1.0, 0.0))\n",
        "\n",
        "num_samples = 5\n",
        "\n",
        "plt.figure(figsize=(15, 5))\n",
        "\n",
        "for i in range(num_samples):\n",
        "    # Original Image\n",
        "    plt.subplot(3, num_samples, i + 1)\n",
        "    plt.imshow(x_train[i], cmap='gray')\n",
        "    plt.title(f\"Original {i + 1}\")\n",
        "\n",
        "    # Normalized Image\n",
        "    plt.subplot(3, num_samples, num_samples + i + 1)\n",
        "    plt.imshow(x_train_normalized[i], cmap='gray')\n",
        "    plt.title(f\"Normalized {i + 1}\")\n",
        "\n",
        "    # Thresholded Image\n",
        "    plt.subplot(3, num_samples, 2 * num_samples + i + 1)\n",
        "    plt.imshow(x_train_thresholded[i], cmap='gray')\n",
        "    plt.title(f\"Thresholded {i + 1}\")\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 503
        },
        "id": "1BktYaB3V4wx",
        "outputId": "2e93f0be-2b20-443d-86e3-b36f318a90f9"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz\n",
            "11490434/11490434 [==============================] - 0s 0us/step\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x500 with 15 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(x_train_thresholded[0])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EOQf3HUAV4tZ",
        "outputId": "057f0638-d7e4-456e-ad30-8ae736c77145"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
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            "  0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
            "  0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
            "  0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
            "  0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
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            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 1. 0. 1. 1. 1. 0.\n",
            "  0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 0.\n",
            "  0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 0. 0. 0. 0. 0. 0.\n",
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            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 0. 0. 0. 0. 0. 0.\n",
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            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 1. 1. 1. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0.\n",
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            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 1. 1. 0. 0. 0. 0. 0. 0. 0.\n",
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            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 1. 1. 1. 0. 0. 0. 0. 0.\n",
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            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 1. 1. 0. 0. 0. 0.\n",
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            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 1. 0. 0. 0. 0.\n",
            "  0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 0. 0. 0. 0. 0. 0.\n",
            "  0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 0. 0. 0. 0. 0. 0. 0. 0.\n",
            "  0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
            "  0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 1. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
            "  0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
            "  0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
            "  0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
            "  0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
            "  0. 0. 0. 0.]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "original_images = x_train_thresholded.reshape(len(x_train_thresholded), -1)\n",
        "\n",
        "# Display some original samples\n",
        "plt.figure(figsize=(10, 5))\n",
        "for i in range(5):\n",
        "    plt.subplot(2, 5, i + 1)\n",
        "    plt.imshow(x_train_thresholded[i], cmap='gray')\n",
        "    plt.title('Original')\n",
        "\n",
        "# Apply PCA\n",
        "n_components = 100\n",
        "pca = PCA(n_components=n_components)\n",
        "pca.fit(original_images)\n",
        "pca_result = pca.transform(original_images)\n",
        "\n",
        "# Reconstruct the images\n",
        "reconstructed_images = pca.inverse_transform(pca_result)\n",
        "\n",
        "# Reshape reconstructed images\n",
        "reconstructed_images = reconstructed_images.reshape(len(x_train_thresholded), 28, 28)\n",
        "\n",
        "# Display some reconstructed samples\n",
        "for i in range(5):\n",
        "    plt.subplot(2, 5, i + 6)\n",
        "    plt.imshow(reconstructed_images[i], cmap='gray')\n",
        "    plt.title('Reconstructed')\n",
        "\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 426
        },
        "id": "eOGYQBhdV4qy",
        "outputId": "f147d022-c066-49a7-9739-cf8b3af564bc"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 10 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Display some original samples\n",
        "plt.figure(figsize=(10, 5))\n",
        "for i in range(5):\n",
        "    plt.subplot(2, 5, i + 1)\n",
        "    plt.imshow(x_train_thresholded[i], cmap='gray')\n",
        "    plt.title('Original')\n",
        "# Apply PCA\n",
        "n_components = 250\n",
        "pca = PCA(n_components=n_components)\n",
        "pca.fit(original_images)\n",
        "pca_result = pca.transform(original_images)\n",
        "\n",
        "# Reconstruct the images\n",
        "reconstructed_images = pca.inverse_transform(pca_result)\n",
        "\n",
        "# Reshape reconstructed images\n",
        "reconstructed_images = reconstructed_images.reshape(len(x_train_thresholded), 28, 28)\n",
        "\n",
        "# Display some reconstructed samples\n",
        "for i in range(5):\n",
        "    plt.subplot(2, 5, i + 6)\n",
        "    plt.imshow(reconstructed_images[i], cmap='gray')\n",
        "    plt.title('Reconstructed')\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 426
        },
        "id": "X2PWkwcIW_fV",
        "outputId": "ac60a91d-cd3e-4d9c-ac87-2dcd757046cf"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 10 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Display some original samples\n",
        "plt.figure(figsize=(10, 5))\n",
        "for i in range(5):\n",
        "    plt.subplot(2, 5, i + 1)\n",
        "    plt.imshow(x_train_thresholded[i], cmap='gray')\n",
        "    plt.title('Original')\n",
        "# Apply PCA\n",
        "n_components = 400\n",
        "pca = PCA(n_components=n_components)\n",
        "pca.fit(original_images)\n",
        "pca_result = pca.transform(original_images)\n",
        "\n",
        "# Reconstruct the images\n",
        "reconstructed_images = pca.inverse_transform(pca_result)\n",
        "\n",
        "# Reshape reconstructed images\n",
        "reconstructed_images = reconstructed_images.reshape(len(x_train_thresholded), 28, 28)\n",
        "\n",
        "# Display some reconstructed samples\n",
        "for i in range(5):\n",
        "    plt.subplot(2, 5, i + 6)\n",
        "    plt.imshow(reconstructed_images[i], cmap='gray')\n",
        "    plt.title('Reconstructed')\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 426
        },
        "id": "Nnfi2W34XAVB",
        "outputId": "6513d6de-9851-45d2-ab4a-431265ac44b0"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 10 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x = x_train_thresholded.reshape(len(x_train_thresholded), -1)\n",
        "mean = np.mean(x, axis=0)\n",
        "centered_data = x - mean\n",
        "cov_matrix = np.cov(centered_data, rowvar=False)\n",
        "eigenvalues, eigenvectors = np.linalg.eig(cov_matrix)\n",
        "sorted_indices = np.argsort(eigenvalues)[::-1]\n",
        "eigenvalues = eigenvalues[sorted_indices]\n",
        "eigenvectors = eigenvectors[:, sorted_indices]"
      ],
      "metadata": {
        "id": "Qhu-WaPkOk6t"
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "explained_variance_ratio = eigenvalues / np.sum(eigenvalues)\n",
        "\n",
        "cumulative_explained_variance = np.cumsum(explained_variance_ratio)\n",
        "\n",
        "plt.plot(cumulative_explained_variance, marker='o', linestyle='-')\n",
        "plt.xlabel('Number of Principal Components')\n",
        "plt.ylabel('Cumulative Explained Variance')\n",
        "plt.title('Cumulative Explained Variance vs. Number of Principal Components')\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "Nq_eyN7rV4oB",
        "outputId": "ce1b1a1d-ff71-4aad-972c-d95725c52bc8"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#From the above plot and the trails of different Q-matrices the result is best at 400 component and doesnt chane alot with Q-matrix more than 400  #"
      ],
      "metadata": {
        "id": "_4MiCvegZyFs"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#**After applying PCA and using the right Q-matrix the result looks like the orginal image with small differences so we reduced the data deminsions while saving all its important information\"features\" and with only 400 feature we represented our 784 feature**"
      ],
      "metadata": {
        "id": "WEo7Jx-APLYj"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "explained_variance = eigenvalues\n",
        "plt.figure(figsize=(10, 5))\n",
        "indices = np.arange(1, len(explained_variance) + 1)\n",
        "plt.bar(indices, explained_variance[indices - 1])\n",
        "plt.bar(range(1, len(explained_variance) + 1), explained_variance)\n",
        "plt.xlabel('Principal Component')\n",
        "plt.ylabel('Variance Explained')\n",
        "plt.title('Variance Explained by Each Principal Component')\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "0-Uz0690V4lm",
        "outputId": "e8f41260-ab0a-4ba1-9cf9-8cde9b9bfb78"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Phase 2:"
      ],
      "metadata": {
        "id": "r09SlCR4KRCw"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "K-means Clustering Implementation"
      ],
      "metadata": {
        "id": "3moPCd9iKLDc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "'''\n",
        "# k-means clustering\n",
        "from sklearn.cluster import KMeans\n",
        "kmeans = KMeans(n_clusters=10, random_state=42)\n",
        "kmeans_labels = kmeans.fit_predict(x_train_thresholded)\n",
        "centroids = kmeans.clustercenters\n",
        "'''"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "k2TdeGVVJYba",
        "outputId": "c208fddf-a902-4b96-83a0-33f0c6e56e28"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'\\n# k-means clustering \\nfrom sklearn.cluster import KMeans\\nkmeans = KMeans(n_clusters=10, random_state=42)\\nkmeans_labels = kmeans.fit_predict(x_train_thresholded)\\ncentroids = kmeans.clustercenters\\n'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def k_means(X, k, iters=100):\n",
        "    # Initialize centroids randomly\n",
        "    centroids = X[np.random.choice(range(len(X)), k, replace=False)]\n",
        "\n",
        "    for _ in range(iters):\n",
        "        # Assign each data point to the nearest centroid\n",
        "        labels = np.argmin(np.linalg.norm(X[:, np.newaxis] - centroids, axis=2), axis=1)\n",
        "\n",
        "        # Update centroids based on the mean of assigned data points\n",
        "        new_centroids = np.array([X[labels == i].mean(axis=0) for i in range(k)])\n",
        "\n",
        "        # Check for convergence\n",
        "        if np.all(centroids == new_centroids):\n",
        "            break\n",
        "\n",
        "        centroids = new_centroids\n",
        "\n",
        "    return centroids, labels"
      ],
      "metadata": {
        "id": "pFglEYjuNNjs"
      },
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Hamming Network Implementation"
      ],
      "metadata": {
        "id": "7MiqoNJtJjDc"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "id": "6Vl_S83Q3Dw9"
      },
      "outputs": [],
      "source": [
        "def hamming_network_cluster(input_vector, centroids):\n",
        "    # Calculate weights by dividing each feature in the cluster by 2\n",
        "    weights_matrix = centroids / 2\n",
        "    n=input_vector.shape[0]\n",
        "    # Calculate (bias) theta by dividing the number of features by 2\n",
        "    theta = np.ones(( weights_matrix.shape[0],1)) * (- n/2)\n",
        "    input_vector= input_vector.reshape(1,input_vector.shape[0])\n",
        "\n",
        "    net_input = np.dot(weights_matrix, input_vector.T) + theta\n",
        "\n",
        "    # Take the absolute value of the vector\n",
        "    net_input_abs = np.abs(net_input)\n",
        "\n",
        "    # Choose the smallest value; it means the point vector belongs to this cluster and is the winner class\n",
        "    winner_clusters = np.argmin(net_input_abs, axis=0)\n",
        "\n",
        "    return winner_clusters"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def evaluate_accuracy(predictions, targets):\n",
        "    accuracy = np.mean(predictions == targets)\n",
        "    return accuracy"
      ],
      "metadata": {
        "id": "vNz26egEB7CR"
      },
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "id": "sBvhav_u3Dw-"
      },
      "outputs": [],
      "source": [
        "# Getting the centroids for the PCA version of the data\n",
        "centroids , labels = k_means(pca_result,k=10)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Evaluating the model (PCA version)\n",
        "winner_clusters = []\n",
        "for i in range (pca_result.shape[0]):\n",
        "  winner_cluster = hamming_network_cluster(pca_result[i],centroids)\n",
        "  winner_clusters.append(winner_cluster[0])\n",
        "\n",
        "\n",
        "\n",
        "accuracy_1 = evaluate_accuracy(winner_clusters , labels)\n",
        "print(accuracy_1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PeDo2oPx6HI3",
        "outputId": "0e23842f-f766-485e-fec1-7e1919b13e1c"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.9020166666666667\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Getting the centroids for the original data\n",
        "original_centroids , labels = k_means(original_images,k=10)"
      ],
      "metadata": {
        "id": "Jt3roDVZFBJZ"
      },
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Evaluating the model\n",
        "winner_clusters = []\n",
        "for i in range (pca_result.shape[0]):\n",
        "  winner_cluster = hamming_network_cluster(original_images[i],original_centroids)\n",
        "  winner_clusters.append(winner_cluster[0])\n",
        "\n",
        "\n",
        "\n",
        "accuracy_2 = evaluate_accuracy(winner_clusters , labels)\n",
        "print(accuracy_2)"
      ],
      "metadata": {
        "id": "LXicgkmzEOye",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ed2ecc55-b9a0-4c48-d061-a2d3524e6cfc"
      },
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.7119166666666666\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "DuAAjZ7_PHlP"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}