notebooks/multivariate-statistics/principal_component_analysis.ipynb

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   "cell_type": "markdown",
   "id": "f9081774-e5f6-4683-9029-923223f63fd7",
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   "source": [
    "### **Prerequisites**\n",
    "\n",
    "1. **Dot Product Between Two Vectors and Scalar Projection:**\n",
    "   $$\n",
    "   \\mathbf{a} \\cdot \\mathbf{b} = \\|\\mathbf{a}\\| \\|\\mathbf{b}\\| \\cos \\theta = \\sum_{i=1}^d a_i b_i\n",
    "   $$\n",
    "   Scalar projection of $ \\mathbf{a} $ onto $ \\mathbf{b} $:\n",
    "   $$\n",
    "   \\text{Projection} = \\frac{\\mathbf{a} \\cdot \\mathbf{b}}{\\|\\mathbf{b}\\|}\n",
    "   $$ \n",
    "\n",
    "2. **Dot Product = Scalar Projection When Projected onto Unit Vector:**\n",
    "   If $ \\|\\mathbf{b}\\| = 1 $, then:\n",
    "   $$\n",
    "   \\text{Projection} = \\mathbf{a} \\cdot \\mathbf{b}\n",
    "   $$ \n",
    "   *If either vector is unit vector, dot product equals scalar projection.*\n",
    "\n",
    "3. **Variance of an Observation Vector If Its Mean Is Zero:**\n",
    "   $$\n",
    "   \\text{Var}(\\mathbf{x}) = \\frac{1}{n - 1} \\|\\mathbf{x}\\|^2 = \\frac{1}{n - 1} \\sum_{i=1}^n x_i^2\n",
    "   $$ \n",
    "   *Variance is the squared norm if the mean is zero.*\n",
    "\n",
    "---\n",
    "\n",
    "### **PCA Derivation**\n",
    "\n",
    "1. **Data Matrix:**\n",
    "   $$\n",
    "   X \\in \\mathbb{R}^{n \\times d}\n",
    "   $$ \n",
    "   *Matrix with $n$ data points and $d$ features.*\n",
    "\n",
    "2. **Mean-Centering:**\n",
    "   $$\n",
    "   \\mathbf{\\mu} = \\frac{1}{n} \\sum_{i=1}^n \\mathbf{x}_i\n",
    "   $$\n",
    "   $$\n",
    "   \\tilde{X} = X - \\mathbf{1}_n \\mathbf{\\mu}^T\n",
    "   $$ \n",
    "   *Center data by subtracting the mean.*\n",
    "\n",
    "3. **Covariance Matrix:**\n",
    "   $$\n",
    "   S = \\frac{1}{n - 1} \\tilde{X}^T \\tilde{X}\n",
    "   $$ \n",
    "   *Covariance matrix captures relationships between features.*\n",
    "\n",
    "4. **Projection onto Unit Vector $ \\mathbf{w} $:**\n",
    "   $$\n",
    "   \\mathbf{z} = \\tilde{X} \\mathbf{w}\n",
    "   $$\n",
    "   Variance of projection:\n",
    "   $$\n",
    "   \\text{Var}(\\tilde{X} \\mathbf{w}) = \\frac{1}{n - 1} (\\tilde{X} \\mathbf{w})^T (\\tilde{X} \\mathbf{w}) = \\mathbf{w}^T S \\mathbf{w}\n",
    "   $$ \n",
    "   *Projection each row vector along $ \\mathbf{w} $ .*\n",
    "\n",
    "5. **Optimization Problem (Maximize Variance):**\n",
    "   $$\n",
    "   \\max_{\\mathbf{w}} \\mathbf{w}^T S \\mathbf{w}, \\quad \\text{subject to } \\mathbf{w}^T \\mathbf{w} = 1\n",
    "   $$ \n",
    "   *Find the direction $ \\mathbf{w} $ that maximizes variance.*\n",
    "\n",
    "6. **Lagrangian and Gradient Condition:**\n",
    "   $$\n",
    "   \\mathcal{L}(\\mathbf{w}, \\lambda) = \\mathbf{w}^T S \\mathbf{w} - \\lambda (\\mathbf{w}^T \\mathbf{w} - 1)\n",
    "   $$ \n",
    "   Gradient condition:\n",
    "   $$\n",
    "   \\nabla_{\\mathbf{w}} \\mathcal{L} = 2S \\mathbf{w} - 2\\lambda \\mathbf{w} = 0\n",
    "   $$ \n",
    "   $$\n",
    "   S \\mathbf{w} = \\lambda \\mathbf{w}\n",
    "   $$ \n",
    "   *Leads to the eigenvalue problem.*\n",
    "\n",
    "7. **Principal Components:**\n",
    "   - Eigenvalue problem:\n",
    "     $$\n",
    "     S \\mathbf{w} = \\lambda \\mathbf{w}\n",
    "     $$ \n",
    "   - $ \\mathbf{w} $ is the eigenvector corresponding to the largest eigenvalue $ \\lambda_1 $.\n",
    "   *The first principal component (explaining the largest variance) is the eigenvector with the largest eigenvalue.*\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5e1c9be4-ee5c-4361-8574-bcc783d1431a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.decomposition import PCA as sklearn_PCA\n",
    "\n",
    "np.random.seed(20250101)\n",
    "plt.style.use('dark_background')\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "55ddbc00-9224-48a3-929a-0bd113fbf0d0",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalues from sklearn:\n",
      " [1.49862507 0.50137493]\n",
      "Eigenvalues from manual method:\n",
      " [1.49862507 0.50137493]\n"
     ]
    }
   ],
   "source": [
    "# Generate the data matrix\n",
    "data_matrix = np.random.multivariate_normal(\n",
    "    mean=[3, 2], cov=[[8, 9], [9, 30]], size=100)\n",
    "\n",
    "# Standardize data matrix (manual standardization)\n",
    "data_matrix_standardized = (\n",
    "    (data_matrix - data_matrix.mean(axis=0)) /\n",
    "    data_matrix.std(axis=0, ddof=1)\n",
    ")\n",
    "\n",
    "# Perform PCA using sklearn\n",
    "sklearn_pca = sklearn_PCA()\n",
    "sklearn_pca.fit(data_matrix_standardized)\n",
    "\n",
    "# Get eigenvalues and eigenvectors from sklearn PCA\n",
    "sklearn_eigenvals = sklearn_pca.explained_variance_\n",
    "sklearn_eigenvecs = sklearn_pca.components_.T\n",
    "\n",
    "# Calculate the covariance matrix manually\n",
    "covariance_matrix = (data_matrix_standardized.T @ data_matrix_standardized) / (data_matrix.shape[0] - 1)\n",
    "\n",
    "\n",
    "# Calculate eigenvalues and eigenvectors from manual covariance matrix\n",
    "eigenvalues, eigenvectors = np.linalg.eig(\n",
    "    covariance_matrix\n",
    ")\n",
    "\n",
    "# Sort eigenvalues and eigenvectors in descending order to match\n",
    "sorted_indices_sklearn = np.argsort(sklearn_eigenvals)[::-1]\n",
    "sorted_indices_manual = np.argsort(eigenvalues)[::-1]\n",
    "\n",
    "# Re-order eigenvectors accordingly\n",
    "sklearn_eigenvals_sorted = sklearn_eigenvals[sorted_indices_sklearn]\n",
    "sklearn_eigenvecs_sorted = sklearn_eigenvecs[:, sorted_indices_sklearn]\n",
    "eigenvalues_sorted = eigenvalues[sorted_indices_manual]\n",
    "eigenvectors_sorted = eigenvectors[:, sorted_indices_manual]\n",
    "\n",
    "# Display results\n",
    "print(\"Eigenvalues from sklearn:\\n\", sklearn_eigenvals_sorted)\n",
    "print(\"Eigenvalues from manual method:\\n\", eigenvalues_sorted)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "394e972d-2269-4635-88fc-ab64a7938539",
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 2400x2400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualization: Eigenvectors (PCs) in 2D space (Scatter plot with eigenvectors)\n",
    "plt.figure(figsize=(8, 8), dpi=300)\n",
    "\n",
    "# Plot the data points\n",
    "plt.scatter(data_matrix_standardized[:, 0], data_matrix_standardized[:, 1], alpha=0.7, \n",
    "            color='white', label=\"Data\", marker='x')\n",
    "\n",
    "# Plot the eigenvectors (from sklearn, for example) as arrows\n",
    "plt.quiver(0, 0, sklearn_eigenvecs_sorted[0, :][0],sklearn_eigenvecs_sorted[0, :][1], \n",
    "           color='cyan', label=\"Principal Component-1\", scale=1/sklearn_eigenvals_sorted[0], scale_units='xy')\n",
    "plt.quiver(0, 0, sklearn_eigenvecs_sorted[1, :][0], sklearn_eigenvecs_sorted[1, :][1], \n",
    "           color='magenta', label=\"Principal Component-2\", scale=1/sklearn_eigenvals_sorted[1], scale_units='xy')\n",
    "plt.xlim([-3, 3])\n",
    "plt.ylim([-3, 3])\n",
    "plt.axhline(0, color='black', linewidth=0.5)\n",
    "plt.axvline(0, color='black', linewidth=0.5)\n",
    "plt.title('Principal Component Analysis')\n",
    "plt.xlabel('Feature-1')\n",
    "plt.ylabel('Feature-2')\n",
    "plt.legend()\n",
    "plt.axis('equal')\n",
    "plt.grid(True, alpha=0.2, linestyle='--')\n",
    "plt.savefig('pca.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2d477b43-11bc-4024-9fa3-c0185c8cf5c2",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e9416324-a978-49f9-92a4-a3aa6aa979d5",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "genai",
   "language": "python",
   "name": "genai"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}