1.4_Principal_Component_Analysis.ipynb

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  "metadata": {
    "colab": {
      "name": "1.4_Principal_Component_Analysis.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyMnolDtNIHBLYGtSL4BTSWp",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/madonnaojorin/MAT494/blob/main/1.4_Principal_Component_Analysis.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "loJwQBdCU3Kk"
      },
      "source": [
        "##1.4.1 Singular Value Decomposition"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T1KFLY7qU58k"
      },
      "source": [
        "####Theorem 1.4.1 <br>\n",
        "If an $m\\times n$ matrix A has $r$ nonzero singular values, $\\sigma_1,\\cdots,\\sigma_r \\geq 0$ with $\\sigma_{r+1}=\\cdots=\\sigma_n=0$, then the dimension of $\\text{col}(A) = r$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "910s7rW1U8f-"
      },
      "source": [
        "####Theorem 1.4.2 (The Singular Value Decomposition) <br>\n",
        "Let A be an $m\\times n$ matrix with the dimension of $\\text{col}(A) = r$. Then there exists an $m\\times n$ matrix $\\Sigma$, where\n",
        "the diagonal entries in $D$ are the first $r$ singular values of $A$ $\\sigma_1 \\geq \\sigma_2 \\geq \\cdots\\geq \\sigma_r\\geq 0$, and there exist an $m\\times m$ orthogonal matrix $U$ and an $n\\times n$ orthogonal\n",
        "matrix $V$ such that \n",
        "$$A = U \\Sigma V^T.$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6yHyYjt1Hzdu"
      },
      "source": [
        "import numpy as np\n",
        "from sklearn.datasets import load_digits\n",
        "from matplotlib import pyplot as plt\n",
        "from sklearn.decomposition import TruncatedSVD\n",
        "float_formatter = lambda x: \"%.2f\" % x\n",
        "np.set_printoptions(formatter={'float_kind':float_formatter})\n",
        "from sklearn.ensemble import RandomForestClassifier"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MN8ZYvytJ6pq",
        "outputId": "2bedecbe-5441-40c3-c2a8-942176b2f695"
      },
      "source": [
        "X, y = load_digits(return_X_y=True)\n",
        "print(X.shape)\n",
        "print(y)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(1797, 64)\n",
            "[0 1 2 ... 8 9 8]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 292
        },
        "id": "47ro-jh2KIwR",
        "outputId": "aeda1746-f0b2-4d67-a62a-c9c9e5716361"
      },
      "source": [
        "image = X[0]\n",
        "image = image.reshape((8, 8))\n",
        "plt.matshow(image, cmap = 'gray')"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7fabe4e1cf50>"
            ]
          },
          "metadata": {},
          "execution_count": 7
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "q0Lu2LJ7KIkS",
        "outputId": "1f807a42-5833-4d54-be71-43e810aa0752"
      },
      "source": [
        "#Singular Value Decomposition \n",
        "U, s, V = np.linalg.svd(image)\n",
        "S = np.zeros((image.shape[0], image.shape[1]))\n",
        "S[:image.shape[0], :image.shape[0]] = np.diag(s)\n",
        "n_component = 2\n",
        "Sigma = S[:, :n_component]\n",
        "VT = VT[:n_component, :]\n",
        "A = U.dot(S.dot(V))\n",
        "print(A)"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.00 0.00 5.00 13.00 9.00 1.00 0.00 0.00]\n",
            " [0.00 0.00 13.00 15.00 10.00 15.00 5.00 0.00]\n",
            " [0.00 3.00 15.00 2.00 -0.00 11.00 8.00 0.00]\n",
            " [0.00 4.00 12.00 -0.00 -0.00 8.00 8.00 0.00]\n",
            " [0.00 5.00 8.00 -0.00 -0.00 9.00 8.00 0.00]\n",
            " [0.00 4.00 11.00 -0.00 1.00 12.00 7.00 0.00]\n",
            " [0.00 2.00 14.00 5.00 10.00 12.00 0.00 0.00]\n",
            " [0.00 -0.00 6.00 13.00 10.00 -0.00 -0.00 0.00]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 292
        },
        "id": "8C73V53nKkz8",
        "outputId": "6bd6b56f-684b-4be8-b448-7e25442fc996"
      },
      "source": [
        "plt.matshow(A, cmap = 'gray')"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7fabe4d651d0>"
            ]
          },
          "metadata": {},
          "execution_count": 19
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7M9GtQr9VAEO"
      },
      "source": [
        "##1.4.2 Low-Rank Matrix Approximations\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tOmY8nioVFzL"
      },
      "source": [
        "####Definition 1.4.3 (Induced Norm) <br>\n",
        "The 2-norm of a matrix $A \\in \\mathbb{R}^{n\\times m}$ is\n",
        "$$||A||^2 = \\max_{0\\neq \\textbf{x}\\in\\mathbb{R}^m}\\frac{||A\\textbf{x||}}{||\\textbf{x}||}=\\max_{\\textbf{x}\\neq 0,||\\textbf{x}||=1}||A\\textbf{x}|| =\\max_{\\textbf{x}\\neq 0,||\\textbf{x}||=1}\\textbf{x}^TA^TA\\textbf{x}$$\n",
        "Let $A \\in \\mathbb{R}^{n\\times m}$ be a matrix with SVD\n",
        "$$A =\\sum_{j=1}^r\\sigma_j\\textbf{u}_j\\textbf{v}_j^T.$$\n",
        "\n",
        "For $k < r$, truncate the sum at the k-th term\n",
        "$$A_k =\\sum_{j=1}^k\\sigma_j\\textbf{u}_j\\textbf{v}_j^T.$$\n",
        "The rank of $A_k$ is exactly $k$. Indeed, by construction,\n",
        "1. the vectors ${\\textbf{u}_j: j = 1,\\cdots, k}$ are orthonormal, and\n",
        "2. since $\\sigma_j > 0$ for $j = 1,\\cdots, k$ and the vectors $\\{\\textbf{v}_j: j = 1,\\cdots, k\\}$ are orthonormal,$\\{\\textbf{u}_j: j = 1,\\cdots, k\\}$ spans the column space of $A_k$.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mFoGpnl4XUb3"
      },
      "source": [
        "####Lemma 1.4.4 (Matrix Norms and Singular Values)<br>\n",
        "Let $A \\in\\mathbb{R}^{n\\times m}$ be a matrix with SVD\n",
        "$$A =\\sum_{j=1}^r\\sigma_j\\textbf{u}_j\\textbf{v}_j^T.$$\n",
        "where recall that $\\sigma_1\\geq\\sigma_2\\geq\\cdots\\sigma_r>0$ and let $A_k$ be the truncation defined\n",
        "above. Then\n",
        "$$||A−A_k||^2_2 = σ^2_{k+1}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OXBWMpanX6Vy"
      },
      "source": [
        "####Theorem 1.4.5 (Eckart-Young-Mirsky theorem) (Low-Rank Approximation in the Induced Norm):<br>\n",
        "Let $A \\in \\mathbb{R}^{n\\times m}$ be a matrix with SVD\n",
        "$$A =\\sum_{j=1}^r\\sigma_j\\textbf{u}_j\\textbf{v}_j^T.$$\n",
        "and let $A_k$ be the truncation defined above with $k < r$. For any matrix $B \\in\\mathbb{R}^{n\\times m}$\n",
        "of rank at most $k$,\n",
        "$$||A−A_k||_2 \\leq ||A−B||_2.$$ "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tqVmfArWX_oD"
      },
      "source": [
        "##1.4.3 Principal Component Analysis\n",
        "###1.4.3.1 Covariance Matrix\n",
        "To prepare for principal component analysis, let $[\\textbf{X}_1\\cdots \\textbf{X}_N]$ be a $p\\times N$ matrix\n",
        "of observation, such as describe above. The sample mean $M$ of the observation vectors $[\\textbf{X}_1\\cdots \\textbf{X}_n]$ is given by\n",
        "$$M=\\frac{1}{N}(\\textbf{X}_1\\cdots \\textbf{X}_N)$$\n",
        "For $k = 1, \\cdots,N$, let\n",
        "$$\\hat{\\textbf{X}_k} = \\textbf{X}_k-\\textbf{M}.$$\n",
        "The columns of the $p\\times N$ matrix\n",
        "$$B =[\\hat{\\textbf{X}_1},\\hat{\\textbf{X}_1},\\cdots,\\hat{\\textbf{X}_N}]$$\n",
        "have a zero sample mean, and $B$ is said to be in mean-deviation form.\n",
        "The (sample) covariance matrix is the $p\\times p$ matrix $S$ defined by\n",
        "$$S =\\frac{1}{N-1}BB^T$$\n",
        "Since any matrix of the form $BB^T$ is positive semidefinite, so is $S$.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "86LNqwtwYEU0"
      },
      "source": [
        "###1.4.3.2 Principal Component Analysis\n",
        "Now assume that the columns of the p×N data matrix\n",
        "$X = [\\textbf{X}_1\\cdots \\textbf{X}_N]$\n",
        "is already in mean-deviation from. The goal of principal component analysis (PCA) is to find $k, (k \\leq p)$ orthonormal vectors $\\textbf{v}_1,\\cdots,\\textbf{v}_k$, (top $k$ principal components) that maximize the objective function\n",
        "$$\\frac{1}{N}\\sum_{i=1}^N\\sum_{j=1}^k\\langle \\textbf{X}_i\\cdot \\textbf{v}_j\\rangle^2$$\n",
        "$\\langle \\textbf{X}_i\\cdot \\textbf{v}_j\\rangle$ is the length of projection of $\\textbf{X}_i$ on $\\textbf{v}_j$.\n",
        "On the other hand, for each $j$, it is easy to see that\n",
        "$$\\textbf{v}_j^TXX^T \\textbf{v}_j = (X^T \\textbf{v}_j)^T (X^T \\textbf{v}_j) = \\sum_{i=1}^N\\langle\\textbf{X}_i \\cdot\\textbf{v}_j\\rangle^2$$\n",
        "where $XX^T$ is a $p \\times p$ matrix. As a result, for each $j \\leq k$, the variance-maximization problem can be rephrased as \n",
        "$$argmax_{\\textbf{v}:||\\textbf{v}||=1}\\textbf{v}_j^TXX^T \\textbf{v}_j$$ \n",
        "Assume that\n",
        "$$XX^T =Vdiag(\\lambda_1,\\cdots,\\lambda_p)V^T, \\text{ or } V^TXX^TV = (\\lambda_1,\\cdots,\\lambda_p)$$.\n",
        "In view of Theorem 1.4.5, we conclude that the optimal choice of the first $k$ eigenvectors of $XX^T$ corresponding to the first $k$ largest eigenvalues, which are also the first $k$ columns of $V =[\\textbf{v}_1,\\cdots,\\textbf{v}_p]$ of the covariance matrix $XX^T$, which are called the principal components of the data (in the matrix’ of observations).\n",
        "The first principal component is the eigenvector corresponding to the largest eigenvalue of $XX^T$ , the second principal component is the eigenvector\n",
        "corresponding to the second largest eigenvalue, and so on.\n",
        "The orthogonal $p\\times p$ matrix $V = [\\textbf{v}_1,\\cdots,\\textbf{v}_p]$ that determines a change of variable, $\\textbf{x} =V\\textbf{y}$, or \n",
        "$$\\begin{pmatrix}\n",
        "x_1\\\\\n",
        "x_2\\\\\n",
        "\\vdots\\\\\n",
        "x_p\n",
        "\\end{pmatrix}=\\begin{pmatrix}\n",
        "\\textbf{v}_1 \\textbf{v}_1 \\cdots\\textbf{v}_p\n",
        "\\end{pmatrix}\n",
        "\\begin{pmatrix}\n",
        "y_1\\\\\n",
        "y_2\\\\\n",
        "\\vdots\\\\\n",
        "y_p\n",
        "\\end{pmatrix}$$\\\\\n",
        "with the property that the new variables $y_1,\\cdots,y_p$ are uncorrelated and are arranged in order of decreasing variance. Indeed, we have\n",
        "$$\\textbf{x}^TXX^T \\textbf{x} = \\textbf{y}^TV^TXX^TV\\textbf{y} = \\textbf{y}^T \\text{diag}(\\lambda_1, \\cdots,\\lambda_p)\\textbf{y} =\\sum_1^p\\lambda_iy_i^2.$$\n",
        "The orthogonal change of variable $\\textbf{x} = V\\textbf{y}$ that each observation vector \\textbf{x} receives a ”new name” $\\textbf{y}$, such that $\\textbf{x} = V\\textbf{y}$. Notice that $\\textbf{y} = V^{-1}\\textbf{x} = V^T \\textbf{x}$.\n",
        "Let $v_{1i},\\cdots,v_{pi}$ be the entries in $v_i$. Since $v^T_i$ the ith row of $V^T$, the equation $\\textbf{y} =V^T \\textbf{x}$ shows that \n",
        "$$y_i = \\textbf{v}^T_i\\textbf{x} = v_{1i}x_1+v_{2i}x_2+\\cdots+v_{pi}x_p$$\n",
        "Thus $y_i$ is a linear combination of the original variables $x_1,\\cdots,x_p$, using the\n",
        "entries the eigenvector $\\textbf{v}_i$ as weights, which are called loadings."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qMObhZ2fP9kl"
      },
      "source": [
        "%matplotlib inline\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns; sns.set()"
      ],
      "execution_count": 25,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        },
        "id": "XL80ErNcP-3_",
        "outputId": "44fd1d4d-5050-4b97-b385-438db4fda033"
      },
      "source": [
        "rng = np.random.RandomState(1)\n",
        "X = np.dot(rng.rand(2, 2), rng.randn(2, 200)).T\n",
        "plt.scatter(X[:, 0], X[:, 1])\n",
        "plt.axis('equal');"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HlKO93hIQC-A",
        "outputId": "0a17ade6-6fc7-4581-f054-238cf11103d7"
      },
      "source": [
        "from sklearn.decomposition import PCA\n",
        "pca = PCA(n_components=2)\n",
        "pca.fit(X)\n",
        "print(pca.components_)\n",
        "print(pca.explained_variance_)"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[-0.94 -0.33]\n",
            " [-0.33 0.94]]\n",
            "[0.76 0.02]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        },
        "id": "uzF9zxyPQC4f",
        "outputId": "130896d6-2792-46a9-f34c-ded0bc2e71d2"
      },
      "source": [
        "def draw_vector(v0, v1, ax=None):\n",
        "    ax = ax or plt.gca()\n",
        "    arrowprops=dict(arrowstyle='->',\n",
        "                    linewidth=2,\n",
        "                    shrinkA=0, shrinkB=0)\n",
        "    ax.annotate('', v1, v0, arrowprops=arrowprops)\n",
        "\n",
        "# plot data\n",
        "plt.scatter(X[:, 0], X[:, 1], alpha=0.2)\n",
        "for length, vector in zip(pca.explained_variance_, pca.components_):\n",
        "    v = vector * 3 * np.sqrt(length)\n",
        "    draw_vector(pca.mean_, pca.mean_ + v)\n",
        "plt.axis('equal');"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ixhn2ToeQCv0",
        "outputId": "0dbbb680-1726-4178-9c28-3d4fad3776b2"
      },
      "source": [
        "# PCA as a dimensionality reduction transform\n",
        "pca = PCA(n_components=1)\n",
        "pca.fit(X)\n",
        "X_pca = pca.transform(X)\n",
        "print(\"original shape:   \", X.shape)\n",
        "print(\"transformed shape:\", X_pca.shape)"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "original shape:    (200, 2)\n",
            "transformed shape: (200, 1)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        },
        "id": "wx0ni8E4QCdD",
        "outputId": "882e9731-3631-4de1-cf74-8bb0a45b0a4f"
      },
      "source": [
        "X_new = pca.inverse_transform(X_pca)\n",
        "plt.scatter(X[:, 0], X[:, 1], alpha=0.2)\n",
        "plt.scatter(X_new[:, 0], X_new[:, 1], alpha=0.8)\n",
        "plt.axis('equal');"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ikFhDv3oQVbC",
        "outputId": "18af9fa9-d07a-481f-db1e-99a68fe26886"
      },
      "source": [
        "from sklearn.datasets import load_digits\n",
        "digits = load_digits()\n",
        "digits.data.shape"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1797, 64)"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gbed6iToQVX6",
        "outputId": "0a7622fb-6013-4985-c590-fb7b899f9caa"
      },
      "source": [
        "pca = PCA(2)  # project from 64 to 2 dimensions\n",
        "projected = pca.fit_transform(digits.data)\n",
        "print(digits.data.shape)\n",
        "print(projected.shape)"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(1797, 64)\n",
            "(1797, 2)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 289
        },
        "id": "oX0G9aLFQVU4",
        "outputId": "d71dc57c-9217-4988-f96d-42fe9e0953dc"
      },
      "source": [
        "plt.scatter(projected[:, 0], projected[:, 1],\n",
        "            c=digits.target, edgecolor='none', alpha=0.5)#,\n",
        "#            cmap=plt.cm.get_cmap('spectral', 10))\n",
        "plt.xlabel('component 1')\n",
        "plt.ylabel('component 2')\n",
        "plt.colorbar();"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tDMZnVtHYSmv"
      },
      "source": [
        "###1.4.3.3 Total Variance\n",
        "Given the columns of the p×N data matrix and assume it is already in mean-deviation from\n",
        "$$X=[\\textbf{X}_1,\\textbf{X}_2,\\cdots, \\textbf{X}_N]$$\n",
        "and let covariance matrix $S$\n",
        "$$S =\\frac{1}{N-1}XX^T.$$\n",
        "The entries in $S=[S_{ij}]$, for $j =1,\\cdots, p$, the diagonal entry $s_{jj}$ in $S$ is called the variance of $x_j$, which is the first $j$-th row of $X$. The variance of $x_j$ measures the spread of the values of $x_j$. The total variance of the data is the sum of the variances on the diagonal of $S$. In general, the sum of the diagonal entries\n",
        "of a square matrix $S$ is called the trace of the matrix, written $tr(S)$. Thus \n",
        "$$\\text{Total Variance} = tr (S)$$\n",
        "Note that if\n",
        "$$XX^T =V\\text{diag}(\\lambda_1,\\cdots,\\lambda_p)V^T , \\text{ or }V^TXX^TV = \\text{diag}(\\lambda_1,\\cdots,\\lambda_p)$$.\n",
        "then\n",
        "$$tr(S) =\n",
        "\\frac{1}{N-1}\\sum_1^p\\lambda_j$$\n",
        "because $tr(VSV^T)=tr(S)$. Thus the fraction of the variances of the first $k$ term truncation is\n",
        "$$\\frac{\\sum_1^k\\lambda_j}{\\sum_1^p\\lambda_j}.$$"
      ]
    }
  ]
}