07_kernel_1d_classification.ipynb

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  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "#### `Recap` linear model"
      ],
      "metadata": {
        "id": "-sZOISX0EI8i"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "We know how to describe a `linear model` to explain the data we observe\n",
        "\n",
        "$$y=ax+b$$\n",
        "\n",
        "where $a$ and $b$ are model `parameters` that we want to find\n",
        "\n",
        "We also show that by plugging $y$ into\n",
        "\n",
        "$$h(y)=\\frac{1}{1+e^{-y}}$$\n",
        "\n",
        "We can use the linear model to do `classification` problems"
      ],
      "metadata": {
        "id": "IohsP4E4B5Zq"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "While we have not touched this point specifically, the fact that $h(y)$ (recall that its `shape` is a not a straight line but a $s$-shaped curve) allows us to predict class of a point in classification problem is demonstrating a way to enhancing the linear model to handle `nonlinearity`\n",
        "\n",
        "In this case, we pass the output of $y=ax+b$ through a `nonlinear function` that is $h(y)$"
      ],
      "metadata": {
        "id": "YdfiLBbE-fIs"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Handle `nonlinearity` by projection into `feature space`"
      ],
      "metadata": {
        "id": "K6eN_B2n9wgw"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "There are also other ways we can handle nonlinearity\n",
        "\n",
        "One idea is to `project` input $x$ into some `feature space` $\\phi(x)$, for example\n",
        "\n",
        "$$\\mathbf{\\phi}(x)=\\begin{bmatrix} x^2 \\\\ x \\\\ 1 \\end{bmatrix}$$\n",
        "\n",
        "This translates the linear model $y=ax+b$ to\n",
        "\n",
        "$$y=\\mathbf{\\phi}(x)^T\\mathbf{\\theta}$$\n",
        "\n",
        "where $\\mathbf{\\theta}$ is a vector containing all parameters"
      ],
      "metadata": {
        "id": "gbNvMnAbCR9K"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### What is a `feature`?"
      ],
      "metadata": {
        "id": "of_5SoGrB9Cb"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The term `feature` generally describes all candidate characteristics of the input that `we believe` is associated to the output we observe\n",
        "\n",
        "For example, by setting $\\phi(x)$ as above, what we are saying is that `we believe the output we observe in data is associated to the input in three potential ways`\n",
        "\n",
        "* constant (that is, regardless of input, the output is the same)\n",
        "* linear (indicated by $x$)\n",
        "* quadratic (indicated by $x^2$)\n",
        "\n",
        "Therefore, what $y=\\phi(x)^T\\theta$ does is to find a `linear combination` of three functions that results in $y$\n",
        "\n",
        "$$\\begin{align*}\n",
        "y&=x^2\\\\\n",
        "y&=x\\\\\n",
        "y&=1\n",
        "\\end{align*}$$"
      ],
      "metadata": {
        "id": "lhX4VcR0B_cL"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### `Local` vs `global` behavior"
      ],
      "metadata": {
        "id": "ftxqoPlTCPZd"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "However, the problem with such setup is that each of the three functions $x^2, x, 1$ are `global` in nature, regardless of the value of input $x$\n",
        "\n",
        "So, our assumption here is that the behavior of the nonlinear function we want to model, no matter what $x$ is, is `always the same` in terms of combination of $x^2, x, 1$\n",
        "\n",
        "This global nature can cause problems when handling with nonlinear functions that have `local patterns`, for example, a function's behavior around $x=-5$ may not be the same as around $x=5$......\n",
        "\n",
        "So what do we do?"
      ],
      "metadata": {
        "id": "2gj4FlygDpqh"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### An `infeasible` way to model local behavior"
      ],
      "metadata": {
        "id": "qBF_CkyOEMKA"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Consider a function $f(x)$ of any `arbitrary form` running from $-\\infty$ to $+\\infty$.\n",
        "\n",
        "`Ideally`, the model that can `perfectly fit` the local behavior of the function should look something like this\n",
        "\n",
        "$$f(x)=...+f(-2)\\cdot\\phi(x, -2)+...+f(-1)\\cdot\\phi(x, -1)+...+f(0)\\cdot\\phi(x, 0)+...+f(1)\\cdot\\phi(x, 1)+...+f(2)\\cdot\\phi(x, 2)+...$$\n",
        "\n",
        "This function containing an `infinite` number of terms, each corresponding to a real number (only some integer terms are shown here)"
      ],
      "metadata": {
        "id": "xIluWv0TERJM"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Each `term` consists of two parts\n",
        "\n",
        "* a function $\\phi(x, x')$ to determine the `exact matching` between the input $x$ and the point $x'$ corresponding to the term (we call $x'$ the `anchor point` of this term for clarity). What we want this function to do is to output `1` if $x=x'$, and `0` otherwise. As an example\n",
        "\n",
        "$$\\begin{align*}\n",
        "\\phi(x, -2) = \\left\\{\n",
        "\\begin{array}{cl}\n",
        "0 & x\\neq-2 \\\\\n",
        "1 & x=-2\n",
        "\\end{array}\n",
        "\\right.\n",
        "\\end{align*}\n",
        "$$\n",
        "\n",
        "* and a `coefficient` corresponding to `function value` at this anchor point $f(-2)$"
      ],
      "metadata": {
        "id": "qY9W6HSSEtck"
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    },
    {
      "cell_type": "markdown",
      "source": [
        "This way, no matter what $x$ is used as input to $f(x)$ (assume $x=x'$ is the input), only the term corresponding to $x'$ will be activated, and the rest will be zero\n",
        "\n",
        "$$f(x')=f(x)\\cdot \\phi(x, x')|_{x=x'}$$\n",
        "\n",
        "This is exactly the `local` behavior that we want to model, as terms corresponding to locations that are not $x'$ are all gone"
      ],
      "metadata": {
        "id": "7UOOc6FjG0YQ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### From `exact matching` to `correlation`"
      ],
      "metadata": {
        "id": "v48utLh0HWA9"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "So, how is this useful for `our purpose`?\n",
        "\n",
        "In our case, we will `not` have infinite number of anchor points to work with, we will only have a few data points from which we try to build the function\n",
        "\n",
        "Assume we only know $f(x)$ at $x=-2,-1,-0,1,2$\n",
        "\n",
        "Then, the model becomes\n",
        "\n",
        "$$f(x)= f(-2)\\cdot\\phi(x, -2)+f(-1)\\cdot\\phi(x, -1)+f(0)\\cdot\\phi(x, 0)+f(1)\\cdot\\phi(x, 1)+f(2)\\cdot\\phi(x, 2)$$\n",
        "\n",
        "Now, the problem becomes tricky: if the input $x$ is not precisely $-2, -1, 0, 1$, or $2$, then, $f(x)$ becomes zero, as no term is remaining...\n",
        "\n",
        "So, how to solve the issue?"
      ],
      "metadata": {
        "id": "q636KvOCGzMV"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "We solve the issue by `relaxing` the criteria for $\\phi(x, x')$\n",
        "\n",
        "Instead of making $\\phi(x, x')$ `go to zero` as soon as $x\\neq x'$\n",
        "* we want the behavior of the function at $x$ to be `similar` to its behavior at $x'$, if $x$ is `not too far away` from $x'$\n",
        "* we want the behavior of the function at $x$ to be `less and less similar` to its behavior at $x'$, if $x$ is `moving away from` $x'$\n",
        "\n",
        "This way, we don't need to worry about $x\\neq x'$ as we are no longer looking for `exact matching`, but rather `correlation` between $x$ and $x'$"
      ],
      "metadata": {
        "id": "2JtGqnqKH6O_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Kernel and `radial basis function` (RBF)"
      ],
      "metadata": {
        "id": "HNwtcgV5ItR2"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "So, how to formulate $\\phi(x, x')$ to achieve the correlation behavior we want for $f(x)$ when $x\\neq x'$?\n",
        "\n",
        "One common formulation is through `radial basis function`\n",
        "\n",
        "(as it measures `correlation or similarity` between two points, it is commonly refered to as a `kernel` function)\n",
        "\n",
        "$$\\phi(x, x')=e^{-\\frac{|x-x'|^2}{2\\sigma^2}}$$\n",
        "\n",
        "This is a `bell curve` centered around $x'$, and `decays` as $x$ pulls away from $x'$, with a decay rate controled by parameter $\\sigma$.\n",
        "\n",
        "It is easy to see that the behavior of RBF kernel satisfies the 2 requirements we want for $\\phi(x, x')$"
      ],
      "metadata": {
        "id": "tXaEF00ZLGuY"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### One more change"
      ],
      "metadata": {
        "id": "ur2qwIWOJ4Ia"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Due the usage of kernel function that measures similarity rather than finds exact matching, we can no longer use function value $f(x')$ as the coefficient for the term $\\phi(x', x')$, as the terms from $x\\neq x'$ will start to `influence` $f(x')$, no matter how small the influence is\n",
        "\n",
        "As a result, we will treat coefficents as `unknown parameters` to quantify such influence, which will be determined during optimization"
      ],
      "metadata": {
        "id": "j_ZB0HUaLq_M"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Putting everything together"
      ],
      "metadata": {
        "id": "dPVbuKzoK6A_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now, we can have the formulation of $f(x)$ with five known data points at $-2, -1, 0, 1, 2$\n",
        "\n",
        "$$\\boxed{f(x)= \\theta_1\\cdot\\phi(x, -2)+\\theta_2\\cdot\\phi(x, -1)+\\theta_3\\cdot\\phi(x, 0)+\\theta_4\\cdot\\phi(x, 1)+\\theta_5\\cdot\\phi(x, 2)}$$\n",
        "\n",
        "This is still in `linear form`, and can be solved using the gradient descent approach we learned before"
      ],
      "metadata": {
        "id": "FZs14_0tK9Fs"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Visualization"
      ],
      "metadata": {
        "id": "Js3wDiUdNnyR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "plt.style.use('dark_background')\n",
        "np.set_printoptions(formatter={'float': '{: 0.4f}'.format})"
      ],
      "metadata": {
        "id": "_5dS5O47Ny_Y"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x_values = np.linspace(-2.5, 2.5, 400)\n",
        "\n",
        "def sigmoid_fn(x):\n",
        "    return (1 / (1 + np.exp(-2 * x)))*3\n",
        "\n",
        "def rbf(x, x_prime, sigma):\n",
        "    return np.exp(-(x - x_prime)**2 / (2 * sigma**2))\n",
        "\n",
        "fig_1, ax_1 = plt.subplots(1, 2, figsize=(16, 5))\n",
        "\n",
        "ax_1[0].plot(x_values, sigmoid_fn(x_values), color='c', label='f(x)')\n",
        "\n",
        "for i in [-2, -1, 0, 1, 2]:\n",
        "    if i==1:\n",
        "        ax_1[0].plot([i,i], [0,1], 'orange', linewidth=2, zorder=0)\n",
        "        ax_1[0].arrow(i, 1, 0.000, 0.001, head_width=0.1, head_length=0.2, color='orange')\n",
        "    else:\n",
        "        ax_1[0].plot([i,i], [0,1], 'w', linewidth=2, zorder=0)\n",
        "        ax_1[0].arrow(i, 1, 0.000, 0.001, head_width=0.1, head_length=0.2, color='w')\n",
        "\n",
        "ax_1[0].text(1.1, 1.3, r\"$\\phi(x, 1)=\\delta_{x1}$\", fontsize=14, c='orange')\n",
        "ax_1[0].plot([1,1], [1.1,sigmoid_fn(1)], 'm', linewidth=2, zorder=0)\n",
        "ax_1[0].scatter(1, sigmoid_fn(1), color='m', s=50, zorder=5)\n",
        "ax_1[0].text(1.1, 2.5, r\"$f(1)=f(1)\\phi(1,1)$\", fontsize=14, c='m')\n",
        "ax_1[0].set_xlabel('x')\n",
        "ax_1[0].legend()\n",
        "ax_1[0].set_title('Model f(x) with exact matching')\n",
        "\n",
        "for i in [-2, -1, 0, 1, 2]:\n",
        "    if i==1:\n",
        "        ax_1[1].plot(x_values, rbf(x_values, i, 0.3), color='orange')\n",
        "    else:\n",
        "        ax_1[1].plot(x_values, rbf(x_values, i, 0.3), color='w')\n",
        "\n",
        "ax_1[1].text(1, 1.2, r\"$\\phi(x, 1)=e^{-\\frac{|x-1|^2}{2\\sigma^2}}$\", fontsize=14, c='orange')\n",
        "ax_1[1].scatter(1, sigmoid_fn(1), color='m', s=50, zorder=5)\n",
        "ax_1[1].text(0.9, 2.3, r\"$f(1)=\\sum_{i=-2}^2 \\theta_i \\phi(1, i)$\", fontsize=14, c='m')\n",
        "\n",
        "ax_1[1].plot(x_values, sigmoid_fn(x_values), color='c', label='f(x)')\n",
        "ax_1[1].set_xlabel('x')\n",
        "ax_1[1].legend()\n",
        "ax_1[1].set_title('Model f(x) with RBF kernel')\n",
        "\n",
        "plt.show()"
      ],
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          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "opOeeVA1Oknt",
        "outputId": "1f3095cf-d63b-4003-ed00-c8d5170f8bfa"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1600x500 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Implemenetation for `nonlinear classification` for 1D data points"
      ],
      "metadata": {
        "id": "mv4OUrHvNpoA"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "We now implement the RBF kernel in Python to help us classify 1D data points that are `not` linearly separable"
      ],
      "metadata": {
        "id": "Z2e1maa4LWxC"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "np.random.seed(42)\n",
        "\n",
        "def generate_class_data(centers, stds, num_points_list):\n",
        "\n",
        "    data = []\n",
        "    for center, std, num_points in zip(centers, stds, num_points_list):\n",
        "        cluster_data = np.random.normal(center, std, num_points)\n",
        "        data.append(cluster_data)\n",
        "\n",
        "    return np.concatenate(data)\n",
        "\n",
        "# Class 0\n",
        "centers_class0 = [-1, 2, 6, 9, 10]\n",
        "stds_class0 = [0.3, 0.2, 0.5, 0.2, 0.1]\n",
        "num_points_class0_list = [5, 15, 15, 3, 19]\n",
        "class0_data = generate_class_data(centers_class0, stds_class0, num_points_class0_list)\n",
        "\n",
        "# Class 1\n",
        "centers_class1 = [0, 4, 8, 9.5]\n",
        "stds_class1 = [0.5, 0.7, 0.2, 0.1]\n",
        "num_points_class1_list = [15, 15, 3, 7]\n",
        "class1_data = generate_class_data(centers_class1, stds_class1, num_points_class1_list)\n",
        "\n",
        "# Combine data\n",
        "x = np.concatenate([class0_data, class1_data])\n",
        "print(f'x shape: {x.shape}')\n",
        "y = np.array([0] * sum(num_points_class0_list) + [1] * sum(num_points_class1_list))\n",
        "print(f'y shape: {y.shape}')\n",
        "\n",
        "plt.figure(figsize=(7, 4))\n",
        "plt.scatter(class0_data, np.zeros(sum(num_points_class0_list)), color='red', label='Class 0', alpha=0.9, edgecolors='w')\n",
        "plt.scatter(class1_data, np.zeros(sum(num_points_class1_list)), color='yellow', label='Class 1', alpha=0.9, edgecolors='w')\n",
        "\n",
        "plt.xlabel('x')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 424
        },
        "id": "OoKS6tEBv2Ip",
        "outputId": "7611ae9a-f1dd-4fed-a61a-d0e3c036b526"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "x shape: (97,)\n",
            "y shape: (97,)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 700x400 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can see that the two classes are `not` separable by a straight line"
      ],
      "metadata": {
        "id": "pLKV5iUpOCbz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "kernel = 'rbf'\n",
        "\n",
        "def square_kernel(x):\n",
        "    return np.vstack([x**2, x, np.ones(len(x))]).T\n",
        "\n",
        "def rbf_kernel(x, sigma):\n",
        "    num_points = x.shape[0]\n",
        "    k = np.zeros((num_points, num_points)) # this matrix is symmetric\n",
        "    for i in range(num_points):\n",
        "        for j in range(num_points):\n",
        "            sq_dist = np.sum((x[i] - x[j])**2)\n",
        "            k[i, j] = np.exp(-sq_dist / (2 * sigma**2))\n",
        "    return k\n",
        "\n",
        "if kernel == 'rbf':\n",
        "    sigma = 0.5\n",
        "    x_k = rbf_kernel(x, sigma)\n",
        "    print(f'x_rbf shape: {x_k.shape}')\n",
        "\n",
        "    # Initial guess\n",
        "    theta = 0.5*np.ones(x_k.shape[1])\n",
        "    print(f'theta shape: {theta.shape}')\n",
        "\n",
        "elif kernel == 'square':\n",
        "    x_k = square_kernel(x)\n",
        "    print(f'x_sq shape: {x_k.shape}')\n",
        "\n",
        "    # Initial guess\n",
        "    theta = 0.5*np.ones(x_k.shape[1])\n",
        "    print(f'theta shape: {theta.shape}')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aeuPHZx8J6Yj",
        "outputId": "f16d8736-1264-4302-cffc-18ae5c80db21"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "x_rbf shape: (97, 97)\n",
            "theta shape: (97,)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "learning_rate = 0.01\n",
        "num_iterations = 1500\n",
        "\n",
        "# Sigmoid\n",
        "def sigmoid(z):\n",
        "    return 1 / (1 + np.exp(-z))\n",
        "\n",
        "# Store loss\n",
        "loss_values = []\n",
        "\n",
        "for i in range(num_iterations):\n",
        "    y_pred = x_k @ theta # same shape as y\n",
        "    h_pred = sigmoid(y_pred)  # same shape as y\n",
        "\n",
        "    # Compute loss\n",
        "    loss = -y*np.log(h_pred) - (1 - y)*np.log(1 - h_pred) # same shape as y\n",
        "    loss = np.mean(loss) # take average, a scalar\n",
        "\n",
        "    loss_values.append(loss)\n",
        "\n",
        "    # Compute gradients\n",
        "    d_theta = x_k.T @ (h_pred - y) # same shape as theta, each row is gradient for each parameter\n",
        "\n",
        "    # Update parameters\n",
        "    theta -= learning_rate * d_theta # same shape as theta\n",
        "\n",
        "    if i % 500 == 0:\n",
        "        print(f'Iteration {i}: Loss = {loss}')\n",
        "\n",
        "def rbf_kernel_test(x_test, x, sigma):\n",
        "    num_test_points = x_test.shape[0]\n",
        "    num_train_points = x.shape[0]\n",
        "    k_test = np.zeros((num_test_points, num_train_points))\n",
        "    for i in range(num_test_points):\n",
        "        for j in range(num_train_points):\n",
        "            sq_dist = np.sum((x_test[i] - x[j])**2)\n",
        "            k_test[i, j] = np.exp(-sq_dist / (2 * sigma**2))\n",
        "    return k_test\n",
        "\n",
        "x_test = np.linspace(x.min(), x.max(), 400)\n",
        "print(f'x_test shape: {x_test.shape}')\n",
        "if kernel == 'rbf':\n",
        "    x_test_kernel = rbf_kernel_test(x_test, x, sigma)\n",
        "    print(f'x_test_rbf shape: {x_test_kernel.shape}')\n",
        "elif kernel == 'square':\n",
        "    x_test_kernel = square_kernel(x_test)\n",
        "    print(f'x_test_sq shape: {x_test_kernel.shape}')\n",
        "\n",
        "y_test = sigmoid(x_test_kernel @ theta)  # same shape as x_test\n",
        "print(f'y_test shape: {y_test.shape}')\n",
        "\n",
        "plt.figure(figsize=(7, 4))\n",
        "plt.scatter(class0_data, np.zeros(sum(num_points_class0_list)), color='red', label='Class 0', alpha=0.9, edgecolors='w')\n",
        "plt.scatter(class1_data, np.zeros(sum(num_points_class1_list)), color='yellow', label='Class 1', alpha=0.9, edgecolors='w')\n",
        "\n",
        "plt.plot(x_test, y_test, color='cyan')\n",
        "\n",
        "plt.xlabel('x')\n",
        "plt.legend(loc='upper right')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 495
        },
        "id": "k-B4NsOdzO59",
        "outputId": "88dc58ba-3f4e-436c-9e6a-b5b958461fb5"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration 0: Loss = 4.544723673325525\n",
            "Iteration 500: Loss = 0.09721915849456433\n",
            "Iteration 1000: Loss = 0.08048690318577655\n",
            "x_test shape: (400,)\n",
            "x_test_rbf shape: (400, 97)\n",
            "y_test shape: (400,)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 700x400 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}