{
  "cells": [
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {
        "id": "8GTL9Gqaxlg4"
      },
      "source": [
        "# The Basics\n",
        "\n",
        "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/myhC3s-8IG8\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen></iframe>\n",
        "\n",
        "[Slides: The Basics 1](https://github.com/ichatnun/brainCodeCamp2023_lectures/blob/main/DimensionalityReduction/dim_reduction_part1a_basics1.pdf)\n",
        "\n",
        "<br>"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {
        "id": "A2t1e5bEBgsy"
      },
      "source": [
        "Dimensionality reduction คือ การลดจำนวนมิติของข้อมูล\n",
        "\n",
        "หากใช้ภาษาทางเทคนิค เราจะเรียกว่าเป็นการแปลงข้อมูลจากข้อมูลใน space ที่มีจำนวนมิติมาก (high-dimensional space) มาสู่ space ที่มีจำนวนมิติน้อย (low-dimensional space) ซึ่งเรามักจะออกแบบการลดจำนวนมิติลง โดยที่สูญเสียข้อมูลน้อยที่สุดเท่าที่ทำได้\n",
        "\n",
        "ตัวอย่างของข้อมูลที่มีจำนวนมิติมาก\n",
        "\n",
        "\n",
        "*   ข้อมูลรูปภาพ gray scale โดยที่แต่ละภาพมีจำนวน pixel เท่ากับ 1,024 x 1,024 = 1,048,576 pixels และเราใช้แต่ละ pixel เป็น feature แปลว่าในกรณีนี้ภาพ 1 ภาพ จะเป็นข้อมูล 1 จุดใน feature space ที่มี 1,048,576 มิติ (1,048,576-dimensional space)\n",
        "\n",
        "*   ข้อมูล vdo ที่มีสี (แดง เขียว น้ำเงิน หรือ RGB) โดยเราสามารถมอง vdo เป็นรูปภาพจำนวนมากที่มาเรียงต่อกันได้ ถ้าหากแต่ละภาพใน vdo มี 1,024 x 1,024 pixels และเป็น vdo ความยาว 5 นาที ที่มี frame rate เท่ากับ 24 frame ต่อวินาที ข้อมูลของเราจะเป็นจุดใน space ที่มีทั้งหมด 1,024 x 1,024 x 3 x 24 x 5 x 60 มิติ หรือประมาณ 22 หมื่นล้านมิติ\n",
        "\n",
        "*   ข้อมูลสัญญาณสมองที่เก็บมาจากเทคนิค electroencephalogram (EEG) ซึ่งมักจะมี sensor เก็บข้อมูลประมาณ 64 ตัว แต่ละตัวจะเก็บข้อมูลที่ประมาณ 1,000 จุดต่อวินาที ถ้าหากเราเก็บข้อมูลทั้งหมดเป็นเวลา 5 วินาที จะส่งผลให้ข้อมูลของเราอยู่ใน space ที่มีทั้งหมด 64 x 1,000 x 5 = 320,000 มิติ\n",
        "\n",
        "\n",
        "ถ้าหากเราสามารถลดจำนวนมิติลงได้ จะส่งผลดีอยู่หลายประการ เช่น\n",
        "\n",
        "1.   เราจะใช้ทรัพยากรการคำนวณน้อยลง เช่น ถ้าหากเราสามารถ represent ภาพ 1 ภาพ ด้วยตัวเลขแค่ 64 ตัว (แทนที่จะ represent ด้วยตัวเลข 1,048,576 ตัว) เราก็จะสามารถนำเอาโมเดลปัญญาประดิษฐ์ที่เรารู้จักมาประมวลผลได้อย่างรวดเร็วและใช้ทรัพยากรการคำนวณน้อย\n",
        "\n",
        "2.   นอกจากนี้ หากเราลดจำนวนมิติของข้อมูลลงจนเหลือไม่เกิน 3 มิติ ก็จะช่วยให้เราสามารถนำเอาข้อมูลมา plot และดูได้ด้วยตาเปล่า\n",
        "\n",
        "ในการลดจำนวนมิติของข้อมูล เราสามารถใช้ทั้งเทคนิคที่เป็นแบบ linear หรือ แบบ non-linear ก็ได้ โดยที่แต่ละเทคนิคก็จะมีข้อดีและข้อเสีย และมีสมมติฐานในการใช้งานที่แตกต่างกัน\n",
        "\n",
        "<br><br>\n",
        "\n",
        "---\n",
        "\n",
        "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/p127ONwUOSg\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen></iframe>\n",
        "\n",
        "[Slides: The Basics 2](https://github.com/ichatnun/brainCodeCamp2023_lectures/blob/main/DimensionalityReduction/dim_reduction_part1b_basics2.pdf)\n",
        "\n",
        "<br>\n",
        "\n",
        "สมมติว่าเรามีชุดข้อมูลชุดหนึ่ง ที่มีจุดข้อมูลอยู่ทั้งหมด 100 จุด แต่ละจุดข้อมูล $(x,y)$ เป็นข้อมูลใน space ที่มี 2 มิติ (ค่า $x$ เป็นมิติแรก และค่า $y$ เป็นมิติที่สอง) และในชุดข้อมูลนี้มีจุดอยู่ 2 ประเภท (2 classes)\n",
        "\n",
        "\n",
        "*   class 1: $y = 1$ โดยที่ $ -4 ≤ x < 0 $\n",
        "*   class 2: $y = 1$ โดยที่ $ 0 < x ≤ 4 $\n",
        "\n",
        "ดังแสดงด้านล่าง"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "GQZLjejKQvxQ"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "from sklearn.decomposition import PCA\n",
        "import matplotlib.pyplot as plt\n",
        "from matplotlib import colors\n",
        "\n",
        "import ipywidgets as widgets  # ใช้สำหรับการทำ interactive display"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "qUyqFRnnA9s8",
        "outputId": "cc3355ae-fdf0-48c6-89e1-79f57001282f"
      },
      "outputs": [
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 600x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "num_points = 50 # # จำนวนจุดข้อมูล\n",
        "x = np.linspace(-4, 4, num_points)\n",
        "y = 1\n",
        "\n",
        "# นำเอาค่า x มาใส่ใน column แรกของ data matrix และ ค่า y มาใส่ใน column ที่สอง\n",
        "data = np.zeros((num_points, 2))\n",
        "data[:, 0] = x\n",
        "data[:, 1] = y\n",
        "\n",
        "# เตรียมแสดงผล\n",
        "x_disp = [-6.0, 6.0] # ค่าต่ำสูงและสูงสุดของ x สำหรับแสดงผล\n",
        "y_disp = [-6.0, 6.0] # ค่าต่ำสูงและสูงสุดของ y สำหรับแสดงผล\n",
        "\n",
        "plt.figure(figsize=(6, 6))\n",
        "\n",
        "# แสดงรูปข้อมูลเริ่มต้น\n",
        "plt.scatter(data[data[:, 0] < 0, 0], data[data[:, 0] < 0, 1], c='b') # Plot จุดข้อมูลที่เป็น class 1\n",
        "plt.scatter(data[data[:, 0] > 0, 0], data[data[:, 0] > 0, 1], c='r') # Plot จุดข้อมูลที่เป็น class 2\n",
        "plt.plot([0, 0], y_disp, c=\"grey\") # Plot แกน y\n",
        "plt.plot(x_disp, [0, 0], c=\"grey\") # Plot แกน x\n",
        "plt.xlabel(\"x\")\n",
        "plt.ylabel(\"y\")\n",
        "plt.title(\"Data with two classes\")\n",
        "plt.show()"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {
        "id": "sbmLiVq_FUD4"
      },
      "source": [
        "ถ้าหากเราต้องการแก้โจทย์ two-class classification หรือ แบ่งจุดข้อมูลที่เรามีออกเป็น 2 ประเภท (ประเภทน้ำเงิน และ ประเภทสีแดง) โดยที่เราใช้ค่า $x$ เป็น feature แรก และใช้ค่า $y$ เป็น feature ที่สอง เราสามารถใช้แกน $y$ (สมการคือ $ x=0$) แบ่งข้อมูลทั้ง 2 ประเภทออกจากกันได้เลย โดยเราจะตอบว่าจุดข้อมูลนั้นเป็น\n",
        "\n",
        "1. class 1 (ประเภทที่ 1) ถ้าหากจุดนั้นมีค่า $x$ น้อยกว่า $0$ หรือถ้าดูจากภาพก็คือจุดนั้นอยู่ทางซ้ายของแกน $y$\n",
        "2.   class 2 (ประเภทที่ 2) ถ้าหากจุดนั้นมีค่า $x$ มากกว่า $0$ หรือถ้าดูจากภาพก็คือจุดนั้นอยู่ทางขวาของแกน $y$\n",
        "\n",
        "จะเห็นว่าเราสามารถแบ่งจุดข้อมูลสองกลุ่มนี้ได้อย่างง่ายดาย โดยการดูแค่ค่า $x$ อย่างเดียว โดยที่ไม่ต้องสนใจค่า $y$ ซึ่งแปลว่าเราจริง ๆ แล้ว เราสามารถลดข้อมูลมิติของข้อมูลจากสองมิติ ($x$ หนึ่งมิติ และ $y$ เป็นอีกมิติ) ให้เหลือแค่มิติเดียว (ค่า $x$ เพียงอย่างเดียว) ก็ยังสามารถ classify จุดเหล่านี้ได้เหมือนเดิม ดังแสดงในภาพด้านล่าง\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 514
        },
        "id": "CtvwaZvFUyya",
        "outputId": "d606fc46-015f-4339-cba9-78cde237bb10"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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UpbQ6nvT4UlB59is3NxcvvfQSMjMzMW7cODRu3BjVqlVDeno6IiIizKotf9l33nmn2PuApn7UpVKFzsqVKwEAoaGhAB69m4iLi8OkSZPwySefGJbLf+f0uOIOkhs3boRer8eGDRuM3rXkX0IpTb169VCvXj0kJibi/Pnzhktg7dq1w+jRo7F27Vrk5uaiXbt2JbZTUQfxktotS+2enp7Iy8vD2bNnjQY6ZGRk4Pbt2/D09Cz2+by9vQEAx48fN6sPu3fvxs2bN/Hjjz8a1XLhwoUil2/evDmaN2+Ojz/+GElJSQgMDMSCBQsMw4atrKzQqVMndOrUCbNmzcLUqVPx0UcfYdeuXQgJCYGPjw+OHj2KTp06lbpdSmtLpps3b6Jz587Q6/WIi4uDm5tboWW++OILo3fh7u7uAB5t17i4ONy9e9foAH/69OkKr9vHxwcA4OTkVK6vmbnbJv9vt6g+p6SkoFatWqhWrZpZNTzp8aUopvar4HFQCIFz584ZDv7Hjh3DmTNnsGLFCrz77ruG5Xbs2GG0nin7rVarhaOjI3Jzc594G1aay2vx8fGYPHkyvLy80LdvXwB/v8so+C5wzpw5hdbP/2MpOAS0qDZ0Oh2WLVtmcm1BQUGIj4/HgQMHDAduPz8/ODo6Ytq0abCzs4O/v3+JbRRX35Oyt7cvsV1za3/55ZcBFH6N888KunXrVmwtWq0W7dq1w9KlS/Hnn38a/VtJ7+SL2kY5OTn45ptvjJbLysrCw4cPjeY1b94cVlZWhqHOmZmZhdrPf3edv0yfPn2Qnp6OxYsXF1r2/v37hkssprQly7179/Dyyy8jPT0dW7ZsKXRpJZ+/vz9CQkIMk6+vL4BH2/Xhw4dGQ3lzc3Mxb968Cq/d398fPj4++Pzzz3H37t1C/27KkPGCyrJt3Nzc4OfnhxUrVhjtL8ePH8f27dsNf/vmKI/jy+PM6de3335rdP/7hx9+wJUrV9C1a9diaxNC4MsvvzRqx5T91traGq+99hrWrVtXZDiZsw0VOdPZunUrUlJS8PDhQ2RkZCA+Ph47duyAp6cnNmzYYPhAl5OTE9q1a4cZM2bgwYMHqFOnDrZv317kO+D8A+dHH32EN998E1WrVkWPHj3QuXNn2NjYoEePHnj//fdx9+5dLF68GC4uLiZ/hUhQUBC+++47qFQqwyUra2trtGnTBtu2bUOHDh1gY2NTYht+fn6wtrbG9OnTodPpoFarDWP7n4SdnR18fX2xZs0aPPPMM6hRowaaNWtmuD5rbu3PPvsswsPDsWjRIsNlrwMHDmDFihXo1asXgoODS6xn7ty5aNu2LVq2bIlBgwbBy8sLqamp2Lx5M44cOVLkOm3atEH16tURHh6O4cOHQ6VSYeXKlYWCKj4+HkOHDkVYWBieeeYZPHz4ECtXrjTsEMCjb7tISEhAt27d4OnpiWvXruGbb75B3bp1Df3v168fvv/+ewwePBi7du1CYGAgcnNzkZKSgu+//x7btm1DQECASW3J0rdvXxw4cAADBgzAqVOnjD5X4uDggF69epW4fo8ePRAYGIjx48cjNTUVvr6++PHHH82+51AWVlZWWLJkCbp27YqmTZuif//+qFOnDtLT07Fr1y44OTlh48aNZrVZ1m0zc+ZMdO3aFS+++CIGDhxoGDKt0WgwceJEs/tWHseXsvarRo0aaNu2Lfr374+MjAzMmTMHDRo0MHzcpHHjxvDx8cG//vUvpKenw8nJCevWrSvy/qEp++20adOwa9cutG7dGpGRkfD19UVmZiaSk5Oxc+fOIgOzSCaNcSsn+cNG8ycbGxvh6uoqXnrpJfHll18aDf/Ld+nSJdG7d2/h7OwsNBqNCAsLE5cvXy5ymPDkyZNFnTp1hJWVldGQzQ0bNogWLVoIW1tbUb9+fTF9+nSxdOnSYodYF3TixAkBQDRp0sRo/pQpUwQA8e9//7vQOgWHzAohxOLFi4W3t7ewtrY2Gj7t6ekpunXrVqgNU4ZYCiFEUlKS8Pf3FzY2NoVel7LU/uDBAzFp0iTh5eUlqlatKjw8PER0dLRh6HJpjh8/bthmtra2olGjRkbPU9SQ6b1794oXXnhB2NnZCXd3dzF27Fixbds2o9fp/PnzYsCAAcLHx0fY2tqKGjVqiODgYLFz505DO3FxcaJnz57C3d1d2NjYCHd3d/HWW2+JM2fOGNWYk5Mjpk+fLpo2bSrUarWoXr268Pf3F5MmTRI6nc6stopS3JDpgh8XyB/+WtRQ+oLtPb7vPD55enqWWo8QQty8eVP069dPODk5CY1GI/r162cYhm7KkOmoqCijeflDkmfOnFlknwoObT98+LB49dVXRc2aNYVarRaenp6iT58+RkO+85+74JDhgn8zpmybooZMCyHEzp07RWBgoLCzsxNOTk6iR48e4uTJk0bLmFqHEKYfX0zZn03pV/7ru2rVKhEdHS1cXFyEnZ2d6NatW6EhzydPnhQhISHCwcFB1KpVS0RGRoqjR48W+bqUtt8KIURGRoaIiooSHh4eomrVqsLV1VV06tRJLFq0qMR+PU4lxBPcqSYiIql2796N4OBgrF27Fq+//rrS5Zit0tzTISKipx9Dh4iIpGHoEBGRNBYVOunp6XjnnXdQs2ZN2NnZoXnz5vj999+VLouISJoOHTpACGGR93OASvbh0JLcunULgYGBCA4OxtatW6HVanH27FnD11IQEVHlZzGj18aPH4+9e/cavjOMiIgsj8WEjq+vL0JDQ3Hp0iXs2bMHderUwQcffGD4IFRR9Hq90ad48/LykJmZiZo1a0r9bjEioooihMCdO3fg7u5erj+RXmFM/kSPwtRqtVCr1SI6OlokJyeLhQsXCltbW7F8+fJi18n/gBcnTpw4Pe1TWlqaxCNy2VnMmY6NjQ0CAgKQlJRkmDd8+HAcPHgQ+/btK3Kdgmc6Op0O9erVw9KlabC3d6rwmumfKTc3B8eOfQEAGNO8OWzK6RuPiYqSlZ0NjwEDDL+eW9lZzEACNzc3w5cX5mvSpAnWrVtX7DpqtRpqtbrQfHt7J4YOVZjc3Jy/vz/Q3p6hQ1JYyi0DC7gA+EhgYGChryQ/c+ZMiV+1T0RElYvFhM6oUaOwf/9+TJ06FefOncN///tfLFq0CFFRUUqXRkREJrKY0Hn++eexfv16rFq1Cs2aNcPkyZMxZ84cw2/vEBFR5Wcx93QAoHv37ujevbvSZRARURlZzJkOERFZPoYOERFJw9AhIiJpGDpERCQNQ4eIiKRh6BARkTQMHSIikoahQ0RE0jB0iIhIGoYOERFJw9AhIiJpGDpERCQNQ4eIiKRh6BARkTQMHSIikoahQ0RE0jB0iIhIGoYOERFJw9AhIiJpGDpERCQNQ4eIiKRh6BARkTQMHSIikoahQ0RE0jB0iIhIGoYOERFJw9AhIiJpGDpERCQNQ4eIiKRh6BARkTQMHSIikoahQ0RE0jB0iIhIGoYOERFJw9AhIiJpGDpERCQNQ4eIiKRh6BARkTQMHSIikoahQ0RE0lhs6EybNg0qlQojR45UuhQiIjKRRYbOwYMHsXDhQrRo0ULpUoiIyAwWFzp3795F3759sXjxYlSvXl3pcoiIyAwWFzpRUVHo1q0bQkJCSl1Wr9cjKyvLaCIiIuVUUboAc6xevRrJyck4ePCgScvHxsZi0qRJFVwVERGZymLOdNLS0jBixAh89913sLW1NWmd6Oho6HQ6w5SWllbBVRIRUUks5kzn0KFDuHbtGlq2bGmYl5ubi4SEBHz11VfQ6/WwtrY2WketVkOtVssulYiIimExodOpUyccO3bMaF7//v3RuHFjjBs3rlDgEBFR5WMxoePo6IhmzZoZzatWrRpq1qxZaD4REVVOFnNPh4iILJ/FnOkUZffu3UqXQEREZuCZDhERScPQISIiaRg6REQkDUOHiIikYegQEZE0DB0iIpKGoUNERNIwdIiISBqGDhERScPQISIiaRg6REQkDUOHiIikYegQEZE0DB0iIpKGoUNERNIwdIiISBqGDhERScPQISIiaRg6REQkDUOHiIikYegQEZE0DB0iIpKGoUNERNIwdIiISBqGDhERScPQISIiaRg6REQkDUOHiIikYegQEZE0DB0iIpKGoUNERNIwdIiISBqGDhERScPQISIiaRg6REQkDUOHiIikYegQEZE0DB0iIpKGoUNERNIwdIiISBqLCZ3Y2Fg8//zzcHR0hIuLC3r16oXTp08rXRYREZnBYkJnz549iIqKwv79+7Fjxw48ePAAnTt3xr1795QujYiITFRF6QJM9csvvxg9Xr58OVxcXHDo0CG0a9dOoaqIiMgcFhM6Bel0OgBAjRo1il1Gr9dDr9cbHmdlZVV4XUREVDyLubz2uLy8PIwcORKBgYFo1qxZscvFxsZCo9EYJg8PD4lVEhFRQRYZOlFRUTh+/DhWr15d4nLR0dHQ6XSGKS0tTVKFRERUFIu7vDZ06FBs2rQJCQkJqFu3bonLqtVqqNVqSZUREVFpLCZ0hBAYNmwY1q9fj927d8PLy0vpkoiIyEwWEzpRUVH473//i59//hmOjo64evUqAECj0cDOzk7h6oiIyBQWc09n/vz50Ol06NChA9zc3AzTmjVrlC6NiIhMZDFnOkIIpUsgIqInZDFnOkREZPkYOkREJA1Dh4iIpGHoEBGRNAwdIiKShqFDRETSMHSIiEgahg4REUnD0CEiImkYOkREJA1Dh4iIpGHoEBGRNAwdIiKShqFDRETSWMxPG9DfcnOBkyeBzEygRg3A1/fR/MfnNWoEnD5t+uPyaMNS2pRRl6Pj/2+sEyeAW7cqT2GVpc3KUpevL2BtXe77KBWPoWNhkpKAxYuBmzf/nufgAKhUwJ07f8+zsgLy8kx/XB5tWEqbFV1X1arARx/9/z9MmgQ8eFA5CqtMbVaWumrWBCIjgTZtQHIwdCxIUhIwbVrh+XfvFp73+H5lyuPyaMNS2qzoul7BhsJPUBkKq0xtVpa6bt58tFONH8/gkYT3dCxEbu6jMxyq3KyQixn4UOkyyFxLljzayajCMXQsxMmTxpfUqHIKQiLqIl3pMshcN2482smowjF0LERmptIVkCnccEXpEqisuJNJwdCxEDVqKF0BmeIK3JQugcqKO5kUDB0L4ev7aKANVW6JCMIl1FG6DDJXrVp/D7mmCsXQsRDW1o9GdlLllgdrjMVMpcsgc733Hj+vIwlDx4K0afNoZGfBMx5Hx8c+jPj/rKzMe1webVhKmxVd1wa8giIpXVhlarOy1FWrFodLS8bP6ViYNm2A1q35jQSVva8GMTH8RoLKXBe/kUA6lRBCKF2ELFlZWdBoNFi9Wgd7eyely6GnVG5uDo4ejQUARD/7LGx4UKMKlJWdDc2bb0Kn08HJqfIf13h5jYiIpGHoEBGRNAwdIiKShqFDRETSMHSIiEgahg4REUnD0CEiImkYOkREJA1Dh4iIpGHoEBGRNAwdIiKShqFDRETSMHSIiEgahg4REUnD0CEiImksLnS+/vpr1K9fH7a2tmjdujUOHDigdElERGQis0MnPDwcCQkJFVFLqdasWYPRo0cjJiYGycnJePbZZxEaGopr164pUg8REZnH7J+r1ul0CAkJgaenJ/r374/w8HDUqVOnImorZNasWYiMjET//v0BAAsWLMDmzZuxdOlSjB8/3uR2cnNzkJubU1Fl0j/c439bObm5ClZC/wSW9jdmduj89NNPuH79OlauXIkVK1YgJiYGISEhGDhwIHr27ImqVatWRJ3IycnBoUOHEB0dbZhnZWWFkJAQ7Nu3r8h19Ho99Hq94XFWVhYA4NixL2Bra1shdRI97ovjx5UugZ5yf/31l9IlmKVM93S0Wi1Gjx6No0eP4rfffkODBg3Qr18/uLu7Y9SoUTh79mx514kbN24gNzcXtWvXNppfu3ZtXL16tch1YmNjodFoDJOHh0e510VERKYz+0zncVeuXMGOHTuwY8cOWFtb4+WXX8axY8fg6+uLGTNmYNSoUeVVZ5lER0dj9OjRhsdZWVnw8PBA8+ZjYG/vpGBl9DTLzc3B8eNfAADGNGsGG2trhSuip1lWdjamKV2EGcwOnQcPHmDDhg1YtmwZtm/fjhYtWmDkyJF4++234eT06EC+fv16DBgwoFxDp1atWrC2tkZGRobR/IyMDLi6uha5jlqthlqtLjTf2toG1tY25VYbUXFsrK0ZOlShLO3vy+zQcXNzQ15eHt566y0cOHAAfn5+hZYJDg6Gs7NzOZT3NxsbG/j7+yMuLg69evUCAOTl5SEuLg5Dhw4t1+ciIqKKYXbozJ49G2FhYSXeiHd2dsaFCxeeqLCijB49GuHh4QgICECrVq0wZ84c3Lt3zzCajYiIKjezQ6dfv34VUYdJ3njjDVy/fh2ffPIJrl69Cj8/P/zyyy+FBhcQEVHl9EQDCZQwdOhQXk4jIrJQFvc1OEREZLkYOkREJA1Dh4iIpGHoEBGRNAwdIiKShqFDRETSMHSIiEgahg4REUnD0CEiImkYOkREJA1Dh4iIpGHoEBGRNAwdIiKShqFDRETSMHSIiEgahg4REUnD0CEiImkYOkREJA1Dh4iIpGHoEBGRNAwdIiKShqFDRETSMHSIiEgahg4REUnD0CEiImkYOkREJA1Dh4iIpGHoEBGRNAwdIiKShqFDRETSMHSIiEgahg4REUnD0CEiImkYOkREJA1Dh4iIpGHoEBGRNAwdIiKShqFDRETSMHSIiEgahg4REUljEaGTmpqKgQMHwsvLC3Z2dvDx8UFMTAxycnKULo2IiMxQRekCTJGSkoK8vDwsXLgQDRo0wPHjxxEZGYl79+7h888/V7o8IiIykUWETpcuXdClSxfDY29vb5w+fRrz589n6BARWRCLCJ2i6HQ61KhRo8Rl9Ho99Hq94XFWVlZFl0VERCWwiHs6BZ07dw7z5s3D+++/X+JysbGx0Gg0hsnDw0NShUREVBRFQ2f8+PFQqVQlTikpKUbrpKeno0uXLggLC0NkZGSJ7UdHR0On0xmmtLS0iuwOERGVQtHLa2PGjEFERESJy3h7exv+//LlywgODkabNm2waNGiUttXq9VQq9VPWiYREZUTRUNHq9VCq9WatGx6ejqCg4Ph7++PZcuWwcrKIq8MEhH9o1nEQIL09HR06NABnp6e+Pzzz3H9+nXDv7m6uipYGRERmcMiQmfHjh04d+4czp07h7p16xr9mxBCoaqIiMhcFnGNKiIiAkKIIiciIrIcFhE6RET0dGDoEBGRNAwdIiKShqFDRETSMHSIiEgahg4REUnD0CEiImkYOkREJA1Dh4iIpGHoEBGRNAwdIiKShqFDRETSMHSIiEgahg4REUnD0CEiImkYOkREJA1Dh4iIpGHoEBGRNAwdIiKShqFDRETSMHSIiEgahg4REUnD0CEiImkYOkREJA1Dh4iIpGHoEBGRNAwdIiKShqFDRETSMHSIiEgahg4REUnD0CEiImkYOkREJA1Dh4iIpGHoEBGRNAwdIiKShqFDRETSMHSIiEgahg4REUnD0CEiImkYOkREJI3FhY5er4efnx9UKhWOHDmidDlERGQGiwudsWPHwt3dXekyiIioDCwqdLZu3Yrt27fj888/V7oUIiIqgypKF2CqjIwMREZG4qeffoK9vb1J6+j1euj1esPjrKysiiqPiIhMYBFnOkIIREREYPDgwQgICDB5vdjYWGg0GsPk4eFRgVUSEVFpFA2d8ePHQ6VSlTilpKRg3rx5uHPnDqKjo81qPzo6GjqdzjClpaVVUE+IiMgUil5eGzNmDCIiIkpcxtvbG/Hx8di3bx/UarXRvwUEBKBv375YsWJFkeuq1epC6xARkXIUDR2tVgutVlvqcnPnzsWUKVMMjy9fvozQ0FCsWbMGrVu3rsgSiYioHFnEQIJ69eoZPXZwcAAA+Pj4oG7dukqUREREZWARAwmIiOjpYBFnOgXVr18fQgilyyAiIjPxTIeIiKRh6BARkTQMHSIikoahQ0RE0jB0iIhIGoYOERFJw9AhIiJpGDpERCQNQ4eIiKRh6BARkTQMHSIikoahQ0RE0jB0iIhIGoYOERFJw9AhIiJpGDpERCQNQ4eIiKRh6BARkTQMHSIikoahQ0RE0jB0iIhIGoYOERFJw9AhIiJpGDpERCQNQ4eIiKRh6BARkTQMHSIikoahQ0RE0jB0iIhIGoYOERFJw9AhIiJpGDpERCQNQ4eIiKRh6BARkTQMHSIikoahQ0RE0jB0iIhIGoYOERFJw9AhIiJpGDpERCQNQ4eIiKSxqNDZvHkzWrduDTs7O1SvXh29evVSuiQiIjJDFaULMNW6desQGRmJqVOnomPHjnj48CGOHz+udFlERGQGiwidhw8fYsSIEZg5cyYGDhxomO/r66tgVUREZC6LCJ3k5GSkp6fDysoKzz33HK5evQo/Pz/MnDkTzZo1K3Y9vV4PvV5veKzT6QAA2dlZFV4z/XPl5ubgr7/+AgBkZWfDxtpa4YroaZaVnQ0AEEIoXImJhAVYtWqVACDq1asnfvjhB/H777+Lt956S9SsWVPcvHmz2PViYmIEAE6cOHF66qc//vhD4lG57FRCKBeP48ePx/Tp00tc5tSpU0hOTkbfvn2xcOFCDBo0CMCjs5i6detiypQpeP/994tct+CZzu3bt+Hp6Yk///wTGo2m/DqigKysLHh4eCAtLQ1OTk5Kl/PE2J/K62nqC/D09Uen06FevXq4desWnJ2dlS6nVIpeXhszZgwiIiJKXMbb2xtXrlwBYHwPR61Ww9vbG3/++Wex66rVaqjV6kLzNRrNU/HHBgBOTk5PTV8A9qcye5r6Ajx9/bGysozByIqGjlarhVarLXU5f39/qNVqnD59Gm3btgUAPHjwAKmpqfD09KzoMomIqJxYxEACJycnDB48GDExMfDw8ICnpydmzpwJAAgLC1O4OiIiMpVFhA4AzJw5E1WqVEG/fv1w//59tG7dGvHx8ahevbrJbajVasTExBR5yc3SPE19Adifyuxp6gvA/ihN0YEERET0z2IZd56IiOipwNAhIiJpGDpERCQNQ4eIiKT5R4fO0/hTCXq9Hn5+flCpVDhy5IjS5ZgtNTUVAwcOhJeXF+zs7ODj44OYmBjk5OQoXZrJvv76a9SvXx+2trZo3bo1Dhw4oHRJZRIbG4vnn38ejo6OcHFxQa9evXD69GmlyyoX06ZNg0qlwsiRI5UupczS09PxzjvvoGbNmrCzs0Pz5s3x+++/K11Wqf6xobNu3Tr069cP/fv3x9GjR7F37168/fbbSpf1xMaOHQt3d3elyyizlJQU5OXlYeHChThx4gRmz56NBQsWYMKECUqXZpI1a9Zg9OjRiImJQXJyMp599lmEhobi2rVrSpdmtj179iAqKgr79+/Hjh078ODBA3Tu3Bn37t1TurQncvDgQSxcuBAtWrRQupQyu3XrFgIDA1G1alVs3boVJ0+exBdffGHWR0gUo+xXvynjwYMHok6dOmLJkiVKl1KutmzZIho3bixOnDghAIjDhw8rXVK5mDFjhvDy8lK6DJO0atVKREVFGR7n5uYKd3d3ERsbq2BV5ePatWsCgNizZ4/SpZTZnTt3RMOGDcWOHTtE+/btxYgRI5QuqUzGjRsn2rZtq3QZZfKPPNMp+FMJbm5u6Nq1q0X/KFxGRgYiIyOxcuVK2NvbK11OudLpdKhRo4bSZZQqJycHhw4dQkhIiGGelZUVQkJCsG/fPgUrKx/5Pw1iCduiOFFRUejWrZvRNrJEGzZsQEBAAMLCwuDi4oLnnnsOixcvVrosk/wjQ+f8+fMAgIkTJ+Ljjz/Gpk2bUL16dXTo0AGZmZkKV2c+IQQiIiIwePBgBAQEKF1OuTp37hzmzZtX7DeJVyY3btxAbm4uateubTS/du3auHr1qkJVlY+8vDyMHDkSgYGBJf6GVWW2evVqJCcnIzY2VulSntj58+cxf/58NGzYENu2bcOQIUMwfPhwrFixQunSSvVUhc748eOhUqlKnPLvGQDARx99hNdeew3+/v5YtmwZVCoV1q5dq3Av/mZqf+bNm4c7d+4gOjpa6ZKLZWpfHpeeno4uXbogLCwMkZGRClVOwKMzhOPHj2P16tVKl1ImaWlpGDFiBL777jvY2toqXc4Ty8vLQ8uWLTF16lQ899xzGDRoECIjI7FgwQKlSyuVxXz3mikq+qcSZDO1P/Hx8di3b1+h714KCAhA3759K8W7H1P7ku/y5csIDg5GmzZtsGjRogqurnzUqlUL1tbWyMjIMJqfkZEBV1dXhap6ckOHDsWmTZuQkJCAunXrKl1OmRw6dAjXrl1Dy5YtDfNyc3ORkJCAr776Cnq9HtYW9Auvbm5uRscvAGjSpAnWrVunUEWme6pC52n7qQRT+zN37lxMmTLF8Pjy5csIDQ3FmjVr0Lp164os0WSm9gV4dIYTHBxsOAO1lN8JsbGxgb+/P+Li4gzD7/Py8hAXF4ehQ4cqW1wZCCEwbNgwrF+/Hrt374aXl5fSJZVZp06dcOzYMaN5/fv3R+PGjTFu3DiLChwACAwMLDR8/cyZM5Xq+FUspUcyKGXEiBGiTp06Ytu2bSIlJUUMHDhQuLi4iMzMTKVLe2IXLlyw2NFrly5dEg0aNBCdOnUSly5dEleuXDFMlmD16tVCrVaL5cuXi5MnT4pBgwYJZ2dncfXqVaVLM9uQIUOERqMRu3fvNtoO2dnZSpdWLix59NqBAwdElSpVxGeffSbOnj0rvvvuO2Fvby/+85//KF1aqf6xoZOTkyPGjBkjXFxchKOjowgJCRHHjx9XuqxyYcmhs2zZsmJ/A95SzJs3T9SrV0/Y2NiIVq1aif379ytdUpkUtx2WLVumdGnlwpJDRwghNm7cKJo1aybUarVo3LixWLRokdIlmYQ/bUBERNJYxsVyIiJ6KjB0iIhIGoYOERFJw9AhIiJpGDpERCQNQ4eIiKRh6BARkTQMHSIikoahQ0RE0jB0iIhIGoYOERFJw9AhKifXr1+Hq6srpk6dapiXlJQEGxsbxMXFKVgZUeXBL/wkKkdbtmxBr169kJSUhEaNGsHPzw89e/bErFmzlC6NqFJg6BCVs6ioKOzcuRMBAQE4duwYDh48WOhXXYn+qRg6ROXs/v37aNasGdLS0nDo0CE0b95c6ZKIKg3e0yEqZ3/88QcuX76MvLw8pKamKl0OUaXCMx2icpSTk4NWrVrBz88PjRo1wpw5c3Ds2DG4uLgoXRpRpcDQISpHH374IX744QccPXoUDg4OaN++PTQaDTZt2qR0aUSVAi+vEZWT3bt3Y86cOVi5ciWcnJxgZWWFlStXIjExEfPnz1e6PKJKgWc6REQkDc90iIhIGoYOERFJw9AhIiJpGDpERCQNQ4eIiKRh6BARkTQMHSIikoahQ0RE0jB0iIhIGoYOERFJw9AhIiJp/g8Yk1dLfIRx/AAAAABJRU5ErkJggg==",
            "text/plain": [
              "<Figure size 400x400 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 400x50 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "x_disp = [-6.0, 6.0] # ค่าต่ำสูงและสูงสุดของ x สำหรับแสดงผล\n",
        "y_disp = [-6.0, 6.0] # ค่าต่ำสูงและสูงสุดของ y สำหรับแสดงผล\n",
        "\n",
        "# สร้างจุด (x,y) จำนวนมาก สำหรับเอามาใช้แสดงผล classification ที่จุดต่าง ๆ โดยใช้สีน้ำเงินแดง class 1 และสีแดงแสดง class 2\n",
        "xx, yy = np.meshgrid(np.linspace(x_disp[0], x_disp[1], 100), np.linspace(y_disp[0], y_disp[1], 100))\n",
        "\n",
        "# เก็บข้อมูลว่าแต่ละจุดถูก classify เป็น class อะไรบ้าง โดยใช้เลข 0 สำหรับ class 1 และ 1 สำหรับ class 2\n",
        "labels_predicted = (xx.ravel() > 0).reshape(xx.shape)\n",
        "\n",
        "# Plot ข้อมูลในสองมิติ\n",
        "plt.figure(figsize=(4, 4))\n",
        "plt.scatter(data[data[:, 0] < 0, 0], data[data[:, 0] < 0, 1], c='b') # Plot จุดข้อมูลที่เป็น class 1 ด้วยสีน้ำเงิน\n",
        "plt.scatter(data[data[:, 0] > 0, 0], data[data[:, 0] > 0, 1], c='r') # Plot จุดข้อมูลที่เป็น class 2 ด้วนสีแดง\n",
        "plt.plot([0, 0], y_disp, c=\"grey\") # Plot แกน y\n",
        "plt.plot(x_disp, [0, 0], c=\"grey\") # Plot แกน x\n",
        "plt.pcolormesh(xx, yy, labels_predicted, cmap=colors.ListedColormap([\"blue\", \"red\"]), norm=colors.Normalize(0.0, 1.0), zorder=0, alpha=0.3) # Plot ผลจากทำนายจากข้อมูล xx และ yy\n",
        "plt.xlabel(\"x\")\n",
        "plt.ylabel(\"y\")\n",
        "plt.xlim(x_disp)\n",
        "plt.ylim(y_disp)\n",
        "plt.title(\"Data with two classes in 2-dimensional space\")\n",
        "\n",
        "# Plot ข้อมูลที่ลดมิติมาแล้ว\n",
        "plt.figure(figsize=(4, 0.5))\n",
        "plt.scatter(data[data[:, 0] < 0, 0], np.zeros_like(data[data[:, 0] < 0, 0]), c='b') # Plot จุดข้อมูลที่เป็น class 1\n",
        "plt.scatter(data[data[:, 0] > 0, 0], np.zeros_like(data[data[:, 0] > 0, 0]), c='r') # Plot จุดข้อมูลที่เป็น class 2\n",
        "plt.plot([0, 0], y_disp, c=\"grey\") # Plot แกน y\n",
        "plt.plot(x_disp, [0, 0], c=\"grey\") # Plot แกน x\n",
        "plt.pcolormesh(xx, yy, labels_predicted, cmap=colors.ListedColormap([\"blue\", \"red\"]), norm=colors.Normalize(0.0, 1.0), zorder=0, alpha=0.3) # Plot ผลจากทำนายจากข้อมูล xx เพึยงอย่างเดียว\n",
        "plt.xlim(x_disp)\n",
        "plt.ylim(-0.5, 0.5)\n",
        "plt.title(\"Data with two classes in 1-dimensional space\")\n",
        "plt.yticks([])\n",
        "plt.show()"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {
        "id": "96rkJatmAmOz"
      },
      "source": [
        "ตัวอย่างด้านบนแสดงให้เห็นว่าในบางชุดข้อมูล เราสามารถลดจำนวนมิติของข้อมูลได้ โดยที่ยังมีความสามารถในการทำ classification ได้เหมือนเดิม\n",
        "\n",
        "---\n",
        "\n",
        "ตัวอย่างถัดมา สมมติว่าเรามีชุดข้อมูลชุดหนึ่ง ที่มีจุดข้อมูลอยู่ทั้งหมด 100 จุด แต่ละจุดข้อมูล $(x,y)$ เป็นข้อมูลใน space ที่มี 2 มิติ (ค่า $x$ เป็นมิติแรก และค่า $y$ เป็นมิติที่สอง) และในชุดข้อมูลนี้มีจุดอยู่ 2 ประเภท (2 classes)\n",
        "\n",
        "\n",
        "*   class 1: $y = x$ โดยที่ $ -4 ≤ x < 0 $\n",
        "*   class 2: $y = x$ โดยที่ $ 0 < x ≤ 4 $\n",
        "\n",
        "ดังแสดงด้านล่าง"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "aJsUTKs38pjz",
        "outputId": "9a771a23-8def-4f16-90b1-fa42f9f34c7e"
      },
      "outputs": [
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 600x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "num_points = 50\n",
        "x = np.linspace(-4, 4, num_points)\n",
        "y = x\n",
        "data = np.zeros((num_points, 2))\n",
        "data[:, 0] = x\n",
        "data[:, 1] = y\n",
        "\n",
        "# เตรียมแสดงผล\n",
        "x_disp = [-6.0, 6.0] # ค่าต่ำสูงและสูงสุดของ x สำหรับแสดงผล\n",
        "y_disp = [-6.0, 6.0] # ค่าต่ำสูงและสูงสุดของ y สำหรับแสดงผล\n",
        "\n",
        "plt.figure(figsize=(6, 6))\n",
        "\n",
        "# แสดงรูปข้อมูลเริ่มต้น\n",
        "plt.scatter(data[data[:, 0] < 0, 0], data[data[:, 0] < 0, 1], c='b') # Plot จุดข้อมูลที่เป็น class 1\n",
        "plt.scatter(data[data[:, 0] > 0, 0], data[data[:, 0] > 0, 1], c='r') # Plot จุดข้อมูลที่เป็น class 2\n",
        "plt.plot([0, 0], y_disp, c=\"grey\") # Plot แกน y\n",
        "plt.plot(x_disp, [0, 0], c=\"grey\") # Plot แกน x\n",
        "plt.xlabel(\"x\")\n",
        "plt.ylabel(\"y\")\n",
        "plt.title(\"Data with two classes\")\n",
        "plt.show()"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {
        "id": "JjMVbZ8eSMUT"
      },
      "source": [
        "จะเห็นว่าถ้าเรานำเอาข้อมูลด้านบนแต่ละจุดมาหมุนตามเข็มนาฬิกาไป $45$ องศา โดยมีจุด $(0,0)$ เป็นจุดหมุน เราจะสามารถแปลงโจทย์ข้อนี้ให้กลายเป็นโจทย์ที่มีหน้าตาคล้ายกับข้อมูลในตัวอย่างก่อนหน้า\n",
        "\n",
        "การหมุนจุดข้อมูลทวนเข็มนาฬิกาไป $\\theta$ องศาโดยมีจุด $(0,0)$ เป็นจุดหมุน สามารถอธิบายได้ด้วย rotation matrix\n",
        "\n",
        "$$\n",
        "  R(θ) =\n",
        "  \\begin{bmatrix}\n",
        "      cos θ        & -sin θ  \\\\\n",
        "      sin θ       & cos θ \\\\\n",
        "  \\end{bmatrix}\n",
        "$$\n",
        "\n",
        "หากเรา represent พิกัด $(x,y)$ ด้วย vector\n",
        "\n",
        "$$\n",
        "  \\begin{bmatrix}\n",
        "      x \\\\\n",
        "      y\\\\\n",
        "  \\end{bmatrix}\n",
        "$$\n",
        "\n",
        "เราจะสามารถหมุนจุดข้อมูลนั้นตามเข็มนาฬิกา 45 องศา ด้วยการใช้ $R(-45°)$\n",
        "\n",
        "\n",
        "\n",
        "$$\n",
        "   \\begin{bmatrix}\n",
        "      x' \\\\\n",
        "      y'\\\\\n",
        "  \\end{bmatrix} =\n",
        "  R(-45°)  \\begin{bmatrix}\n",
        "      x \\\\\n",
        "      y\\\\\n",
        "  \\end{bmatrix}\n",
        "$$\n",
        "\n",
        "เกิดเป็นพิกัด $(x',y')$"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "ก่อนอื่นเรามาลองเล่นดูใน widget นี้ว่าเมื่อเปลี่ยน องศา แล้วข้อมูลจะเปลี่ยนไปอย่างไรบ้าง"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "tags": [
          "hide-input"
        ]
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "\n",
              "<!DOCTYPE html>\n",
              "<html>\n",
              "<head>\n",
              "  <style>\n",
              "    canvas {\n",
              "      border: 1px solid black;\n",
              "    }\n",
              "  </style>\n",
              "</head>\n",
              "<body>\n",
              "  <input type=\"range\" id=\"angleSlider\" min=\"-180\" max=\"180\" value=\"0\" step=\"1\">\n",
              "  <div id=\"angleValue\"></div>\n",
              "  <div id=\"transformationMatrix\"></div>\n",
              "  <canvas id=\"canvas\"></canvas>\n",
              "  <script>\n",
              "    // Generate x and y data points from Python code\n",
              "    const numPoints = 50;\n",
              "    const x = [-2.8284271247461903,-2.7129811169126663,-2.5975351161502105,-2.4820891083166865,-2.3666431075542302,-2.2511970997207067,-2.1357510918871827,-2.020305091124727,-1.9048590832912027,-1.789413075457679,-1.6739670746952229,-1.5585210668616991,-1.4430750660992433,-1.3276290582657193,-1.2121830504321953,-1.0967370496697393,-0.9812910418362154,-0.8658450410737594,-0.7503990332402356,-0.6349530254067116,-0.5195070246442557,-0.4040610168107318,-0.2886150160482758,-0.17316900821475187,-0.057723000381228025,0.057723000381228025,0.17316900821475187,0.2886150160482758,0.4040610168107318,0.5195070246442557,0.6349530254067116,0.7503990332402356,0.8658450410737594,0.9812910418362154,1.0967370496697393,1.2121830504321953,1.3276290582657193,1.4430750660992433,1.5585210668616991,1.6739670746952229,1.789413075457679,1.9048590832912027,2.020305091124727,2.1357510918871827,2.2511970997207067,2.3666431075542302,2.4820891083166865,2.5975351161502105,2.7129811169126663,2.8284271247461903];\n",
              "    const y = [-2.82842712474619,-2.7129811169126663,-2.59753511615021,-2.482089108316686,-2.3666431075542302,-2.2511970997207063,-2.1357510918871827,-2.0203050911247264,-1.9048590832912025,-1.7894130754576787,-1.6739670746952227,-1.558521066861699,-1.4430750660992429,-1.327629058265719,-1.212183050432195,-1.096737049669739,-0.9812910418362152,-0.8658450410737593,-0.7503990332402355,-0.6349530254067116,-0.5195070246442556,-0.40406101681073175,-0.2886150160482757,-0.17316900821475184,-0.05772300038122801,0.05772300038122801,0.17316900821475184,0.2886150160482757,0.40406101681073175,0.5195070246442556,0.6349530254067116,0.7503990332402355,0.8658450410737593,0.9812910418362152,1.096737049669739,1.212183050432195,1.327629058265719,1.4430750660992429,1.558521066861699,1.6739670746952227,1.7894130754576787,1.9048590832912025,2.0203050911247264,2.1357510918871827,2.2511970997207063,2.3666431075542302,2.482089108316686,2.59753511615021,2.7129811169126663,2.82842712474619];\n",
              "\n",
              "    // Combine x and y data into points array\n",
              "    const points = x.map((xVal, index) => ({\n",
              "      x: xVal * 50, // Scale x values to fit canvas\n",
              "      y: y[index] * 50, // Scale y values to fit canvas\n",
              "      original: true // Flag to indicate original points\n",
              "    }));\n",
              "\n",
              "    // Get the angle slider element\n",
              "    const angleSlider = document.getElementById('angleSlider');\n",
              "\n",
              "    // Get the value display elements\n",
              "    const angleValue = document.getElementById('angleValue');\n",
              "    const transformationMatrix = document.getElementById('transformationMatrix');\n",
              "\n",
              "    // Get the canvas element\n",
              "    const canvas = document.getElementById('canvas');\n",
              "    const context = canvas.getContext('2d');\n",
              "\n",
              "    // Function to update the rotation based on the slider value\n",
              "    function updateRotation() {\n",
              "      // Angle in degrees\n",
              "      const theta = angleSlider.value;\n",
              "\n",
              "      // Convert angle to radians\n",
              "      const thetaRad = (theta * Math.PI) / 180;\n",
              "\n",
              "      // Rotation matrix\n",
              "      const cosTheta = Math.cos(thetaRad);\n",
              "      const sinTheta = Math.sin(thetaRad);\n",
              "      const rotationMatrix = [\n",
              "        cosTheta, -sinTheta,\n",
              "        sinTheta, cosTheta\n",
              "      ];\n",
              "\n",
              "      // Apply rotation transformation to each point\n",
              "      const rotatedPoints = points.map(point => ({\n",
              "        x: (point.x * rotationMatrix[0]) + (point.y * rotationMatrix[1]),\n",
              "        y: (point.x * rotationMatrix[2]) + (point.y * rotationMatrix[3]),\n",
              "        original: point.original\n",
              "      }));\n",
              "\n",
              "      // Find the maximum distance between the points\n",
              "      const distances = rotatedPoints.map(point => Math.sqrt(point.x ** 2 + point.y ** 2));\n",
              "      const maxDistance = Math.max(...distances);\n",
              "\n",
              "      // Calculate the canvas dimensions based on the maximum distance\n",
              "      const canvasSize = 2 * maxDistance + 20; // Add some padding\n",
              "\n",
              "      // Update canvas dimensions\n",
              "      canvas.width = canvasSize;\n",
              "      canvas.height = canvasSize;\n",
              "\n",
              "      // Calculate the center of the canvas\n",
              "      const centerX = canvas.width / 2;\n",
              "      const centerY = canvas.height / 2;\n",
              "\n",
              "      // Adjust the points to be relative to the center\n",
              "      const adjustedPoints = rotatedPoints.map(point => ({\n",
              "        x: centerX + point.x,\n",
              "        y: centerY - point.y, // Subtract to invert the y-axis\n",
              "        original: false\n",
              "      }));\n",
              "\n",
              "      const adjustedOriginalPoints = points.map(point => ({\n",
              "        x: centerX + point.x,\n",
              "        y: centerY - point.y, // Subtract to invert the y-axis\n",
              "        original: true\n",
              "      }));\n",
              "\n",
              "      // Clear canvas\n",
              "      context.clearRect(0, 0, canvas.width, canvas.height);\n",
              "\n",
              "      // Draw axes\n",
              "      context.beginPath();\n",
              "      context.moveTo(centerX, 0);\n",
              "      context.lineTo(centerX, canvas.height);\n",
              "      context.moveTo(0, centerY);\n",
              "      context.lineTo(canvas.width, centerY);\n",
              "      context.strokeStyle = 'gray';\n",
              "      context.stroke();\n",
              "\n",
              "      // Draw points\n",
              "      adjustedOriginalPoints.forEach((point, i) => {\n",
              "        let alpha = 0.1;\n",
              "\n",
              "        if (i < numPoints/2) {\n",
              "          context.fillStyle = `rgba(0, 0, 255, ${alpha})`; // First half of rotated points with blue color\n",
              "        } else {\n",
              "          context.fillStyle = `rgba(255, 0, 0, ${alpha})`; // Second half of rotated points with red color\n",
              "        }\n",
              "        context.beginPath();\n",
              "        context.arc(point.x, point.y, 4, 0, 2 * Math.PI);\n",
              "        context.fill();\n",
              "      });\n",
              "\n",
              "      adjustedPoints.forEach((point, i) => {\n",
              "        let alpha = 1;\n",
              "\n",
              "        if (i < numPoints/2) {\n",
              "          context.fillStyle = `rgba(0, 0, 255, ${alpha})`; // First half of rotated points with blue color\n",
              "        } else {\n",
              "          context.fillStyle = `rgba(255, 0, 0, ${alpha})`; // Second half of rotated points with red color\n",
              "        }\n",
              "        context.beginPath();\n",
              "        context.arc(point.x, point.y, 4, 0, 2 * Math.PI);\n",
              "        context.fill();\n",
              "      });\n",
              "\n",
              "      // Update angle value display\n",
              "      angleValue.textContent = `Angle: ${theta}°`;\n",
              "\n",
              "      // Update transformation matrix display\n",
              "      transformationMatrix.innerHTML = `\n",
              "        <table>\n",
              "          <tr>\n",
              "            <td>${rotationMatrix[0].toFixed(2)}</td>\n",
              "            <td>${rotationMatrix[1].toFixed(2)}</td>\n",
              "          </tr>\n",
              "          <tr>\n",
              "            <td>${rotationMatrix[2].toFixed(2)}</td>\n",
              "            <td>${rotationMatrix[3].toFixed(2)}</td>\n",
              "          </tr>\n",
              "        </table>\n",
              "      `;\n",
              "    }\n",
              "\n",
              "    // Add event listener to the angle slider\n",
              "    angleSlider.addEventListener('input', updateRotation);\n",
              "\n",
              "    // Initial rotation update\n",
              "    updateRotation();\n",
              "  </script>\n",
              "</body>\n",
              "</html>\n"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "execution_count": 1,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "from IPython.core.display import HTML\n",
        "HTML(\"\"\"\n",
        "<!DOCTYPE html>\n",
        "<html>\n",
        "<head>\n",
        "  <style>\n",
        "    canvas {\n",
        "      border: 1px solid black;\n",
        "    }\n",
        "  </style>\n",
        "</head>\n",
        "<body>\n",
        "  <input type=\"range\" id=\"angleSlider\" min=\"-180\" max=\"180\" value=\"0\" step=\"1\">\n",
        "  <div id=\"angleValue\"></div>\n",
        "  <div id=\"transformationMatrix\"></div>\n",
        "  <canvas id=\"canvas\"></canvas>\n",
        "  <script>\n",
        "    // Generate x and y data points from Python code\n",
        "    const numPoints = 50;\n",
        "    const x = [-2.8284271247461903,-2.7129811169126663,-2.5975351161502105,-2.4820891083166865,-2.3666431075542302,-2.2511970997207067,-2.1357510918871827,-2.020305091124727,-1.9048590832912027,-1.789413075457679,-1.6739670746952229,-1.5585210668616991,-1.4430750660992433,-1.3276290582657193,-1.2121830504321953,-1.0967370496697393,-0.9812910418362154,-0.8658450410737594,-0.7503990332402356,-0.6349530254067116,-0.5195070246442557,-0.4040610168107318,-0.2886150160482758,-0.17316900821475187,-0.057723000381228025,0.057723000381228025,0.17316900821475187,0.2886150160482758,0.4040610168107318,0.5195070246442557,0.6349530254067116,0.7503990332402356,0.8658450410737594,0.9812910418362154,1.0967370496697393,1.2121830504321953,1.3276290582657193,1.4430750660992433,1.5585210668616991,1.6739670746952229,1.789413075457679,1.9048590832912027,2.020305091124727,2.1357510918871827,2.2511970997207067,2.3666431075542302,2.4820891083166865,2.5975351161502105,2.7129811169126663,2.8284271247461903];\n",
        "    const y = [-2.82842712474619,-2.7129811169126663,-2.59753511615021,-2.482089108316686,-2.3666431075542302,-2.2511970997207063,-2.1357510918871827,-2.0203050911247264,-1.9048590832912025,-1.7894130754576787,-1.6739670746952227,-1.558521066861699,-1.4430750660992429,-1.327629058265719,-1.212183050432195,-1.096737049669739,-0.9812910418362152,-0.8658450410737593,-0.7503990332402355,-0.6349530254067116,-0.5195070246442556,-0.40406101681073175,-0.2886150160482757,-0.17316900821475184,-0.05772300038122801,0.05772300038122801,0.17316900821475184,0.2886150160482757,0.40406101681073175,0.5195070246442556,0.6349530254067116,0.7503990332402355,0.8658450410737593,0.9812910418362152,1.096737049669739,1.212183050432195,1.327629058265719,1.4430750660992429,1.558521066861699,1.6739670746952227,1.7894130754576787,1.9048590832912025,2.0203050911247264,2.1357510918871827,2.2511970997207063,2.3666431075542302,2.482089108316686,2.59753511615021,2.7129811169126663,2.82842712474619];\n",
        "\n",
        "    // Combine x and y data into points array\n",
        "    const points = x.map((xVal, index) => ({\n",
        "      x: xVal * 50, // Scale x values to fit canvas\n",
        "      y: y[index] * 50, // Scale y values to fit canvas\n",
        "      original: true // Flag to indicate original points\n",
        "    }));\n",
        "\n",
        "    // Get the angle slider element\n",
        "    const angleSlider = document.getElementById('angleSlider');\n",
        "\n",
        "    // Get the value display elements\n",
        "    const angleValue = document.getElementById('angleValue');\n",
        "    const transformationMatrix = document.getElementById('transformationMatrix');\n",
        "\n",
        "    // Get the canvas element\n",
        "    const canvas = document.getElementById('canvas');\n",
        "    const context = canvas.getContext('2d');\n",
        "\n",
        "    // Function to update the rotation based on the slider value\n",
        "    function updateRotation() {\n",
        "      // Angle in degrees\n",
        "      const theta = angleSlider.value;\n",
        "\n",
        "      // Convert angle to radians\n",
        "      const thetaRad = (theta * Math.PI) / 180;\n",
        "\n",
        "      // Rotation matrix\n",
        "      const cosTheta = Math.cos(thetaRad);\n",
        "      const sinTheta = Math.sin(thetaRad);\n",
        "      const rotationMatrix = [\n",
        "        cosTheta, -sinTheta,\n",
        "        sinTheta, cosTheta\n",
        "      ];\n",
        "\n",
        "      // Apply rotation transformation to each point\n",
        "      const rotatedPoints = points.map(point => ({\n",
        "        x: (point.x * rotationMatrix[0]) + (point.y * rotationMatrix[1]),\n",
        "        y: (point.x * rotationMatrix[2]) + (point.y * rotationMatrix[3]),\n",
        "        original: point.original\n",
        "      }));\n",
        "\n",
        "      // Find the maximum distance between the points\n",
        "      const distances = rotatedPoints.map(point => Math.sqrt(point.x ** 2 + point.y ** 2));\n",
        "      const maxDistance = Math.max(...distances);\n",
        "\n",
        "      // Calculate the canvas dimensions based on the maximum distance\n",
        "      const canvasSize = 2 * maxDistance + 20; // Add some padding\n",
        "\n",
        "      // Update canvas dimensions\n",
        "      canvas.width = canvasSize;\n",
        "      canvas.height = canvasSize;\n",
        "\n",
        "      // Calculate the center of the canvas\n",
        "      const centerX = canvas.width / 2;\n",
        "      const centerY = canvas.height / 2;\n",
        "\n",
        "      // Adjust the points to be relative to the center\n",
        "      const adjustedPoints = rotatedPoints.map(point => ({\n",
        "        x: centerX + point.x,\n",
        "        y: centerY - point.y, // Subtract to invert the y-axis\n",
        "        original: false\n",
        "      }));\n",
        "\n",
        "      const adjustedOriginalPoints = points.map(point => ({\n",
        "        x: centerX + point.x,\n",
        "        y: centerY - point.y, // Subtract to invert the y-axis\n",
        "        original: true\n",
        "      }));\n",
        "\n",
        "      // Clear canvas\n",
        "      context.clearRect(0, 0, canvas.width, canvas.height);\n",
        "\n",
        "      // Draw axes\n",
        "      context.beginPath();\n",
        "      context.moveTo(centerX, 0);\n",
        "      context.lineTo(centerX, canvas.height);\n",
        "      context.moveTo(0, centerY);\n",
        "      context.lineTo(canvas.width, centerY);\n",
        "      context.strokeStyle = 'gray';\n",
        "      context.stroke();\n",
        "\n",
        "      // Draw points\n",
        "      adjustedOriginalPoints.forEach((point, i) => {\n",
        "        let alpha = 0.1;\n",
        "\n",
        "        if (i < numPoints/2) {\n",
        "          context.fillStyle = `rgba(0, 0, 255, ${alpha})`; // First half of rotated points with blue color\n",
        "        } else {\n",
        "          context.fillStyle = `rgba(255, 0, 0, ${alpha})`; // Second half of rotated points with red color\n",
        "        }\n",
        "        context.beginPath();\n",
        "        context.arc(point.x, point.y, 4, 0, 2 * Math.PI);\n",
        "        context.fill();\n",
        "      });\n",
        "\n",
        "      adjustedPoints.forEach((point, i) => {\n",
        "        let alpha = 1;\n",
        "\n",
        "        if (i < numPoints/2) {\n",
        "          context.fillStyle = `rgba(0, 0, 255, ${alpha})`; // First half of rotated points with blue color\n",
        "        } else {\n",
        "          context.fillStyle = `rgba(255, 0, 0, ${alpha})`; // Second half of rotated points with red color\n",
        "        }\n",
        "        context.beginPath();\n",
        "        context.arc(point.x, point.y, 4, 0, 2 * Math.PI);\n",
        "        context.fill();\n",
        "      });\n",
        "\n",
        "      // Update angle value display\n",
        "      angleValue.textContent = `Angle: ${theta}°`;\n",
        "\n",
        "      // Update transformation matrix display\n",
        "      transformationMatrix.innerHTML = `\n",
        "        <table>\n",
        "          <tr>\n",
        "            <td>${rotationMatrix[0].toFixed(2)}</td>\n",
        "            <td>${rotationMatrix[1].toFixed(2)}</td>\n",
        "          </tr>\n",
        "          <tr>\n",
        "            <td>${rotationMatrix[2].toFixed(2)}</td>\n",
        "            <td>${rotationMatrix[3].toFixed(2)}</td>\n",
        "          </tr>\n",
        "        </table>\n",
        "      `;\n",
        "    }\n",
        "\n",
        "    // Add event listener to the angle slider\n",
        "    angleSlider.addEventListener('input', updateRotation);\n",
        "\n",
        "    // Initial rotation update\n",
        "    updateRotation();\n",
        "  </script>\n",
        "</body>\n",
        "</html>\n",
        "\"\"\")"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "ตอนนี้เรามาลองหมุนข้อมูลกันโดยใช้ code ใน cell ถัดมากันดีกว่า"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 609,
          "referenced_widgets": [
            "2d787ffdf4c94dd4a8a88f833496b353",
            "31b8ca5aa2304f068e007da563e8b019",
            "45a8de9b85d54b9ba2bbb977ae083ea9",
            "910620c927354643aed174092199224a",
            "048dd357bc0448d991c54f8b36b515f8",
            "121b0e173d204bfab5ca5bba7c7d2a54",
            "ad58a360753447df9c875caa226f49f3",
            "8f653d9884944f4d925aa5f1ac9d9353",
            "5e0673fe9c9441efb72ab03524f3c015",
            "2b02548563cb44c5baa76da35e740953"
          ]
        },
        "id": "T7QbR_UeHtFs",
        "outputId": "de8251cd-17c2-4046-d60c-b8c2b9420e45"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "2d787ffdf4c94dd4a8a88f833496b353",
              "version_major": 2,
              "version_minor": 0
            },
            "text/plain": [
              "interactive(children=(IntSlider(value=0, description='Angle (deg)', max=180, min=-180), Checkbox(value=True, d…"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def rotate_counterclockwise(data, degree):\n",
        "\n",
        "    # สร้าง rotation matrix R ที่ทำหน้าที่ใช้หมุนพิกัดทวนเข็มนาฬิกา\n",
        "    R = np.array([[np.cos(degree), -np.sin(degree)],\n",
        "                  [np.sin(degree), np.cos(degree)]])\n",
        "\n",
        "    return np.transpose(np.matmul(R, np.transpose(data)))\n",
        "\n",
        "\n",
        "@widgets.interact(angle_counter_clock_degree=widgets.IntSlider(0, min=-180, max=180, description='Angle (deg)'),\n",
        "                  show_original=widgets.Checkbox(True, description='Show original data'))\n",
        "def plot_rotated_results(angle_counter_clock_degree, show_original):\n",
        "\n",
        "    # ทำการหมุนข้อมูล\n",
        "    data_rot = rotate_counterclockwise(data, angle_counter_clock_degree*(np.pi/180))\n",
        "\n",
        "    # สร้าง figure\n",
        "    fig, ax = plt.subplots(figsize=(6,6))\n",
        "\n",
        "    # Plot ข้อมูล x, y ที่มีอยู่ด้วยสีน้ำเงิน\n",
        "    ax.scatter(data_rot[data[:, 0] < 0, 0], data_rot[data[:, 0] < 0, 1], c='b') # Plot จุดข้อมูลที่เป็น class 1\n",
        "    ax.scatter(data_rot[data[:, 0] > 0, 0], data_rot[data[:, 0] > 0, 1], c='r') # Plot จุดข้อมูลที่เป็น class 2\n",
        "    ax.plot([0, 0], [-6.0, 6.0], c=\"m\", alpha=0.5) # Plot แกน y ที่ถูกหมุน\n",
        "    ax.plot([-6.0, 6.0], [0, 0], c=\"m\", alpha=0.5) # Plot แกน x ที่ถูกหมุน\n",
        "\n",
        "\n",
        "    if show_original:\n",
        "        ax.scatter(data[data[:, 0] < 0, 0], data[data[:, 0] < 0, 1], c='b', alpha=0.1) # Plot จุดข้อมูลที่เป็น class 1\n",
        "        ax.scatter(data[data[:, 0] > 0, 0], data[data[:, 0] > 0, 1], c='r', alpha=0.1) # Plot จุดข้อมูลที่เป็น class 2\n",
        "\n",
        "    ax.set_title(f\"Data rotated by {angle_counter_clock_degree} degrees (counter-clockwise centered at (0,0))\")\n",
        "    plt.show()"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {
        "id": "qJLigsRHL6Is"
      },
      "source": [
        "เรามาลองดูว่า ถ้าหมุนจุดข้อมูลเหล่านี้ตามเข็มนาฬิกาไป 45 องศา โดยมีจุดหมุนคือ $(0,0)$ ผลจะเป็นอย่างไร"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 668
        },
        "id": "P-d8rpQyS6ta",
        "outputId": "8ceffb28-81f8-43a4-de39-788ceb840f42"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1200x600 with 2 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 400x50 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# ใช้ rotation matrix คำนวณพิกัดใหม่ของจุดทั้งหมด\n",
        "data_rot45 = rotate_counterclockwise(data, -np.pi/4)\n",
        "\n",
        "# เตรียมแสดงผล\n",
        "x_disp = [-6.0, 6.0] # ค่าต่ำสูงและสูงสุดของ x สำหรับแสดงผล\n",
        "y_disp = [-6.0, 6.0] # ค่าต่ำสูงและสูงสุดของ y สำหรับแสดงผล\n",
        "\n",
        "fig, ax = plt.subplots(1, 2, figsize=(12, 6))\n",
        "\n",
        "# แสดงรูปข้อมูลเริ่มต้น\n",
        "ax[0].scatter(data[data[:, 0] < 0, 0], data[data[:, 0] < 0, 1], c='b') # Plot จุดข้อมูลที่เป็น class 1\n",
        "ax[0].scatter(data[data[:, 0] > 0, 0], data[data[:, 0] > 0, 1], c='r') # Plot จุดข้อมูลที่เป็น class 2\n",
        "ax[0].plot([0, 0], y_disp, c=\"grey\") # Plot แกน y\n",
        "ax[0].plot(x_disp, [0, 0], c=\"grey\") # Plot แกน x\n",
        "ax[0].set(xlabel=\"x\", ylabel=\"y\")\n",
        "ax[0].set_title(\"Data with two classes\")\n",
        "\n",
        "\n",
        "# แสดงรูปหลังหมุนข้อมูลตามเข็มนาฬิกาไป 45 องศา\n",
        "ax[1].scatter(data_rot45[data[:, 0] < 0, 0], data_rot45[data[:, 0] < 0, 1], c='b') # Plot จุดข้อมูลที่เป็น class 1\n",
        "ax[1].scatter(data_rot45[data[:, 0] > 0, 0], data_rot45[data[:, 0] > 0, 1], c='r') # Plot จุดข้อมูลที่เป็น class 2\n",
        "ax[1].plot([0, 0], y_disp, c=\"grey\") # Plot แกน y\n",
        "ax[1].plot(x_disp, [0, 0], c=\"grey\") # Plot แกน x\n",
        "ax[1].set(xlabel=\"Rotated x\", ylabel=\"Rotated y\")\n",
        "ax[1].set_title(\"Rotated data (45 degrees clockwise)\")\n",
        "\n",
        "plt.setp(ax, xlim=x_disp, ylim=y_disp)\n",
        "\n",
        "# Plot ข้อมูลที่ลดมิติมาแล้ว\n",
        "plt.figure(figsize=(4, 0.5))\n",
        "plt.scatter(data_rot45[data[:, 0] < 0, 0], np.zeros_like(data_rot45[data[:, 0] < 0, 0]), c='b') # Plot จุดข้อมูลที่เป็น class 1\n",
        "plt.scatter(data_rot45[data[:, 0] > 0, 0], np.zeros_like(data_rot45[data[:, 0] > 0, 0]), c='r') # Plot จุดข้อมูลที่เป็น class 2\n",
        "plt.plot([0, 0], y_disp, c=\"grey\") # Plot แกน y\n",
        "plt.plot(x_disp, [0, 0], c=\"grey\") # Plot แกน x\n",
        "plt.xlim(x_disp)\n",
        "plt.ylim(-0.5, 0.5)\n",
        "plt.title(\"Rotated data with two classes in 1-dimensional space\")\n",
        "plt.yticks([])\n",
        "plt.show()\n",
        "\n",
        "\n",
        "plt.show()"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {
        "id": "8uJxbarnceuh"
      },
      "source": [
        "มีข้อสังเกตดังนี้\n",
        "\n",
        "\n",
        "*   ข้อมูลเริ่มต้นอยู่ใน space ขนาด 2 มิติ โดยมีลักษณะเป็นเส้นตรงที่ทำมุม $45$ องศากับแกน $x$\n",
        "\n",
        "*   ถ้าหากเราหมุนจุดข้อมูลเหล่านั้นตามเข็มนาฬิกาไป $45$ องศา เราจะเห็นข้อมูลจัดเรียงกันอยู่บนแกน $x$ โดยที่ค่าใน แกน $y$ ทุกตัวเป็น $0$\n",
        "\n",
        "* ถ้าหากเราต้องการจะ classify ข้อมูลนี้ เราสามารถทำได้โดยการดูแค่ค่าในแกน $x$ (ไม่ต้องดูแกน $y$ เลย) แสดงว่าเราสามารถลดจำนวนมิติของข้อมูลให้เหลือ $1$ มิติได้ โดยที่ยังมีความสามารถในการทำ classification ได้เหมือนเดิม\n",
        "\n",
        "<br><br>\n",
        "\n",
        "จะเห็นได้ว่าในหลาย ๆ ครั้ง เราสามารถลดจำนวนมิติได้  ซึ่งในตัวอย่างเหล่านี้เราแค่ใช้การ transform จุดข้อมูลอย่างง่าย เช่น การหมุน ก็ส่งผลให้ข้อมูลมาอยู่ในรูปแบบที่เราสามารถกำจัดแกน $y$ ได้เลย ส่งผลให้จำนวนมิติลดลงจาก 2 มิติ ไปเป็น 1 มิติ\n",
        "และเรายังพบว่าเราสามารถนำเอาข้อมูลใน 1 มิตินี้ไปใช้งานต่อได้ เช่น เรายังสามารถนำเอาไปใช้เป็น feature ในการ classify ได้เหมือนเดิม"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {
        "id": "zAQOn8urHNfg"
      },
      "source": [
        "---\n",
        "\n",
        "\n",
        "\n",
        "**ข้อสังเกต** ในตัวอย่างล่าสุด เราหมุนจุดข้อมูลไป $45$ องศาแบบตามเข็มนาฬิกา โดยที่ไม่ขยับแกน $x$ และ แกน $y$ เลย ซึ่งการทำแบบนี้ ในอีกมุมมองนึง ก็เหมือนกับการหมุนแกน $x$ และ แกน $y$ ไป $45$ องศาแบบทวนเข็มนาฬิกา โดยที่ไม่ขยับจุดข้อมูล ซึ่งเราจะใช้สีชมพูเข้มแสดงแกน $x$ ที่ถูกหมุน และ สีชมพูอ่อนแสดงแกน $y$ ที่ถูกหมุน (แล้วเอียงศีรษะไป $45$ องศาทวนเข็มนาฬิกาขณะดูภาพ) ดังแสดงด้วยตัวอย่าง code ใน cell ถัดมา"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "SujC2Kh4NJ2O",
        "outputId": "a9ac2bb4-4746-408b-ec91-4bf17859ac4a"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 950x600 with 2 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1800x600 with 3 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "fig, ax = plt.subplots(1, 2, figsize=(9.5, 6))\n",
        "\n",
        "# แสดงรูปข้อมูลเริ่มต้น\n",
        "ax[0].scatter(data[data[:, 0] < 0, 0], data[data[:, 0] < 0, 1], c='b') # Plot จุดข้อมูลที่เป็น class 1\n",
        "ax[0].scatter(data[data[:, 0] > 0, 0], data[data[:, 0] > 0, 1], c='r') # Plot จุดข้อมูลที่เป็น class 2\n",
        "ax[0].plot([0, 0], y_disp, c=\"grey\") # Plot แกน y\n",
        "ax[0].plot(x_disp, [0, 0], c=\"grey\") # Plot แกน x\n",
        "ax[0].set(xlabel=\"x\", ylabel=\"y\")\n",
        "ax[0].set_title(\"Original data\")\n",
        "\n",
        "\n",
        "# แสดงรูปหลังหมุนข้อมูลตามเข็มนาฬิกาไป 45 องศา\n",
        "ax[1].scatter(data_rot45[data[:, 0] < 0, 0], data_rot45[data[:, 0] < 0, 1], c='b') # Plot จุดข้อมูลที่เป็น class 1\n",
        "ax[1].scatter(data_rot45[data[:, 0] > 0, 0], data_rot45[data[:, 0] > 0, 1], c='r') # Plot จุดข้อมูลที่เป็น class 2\n",
        "ax[1].plot([0, 0], y_disp, c=\"grey\") # Plot แกน y\n",
        "ax[1].plot(x_disp, [0, 0], c=\"grey\") # Plot แกน x\n",
        "ax[1].set(xlabel=\"Rotated x\", ylabel=\"Rotated y\")\n",
        "ax[1].set_title(\"Rotated data (45 degrees clockwise)\")\n",
        "\n",
        "fig, ax = plt.subplots(1, 3, figsize=(18, 6))\n",
        "\n",
        "# แสดงรูปข้อมูลเริ่มต้น\n",
        "ax[0].scatter(data[data[:, 0] < 0, 0], data[data[:, 0] < 0, 1], c='b') # Plot จุดข้อมูลที่เป็น class 1\n",
        "ax[0].scatter(data[data[:, 0] > 0, 0], data[data[:, 0] > 0, 1], c='r') # Plot จุดข้อมูลที่เป็น class 2\n",
        "ax[0].plot([0, 0], y_disp, c=\"grey\") # Plot แกน y\n",
        "ax[0].plot(x_disp, [0, 0], c=\"grey\") # Plot แกน x\n",
        "ax[0].set(xlabel=\"x\", ylabel=\"y\")\n",
        "ax[0].set_title(\"Original data\")\n",
        "\n",
        "# แสดงรูปข้อมูลที่มีการหมุนแกนทวนเข็มนาฬิการไป 45 องศา\n",
        "\n",
        "# แสดงรูปข้อมูลเริ่มต้นโดยมี principal component ทั้ง 2 อันแสดงอยู่ด้วย\n",
        "ax[1].scatter(data[data[:, 0] < 0, 0], data[data[:, 0] < 0, 1], c='b') # Plot จุดข้อมูลที่เป็น class 1\n",
        "ax[1].scatter(data[data[:, 0] > 0, 0], data[data[:, 0] > 0, 1], c='r') # Plot จุดข้อมูลที่เป็น class 2\n",
        "ax[1].plot(x_disp, [x_disp[0], x_disp[1]], c=\"m\", alpha=1) # แสดง pc1 โดยใช้สมการ y = x\n",
        "ax[1].plot(x_disp, [-x_disp[0], -x_disp[1]], c=\"m\", alpha=0.3) # แสดง pc2 โดยใช้สมการ y = -x\n",
        "ax[1].set(xlabel='x', ylabel='y')\n",
        "ax[1].set_title(\"Original data with the rotated axes\")\n",
        "\n",
        "# แสดงข้อมูลที่หมุนแกนและเอียงศีรษะดู\n",
        "ax[2].scatter(data_rot45[data[:, 0] < 0, 0], data_rot45[data[:, 0] < 0, 1], c='b') # Plot จุดข้อมูลที่เป็น class 1\n",
        "ax[2].scatter(data_rot45[data[:, 0] > 0, 0], data_rot45[data[:, 0] > 0, 1], c='r') # Plot จุดข้อมูลที่เป็น class 2\n",
        "ax[2].plot(x_disp, [0, 0], c=\"m\", alpha=1)\n",
        "ax[2].plot([0, 0], y_disp, c=\"m\", alpha=0.3)\n",
        "ax[2].set(xlabel=\"Rotated x\", ylabel=\"Rotated y\")\n",
        "ax[2].set_title(\"Rotating your head by 45 degrees and look at the previous plot\")\n",
        "\n",
        "plt.setp(ax, xlim=x_disp, ylim=y_disp)\n",
        "plt.show()"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "metadata": {
        "id": "2iqRDO8xNa2J"
      },
      "source": [
        "<br><br>\n",
        "\n",
        "ในสถานการณ์การทำงานจริง เรามักเจอข้อมูลที่มีความซับซ้อนมาก เช่น ข้อมูลที่อยู่ใน space ที่มีจำนวนมิติสูงมาก เราอาจจะไม่สามารถใช้การ transform แบบง่าย ๆ ที่เราใช้ในตัวอย่างนี้ จึงมีเทคนิคมากมายถูกคิดค้นขึ้นเพื่อใช้ช่วยลดมิติของข้อมูลของเราได้อย่างมีประสิทธิภาพ"
      ]
    },
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        "**ผู้จัดเตรียม code ใน tutorial**: ดร. อิทธิ ฉัตรนันทเวช และ ดร. สุรัฐ ธีรพิทยานนท์"
      ]
    }
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\n",
                  "text/plain": "<Figure size 600x600 with 1 Axes>"
                },
                "metadata": {},
                "output_type": "display_data"
              }
            ]
          }
        },
        "ad58a360753447df9c875caa226f49f3": {
          "model_module": "@jupyter-widgets/controls",
          "model_module_version": "1.5.0",
          "model_name": "SliderStyleModel",
          "state": {
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "SliderStyleModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "StyleView",
            "description_width": "",
            "handle_color": null
          }
        }
      }
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}