{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ea0786c2",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# A quick introduction to machine learning\n",
    "\n",
    "\n",
    "- These notebooks are a brief, hands-on, introduction to machine learning.\n",
    "- We will revise some of the nomenclature, principles, and applications from [Valentina's presentation](https://github.com/oceanhackweek/ohw-tutorials/tree/OHW22/01-Tue/01-machine-learning-intro)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a4c4301",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## ML will solve all of our problems, right?\n",
    "\n",
    "![](cow.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "987fda81",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## What is Machine Learning (ML)?\n",
    "\n",
    "**Caveat:** I'm not a Statistician, Mathematician, or ML expert. I only play one online. You can find my work on movies like \"How to get by with little to no data\" or \"Oh gosh, the PI wants some buzz-words in the report\" and \"Fuzzy logic no longer does it, we need ML → AI → DL\"\n",
    "\n",
    "What is ML (a personal point of view):\n",
    "\n",
    "* Focus on practical problems\n",
    "* Learn from the data and/or make predictions with it\n",
    "* Middle ground between statistics and optimization techniques\n",
    "* We have fast computers now, right? Let them do the work! ([Must see JVP talk on this](https://www.youtube.com/watch?app=desktop&v=Iq9DzN6mvYA).)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00cc5ce5",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Oversimplified take:** Fit a model to data and use it to make predictions. (This is how scikit-learn designed its API BTW)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2cf395e",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Vocabulary \n",
    "\n",
    "\n",
    "- **parameters:** Variables that define the model and control its behavior.\n",
    "\n",
    "- **model:** Set of mathematical equations used to approximate the data.\n",
    "\n",
    "- **labels/classes:** Quantity/category that we want to predict\n",
    "\n",
    "- **features:** Observations (information) used as predictors of labels/classes.\n",
    "\n",
    "- **training:** Use **features** and known **labels/classes** to fit the **model** estimate its **parameters** (full circle, right? But why stop now?).\n",
    "\n",
    "Please check out [this awesome lecture](https://docs.google.com/presentation/d/1Fa9SuyK9DIpd-MkJJjGqjCbAa-sHtr3qufC9MhmewDQ/edit) on ML for climate science."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed4313fa",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- **hyper-parameters:** Variables that influence the **training** and the **model** but are not estimated during training.\n",
    "- **unsupervised learning:** Extract information and structure from the data without **training** with known **labels**. We will see clustering, and Principal Component Analysis (PCA).\n",
    "\n",
    "- **supervised learning:** Fit a model using data to \"train\" it for making predictions. Examples: regression, classification, spam detection, recommendation systems. We'll see KNN, a classification type of ML in this tutorial."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97fe276c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Unsupervised: PCA\n",
    "\n",
    "The dataset we will use was consists of Red, Green, Blue composites (**parameters**) from plastic pellets photos. We also have some extra information on the pellet size, shape, etc.\n",
    "\n",
    "The **labels** are the yellowing index. The goal is to predict the yellowing based the pellets image, broken down to its RGB info."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6f449af4",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "048ff44d",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>r</th>\n",
       "      <th>g</th>\n",
       "      <th>b</th>\n",
       "      <th>size (mm)</th>\n",
       "      <th>color</th>\n",
       "      <th>description</th>\n",
       "      <th>erosion</th>\n",
       "      <th>erosion index</th>\n",
       "      <th>yellowing</th>\n",
       "      <th>yellowing index</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>image</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>cl1_p11_moca2_deixa5_a0001</th>\n",
       "      <td>152</td>\n",
       "      <td>150</td>\n",
       "      <td>143</td>\n",
       "      <td>4.021</td>\n",
       "      <td>transparent</td>\n",
       "      <td>sphere</td>\n",
       "      <td>high erosion</td>\n",
       "      <td>3</td>\n",
       "      <td>low</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cl1_p12_lagoinha_deixa1_g0006</th>\n",
       "      <td>221</td>\n",
       "      <td>218</td>\n",
       "      <td>219</td>\n",
       "      <td>4.244</td>\n",
       "      <td>white</td>\n",
       "      <td>light erosion</td>\n",
       "      <td>low erosion</td>\n",
       "      <td>1</td>\n",
       "      <td>low</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cl1_p12_lagoinha_deixa1_g0007</th>\n",
       "      <td>140</td>\n",
       "      <td>137</td>\n",
       "      <td>129</td>\n",
       "      <td>3.946</td>\n",
       "      <td>white</td>\n",
       "      <td>not erosion</td>\n",
       "      <td>low erosion</td>\n",
       "      <td>1</td>\n",
       "      <td>low</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cl1_p12_lagoinha_deixa1_g0008</th>\n",
       "      <td>188</td>\n",
       "      <td>178</td>\n",
       "      <td>146</td>\n",
       "      <td>3.948</td>\n",
       "      <td>white</td>\n",
       "      <td>moderate erosion</td>\n",
       "      <td>high erosion</td>\n",
       "      <td>3</td>\n",
       "      <td>moderate</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cl1_p12_lagoinha_deixa2_h0004</th>\n",
       "      <td>207</td>\n",
       "      <td>200</td>\n",
       "      <td>189</td>\n",
       "      <td>6.043</td>\n",
       "      <td>white</td>\n",
       "      <td>light erosion</td>\n",
       "      <td>low erosion</td>\n",
       "      <td>1</td>\n",
       "      <td>moderate</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cl1_p6_moca2_deixa3_a0006</th>\n",
       "      <td>186</td>\n",
       "      <td>193</td>\n",
       "      <td>155</td>\n",
       "      <td>4.546</td>\n",
       "      <td>transparent</td>\n",
       "      <td>cylinder</td>\n",
       "      <td>moderate erosion</td>\n",
       "      <td>2</td>\n",
       "      <td>low</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cl1_p8_moca2_deixa5_b0001</th>\n",
       "      <td>169</td>\n",
       "      <td>168</td>\n",
       "      <td>106</td>\n",
       "      <td>3.082</td>\n",
       "      <td>transparent</td>\n",
       "      <td>sphere</td>\n",
       "      <td>low erosion</td>\n",
       "      <td>1</td>\n",
       "      <td>low</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cl1_p8_moca2_deixa5_b0003</th>\n",
       "      <td>191</td>\n",
       "      <td>189</td>\n",
       "      <td>152</td>\n",
       "      <td>3.932</td>\n",
       "      <td>white</td>\n",
       "      <td>sphere</td>\n",
       "      <td>low erosion</td>\n",
       "      <td>1</td>\n",
       "      <td>low</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cl1_p8_moca2_deixa5_b0004</th>\n",
       "      <td>181</td>\n",
       "      <td>156</td>\n",
       "      <td>70</td>\n",
       "      <td>3.230</td>\n",
       "      <td>white</td>\n",
       "      <td>sphere</td>\n",
       "      <td>moderate erosion</td>\n",
       "      <td>3</td>\n",
       "      <td>moderate</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cl1_p9_moca2_deixa5_b0001</th>\n",
       "      <td>193</td>\n",
       "      <td>192</td>\n",
       "      <td>198</td>\n",
       "      <td>3.763</td>\n",
       "      <td>transparent</td>\n",
       "      <td>sphere</td>\n",
       "      <td>high erosion</td>\n",
       "      <td>3</td>\n",
       "      <td>low</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>127 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                                 r    g    b  size (mm)        color  \\\n",
       "image                                                                  \n",
       "cl1_p11_moca2_deixa5_a0001     152  150  143      4.021  transparent   \n",
       "cl1_p12_lagoinha_deixa1_g0006  221  218  219      4.244        white   \n",
       "cl1_p12_lagoinha_deixa1_g0007  140  137  129      3.946        white   \n",
       "cl1_p12_lagoinha_deixa1_g0008  188  178  146      3.948        white   \n",
       "cl1_p12_lagoinha_deixa2_h0004  207  200  189      6.043        white   \n",
       "...                            ...  ...  ...        ...          ...   \n",
       "cl1_p6_moca2_deixa3_a0006      186  193  155      4.546  transparent   \n",
       "cl1_p8_moca2_deixa5_b0001      169  168  106      3.082  transparent   \n",
       "cl1_p8_moca2_deixa5_b0003      191  189  152      3.932        white   \n",
       "cl1_p8_moca2_deixa5_b0004      181  156   70      3.230        white   \n",
       "cl1_p9_moca2_deixa5_b0001      193  192  198      3.763  transparent   \n",
       "\n",
       "                                    description           erosion  \\\n",
       "image                                                               \n",
       "cl1_p11_moca2_deixa5_a0001               sphere      high erosion   \n",
       "cl1_p12_lagoinha_deixa1_g0006     light erosion       low erosion   \n",
       "cl1_p12_lagoinha_deixa1_g0007       not erosion       low erosion   \n",
       "cl1_p12_lagoinha_deixa1_g0008  moderate erosion      high erosion   \n",
       "cl1_p12_lagoinha_deixa2_h0004     light erosion       low erosion   \n",
       "...                                         ...               ...   \n",
       "cl1_p6_moca2_deixa3_a0006              cylinder  moderate erosion   \n",
       "cl1_p8_moca2_deixa5_b0001                sphere       low erosion   \n",
       "cl1_p8_moca2_deixa5_b0003                sphere       low erosion   \n",
       "cl1_p8_moca2_deixa5_b0004                sphere  moderate erosion   \n",
       "cl1_p9_moca2_deixa5_b0001                sphere      high erosion   \n",
       "\n",
       "                               erosion index yellowing  yellowing index  \n",
       "image                                                                    \n",
       "cl1_p11_moca2_deixa5_a0001                 3       low                1  \n",
       "cl1_p12_lagoinha_deixa1_g0006              1       low                1  \n",
       "cl1_p12_lagoinha_deixa1_g0007              1       low                1  \n",
       "cl1_p12_lagoinha_deixa1_g0008              3  moderate                2  \n",
       "cl1_p12_lagoinha_deixa2_h0004              1  moderate                2  \n",
       "...                                      ...       ...              ...  \n",
       "cl1_p6_moca2_deixa3_a0006                  2       low                1  \n",
       "cl1_p8_moca2_deixa5_b0001                  1       low                1  \n",
       "cl1_p8_moca2_deixa5_b0003                  1       low                1  \n",
       "cl1_p8_moca2_deixa5_b0004                  3  moderate                2  \n",
       "cl1_p9_moca2_deixa5_b0001                  3       low                1  \n",
       "\n",
       "[127 rows x 10 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"pellets-visual-classes-rgb.csv\", index_col=\"image\").dropna()\n",
    "df[\"yellowing index\"] = df[\"yellowing index\"].astype(int)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "121bde11",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def histograms():\n",
    "    fig, axes = plt.subplots(figsize=(11, 11), nrows=2, ncols=2)\n",
    "\n",
    "    axes = axes.ravel()\n",
    "\n",
    "    df[\"erosion\"].value_counts().plot.barh(ax=axes[0], title=\"erosion\")\n",
    "    df[\"color\"].value_counts().plot.barh(ax=axes[1], title=\"color\")\n",
    "    df[\"description\"].value_counts().plot.barh(ax=axes[2], title=\"description\")\n",
    "    df[\"yellowing\"].value_counts().plot.barh(ax=axes[3], title=\"yellowing\")\n",
    "\n",
    "    axes[1].yaxis.set_label_position(\"right\")\n",
    "    axes[1].yaxis.tick_right()\n",
    "\n",
    "    axes[3].yaxis.set_label_position(\"right\")\n",
    "    axes[3].yaxis.tick_right()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5f6c5a63",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 1100x1100 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "histograms();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d00fb82b",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We will be using only the R, G, B data for now."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "82ef1547",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "RGB = df[[\"r\", \"g\", \"b\"]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9c3c0700",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import seaborn\n",
    "\n",
    "corr = RGB.corr()\n",
    "\n",
    "seaborn.heatmap(corr, vmin=-1, vmax=1, annot=True);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "614f713c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The first step to most ML techniques is to standardize the data. We do not want high variance data to bias our model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9dd44aa7",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "r    1.0\n",
       "g    1.0\n",
       "b    1.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def z_score(x):\n",
    "    return (x - x.mean()) / x.std()\n",
    "\n",
    "\n",
    "zs = RGB.apply(z_score).T\n",
    "\n",
    "zs.std(axis=1)  # Should be 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "9a5930af",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "r    3.020331e-16\n",
       "g    4.056248e-16\n",
       "b   -1.188900e-16\n",
       "dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zs.mean(axis=1)  # Should be zero"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "82f65e58",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(n_components=None)\n",
    "pca.fit(zs);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41df5061",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The pca object, or fitted model, was designed before pandas existed and it is based on numpy arrays. We can do better nowadays and add meaningful labels to it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1f8a6e3a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TS 1</th>\n",
       "      <th>TS 2</th>\n",
       "      <th>TS 3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>PC 1</th>\n",
       "      <td>0.106617</td>\n",
       "      <td>-0.020035</td>\n",
       "      <td>0.796085</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PC 2</th>\n",
       "      <td>0.038558</td>\n",
       "      <td>-0.015377</td>\n",
       "      <td>0.045291</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PC 3</th>\n",
       "      <td>0.118255</td>\n",
       "      <td>-0.029110</td>\n",
       "      <td>-0.071213</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PC 4</th>\n",
       "      <td>0.032419</td>\n",
       "      <td>-0.036895</td>\n",
       "      <td>-0.025253</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PC 5</th>\n",
       "      <td>0.037738</td>\n",
       "      <td>-0.033506</td>\n",
       "      <td>0.003937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PC 123</th>\n",
       "      <td>0.037121</td>\n",
       "      <td>0.082580</td>\n",
       "      <td>0.065741</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PC 124</th>\n",
       "      <td>0.023213</td>\n",
       "      <td>0.049475</td>\n",
       "      <td>0.000340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PC 125</th>\n",
       "      <td>0.027663</td>\n",
       "      <td>0.022751</td>\n",
       "      <td>-0.036524</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PC 126</th>\n",
       "      <td>-0.032039</td>\n",
       "      <td>-0.082355</td>\n",
       "      <td>0.004122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PC 127</th>\n",
       "      <td>0.076820</td>\n",
       "      <td>-0.015290</td>\n",
       "      <td>-0.064717</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>127 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            TS 1      TS 2      TS 3\n",
       "PC 1    0.106617 -0.020035  0.796085\n",
       "PC 2    0.038558 -0.015377  0.045291\n",
       "PC 3    0.118255 -0.029110 -0.071213\n",
       "PC 4    0.032419 -0.036895 -0.025253\n",
       "PC 5    0.037738 -0.033506  0.003937\n",
       "...          ...       ...       ...\n",
       "PC 123  0.037121  0.082580  0.065741\n",
       "PC 124  0.023213  0.049475  0.000340\n",
       "PC 125  0.027663  0.022751 -0.036524\n",
       "PC 126 -0.032039 -0.082355  0.004122\n",
       "PC 127  0.076820 -0.015290 -0.064717\n",
       "\n",
       "[127 rows x 3 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loadings = pd.DataFrame(pca.components_.T)\n",
    "loadings.index = [\"PC %s\" % pc for pc in loadings.index + 1]\n",
    "loadings.columns = [\"TS %s\" % pc for pc in loadings.columns + 1]\n",
    "loadings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "78ce6ab9",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "PCs = np.dot(loadings.values.T, RGB)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "179811b8",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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///M/V10UAAAAuhjUTp06pbS0tE7709LSdOrUqasuCgAAAF0MauHh4aquru60v7q6WmFhPOcdAACgO3QpVX3ve9/T9u3bO+3ftm2bvve9711tTQAAAFAX91HLzc3V9OnTlZycrHnz5ik8PFyS1NraqnXr1qmwsFCvvvpqjxQKAADQ33R5H7Xly5eroKBAsbGxuummm+RwOHTq1Ck1NDToiSee0MqVK3uq1h7DPmoAAKC3dCV3fKMNb48cOaJXXnlFH3/8sYwxGjZsmGbOnHnNPpSdoAYAAHpLV3JHl976/OKLL/TEE09o+/btamlpUXZ2ttasWaOEhISrKhgAAADtdelmgqeeekobN27UxIkTNWPGDO3Zs0fz5s3rqdoAAAD6tS6tqG3dulUvvPCCpk+fLkl6+OGHdffdd6u1tdW6sQAAAADdo0srapWVlfrBD35gvb7zzjsVERFx2b3VAAAA8M10Kai1trYqKioqqC0iIkIXLlzo1qIAAADQxbc+jTHKycmR0+m02r788kvNnTtXMTExVtvWrVu7r0IAAIB+qktBbdasWe3afvrTn3ZbMQAAAPi7LgW1oqKinqoDAAAAl+AJ6gAAADZFUAMAALApghoAAIBNEdQAAABsiqAGAABgUwQ1AAAAmyKoAQAA2BRBDQAAwKYIagAAADZFUAMAALApghoAAIBNEdQAAABsiqAGAABgUwQ1AAAAmyKoAQAA2BRBDQAAwKYIagAAADZFUAMAALCpkAa1kpISTZ48WR6PRw6HQ9u3bw/qz8nJkcPhCDpGjRoVNKapqUl5eXlKSEhQTEyMpkyZoqqqql48CwAAgJ4R0qB2/vx5jRgxQmvXru10zP3336+amhrr2LVrV1B/fn6+tm3bps2bN+vAgQNqaGjQpEmT1Nra2tPlAwAA9KiIUH7zBx54QA888MBlxzidTrnd7g77fD6fXnjhBW3atEnjxo2TJL388stKSUnRnj17NGHChG6vGQAAoLfY/hq1t99+W0OGDNGwYcP06KOPqra21uorLS1VS0uLxo8fb7V5PB6lp6fr0KFDnX7NpqYm+f3+oAMAAMBubB3UHnjgAb3yyivau3evVq1apSNHjui+++5TU1OTJMnr9SoqKkqDBg0K+rzExER5vd5Ov25BQYFcLpd1pKSk9Oh5AAAAfBMhfevzSqZNm2Z9nJ6erjvuuENDhw7VG2+8oR/96Eedfp4xRg6Ho9P+pUuXauHChdZrv99PWAMAALZj6xW1SyUlJWno0KH6+OOPJUlut1vNzc2qq6sLGldbW6vExMROv47T6VRcXFzQAQAAYDfXVFD7y1/+osrKSiUlJUmSMjIyFBkZqeLiYmtMTU2NysvLNWbMmFCVCQAA0C1C+tZnQ0ODPvnkE+v16dOndfz4ccXHxys+Pl4rVqzQj3/8YyUlJamiokLLli1TQkKCHnzwQUmSy+XS7NmztWjRIl1//fWKj4/X4sWLNXz4cOsuUAAAgGtVSIPa+++/r6ysLOv1xevGZs2apfXr16usrEwvvfSSzp07p6SkJGVlZel3v/udYmNjrc8pLCxURESEHnroITU2Nio7O1sbN25UeHh4r58PAABAd3IYY0yoiwg1v98vl8sln8/H9WoAAKBHdSV3XFPXqAEAAPQnBDUAAACbIqgBAADYFEENAADApghqAAAANkVQAwAAsCmCGgAAgE0R1AAAAGyKoAYAAGBTBDUAAACbIqgBAADYFEENAADApghqAAAANkVQAwAAsCmCGgAAgE0R1AAAAGyKoAYAAGBTBDUAAACbIqgBAADYFEENAADApghqAAAANkVQAwAAsCmCGgAAgE0R1AAAAGyKoAYAAGBTBDUAAACbIqgBAADYFEENAADApghqAAAANkVQAwAAsCmCGgAAgE0R1AAAAGyKoAYAAGBTBDUAAACbIqgBAADYFEENAADApghqAAAANkVQAwAAsCmCGgAAgE0R1AAAAGyKoAYAAGBTBDUAAACbIqiFWHNzc6hLAAAANhUR6gL6m8zMTKWnpysqKkovvfSS/vEf/1H79+8PdVkAAMCGCGoh8OKLL2revHk6ePCgjDGhLgcAANgUQa2XGCO1tAQ+vuWWW/Tcc8+FtiAAAGB7Ib1GraSkRJMnT5bH45HD4dD27duD+o0xWrFihTwej6Kjo5WZmakPPvggaExTU5Py8vKUkJCgmJgYTZkyRVVVVb14Fpfn9UrbtklLlkj5+dKpU1JCwh3yekNdGQAAsLuQBrXz589rxIgRWrt2bYf9zz33nFavXq21a9fqyJEjcrvd+uEPf6j6+nprTH5+vrZt26bNmzfrwIEDamho0KRJk9Ta2tpbp9GpsjLpmWekTZuks2f/vqp2+nSMnnkm0A8AANAZh7HJRVIOh0Pbtm3T1KlTJQVW0zwej/Lz8/Xkk09KCqyeJSYm6le/+pUee+wx+Xw+DR48WJs2bdK0adMkSdXV1UpJSdGuXbs0YcKEDr9XU1OTmpqarNd+v18pKSny+XyKi4vrlvPxegMh7exZadgwKexvkXjjxkwlJt6u1NTnNXiwtHy55HZ3y7cEAADXAL/fL5fL9bVyh2235zh9+rS8Xq/Gjx9vtTmdTo0dO1aHDh2SJJWWlqqlpSVojMfjUXp6ujWmIwUFBXK5XNaRkpLS7fW/+6505kxwSLvI4Qi0V1VJhw93+7cGAAB9hG2DmvdvF3ElJiYGtScmJlp9Xq9XUVFRGjRoUKdjOrJ06VL5fD7rqKys7NbajZEOHZLi4tqHtIvCwiSXSzp4MDAeAADgUra/69PhcAS9Nsa0a7vUlcY4nU45nc5uqa8jLS3S+fNSdHT7vpyct62Po6MD4y5ckCIje6wcAABwjbLtipr7bxduXboyVltba62yud1uNTc3q66urtMxoRAZKcXESI2Nlx/X2BgYF2H7uAwAAELBtkEtNTVVbrdbxcXFVltzc7P279+vMWPGSJIyMjIUGRkZNKampkbl5eXWmFBwOKQxYyS/X2pr63hMW5vk80l33x0YDwAAcKmQruU0NDTok08+sV6fPn1ax48fV3x8vL797W8rPz9fzz77rNLS0pSWlqZnn31W1113nWbOnClJcrlcmj17thYtWqTrr79e8fHxWrx4sYYPH65x48aF6rQkSaNHS3v3Sh991P6Ggra2QHtysjRqVOhqBAAA9hbSoPb+++8rKyvLer1w4UJJ0qxZs7Rx40YtWbJEjY2Nevzxx1VXV6e77rpLu3fvVmxsrPU5hYWFioiI0EMPPaTGxkZlZ2dr48aNCg8P7/Xz+Sq3W5ozR9qwIbBfmssVuCatsTGwkpacHOhnaw4AANAZ2+yjFkpd2c+kq7zewBYcBw8GbhyIiQm83TlqFCENAID+qCu5g6Cmng1qF118KkFkJNekAQDQn3Uld3C/YS9xOKSoqFBXAQAAriW2vesTAACgv2NFTYENcqXAUiQAAEBPupg3vs7VZwQ1SfX19ZLUI8/8BAAA6Eh9fb1cLtdlx3AzgaS2tjZVV1crNjb2io+nuhb4/X6lpKSosrKyx26OuNYxR1fGHF0Zc/T1ME9XxhxdWV+aI2OM6uvr5fF4FNbZQ8H/hhU1SWFhYUpOTg51Gd0uLi7umv9h7mnM0ZUxR1fGHH09zNOVMUdX1lfm6EoraRdxMwEAAIBNEdQAAABsiqDWBzmdTj311FNyOp2hLsW2mKMrY46ujDn6epinK2OOrqy/zhE3EwAAANgUK2oAAAA2RVADAACwKYIaAACATRHUAAAAbIqgdo2qqKjQ7NmzlZqaqujoaN1888166qmn1NzcHDTuz3/+syZPnqyYmBglJCToX/7lX9qNKSsr09ixYxUdHa0bbrhBv/jFL77W88euFc8884zGjBmj6667Tt/61rc6HMM8tbdu3TqlpqZqwIABysjI0DvvvBPqknpNSUmJJk+eLI/HI4fDoe3btwf1G2O0YsUKeTweRUdHKzMzUx988EHQmKamJuXl5SkhIUExMTGaMmWKqqqqevEsek5BQYFGjhyp2NhYDRkyRFOnTtXJkyeDxvT3OVq/fr1uu+02a3PW0aNH680337T6+/v8dKSgoEAOh0P5+flWG/MkyeCa9Oabb5qcnBzzv//7v+bUqVNmx44dZsiQIWbRokXWmAsXLpj09HSTlZVljh49aoqLi43H4zG5ubnWGJ/PZxITE8306dNNWVmZ2bJli4mNjTX/8R//EYrT6hH/9m//ZlavXm0WLlxoXC5Xu37mqb3NmzebyMhI89///d/mww8/NAsWLDAxMTHm008/DXVpvWLXrl1m+fLlZsuWLUaS2bZtW1D/ypUrTWxsrNmyZYspKysz06ZNM0lJScbv91tj5s6da2644QZTXFxsjh49arKyssyIESPMhQsXevlsut+ECRNMUVGRKS8vN8ePHzcTJ0403/72t01DQ4M1pr/P0c6dO80bb7xhTp48aU6ePGmWLVtmIiMjTXl5uTGG+bnUe++9Z2688UZz2223mQULFljtzJMxBLU+5LnnnjOpqanW6127dpmwsDBz5swZq+21114zTqfT+Hw+Y4wx69atMy6Xy3z55ZfWmIKCAuPxeExbW1vvFd8LioqKOgxqzFN7d955p5k7d25Q23e+8x3zr//6ryGqKHQuDWptbW3G7XablStXWm1ffvmlcblc5je/+Y0xxphz586ZyMhIs3nzZmvMmTNnTFhYmHnrrbd6rfbeUltbaySZ/fv3G2OYo84MGjTI/Pa3v2V+LlFfX2/S0tJMcXGxGTt2rBXUmKcA3vrsQ3w+n+Lj463X7777rtLT0+XxeKy2CRMmqKmpSaWlpdaYsWPHBm0gOGHCBFVXV6uioqLXag8l5ilYc3OzSktLNX78+KD28ePH69ChQyGqyj5Onz4tr9cbND9Op1Njx4615qe0tFQtLS1BYzwej9LT0/vkHPp8Pkmy/v1hjoK1trZq8+bNOn/+vEaPHs38XGL+/PmaOHGixo0bF9TOPAUQ1PqIU6dOac2aNZo7d67V5vV6lZiYGDRu0KBBioqKktfr7XTMxdcXx/R1zFOwzz//XK2trR2eb18712/i4hxcbn68Xq+ioqI0aNCgTsf0FcYYLVy4UPfcc4/S09MlMUcXlZWVaeDAgXI6nZo7d662bdum7373u8zPV2zevFlHjx5VQUFBuz7mKYCgZjMrVqyQw+G47PH+++8HfU51dbXuv/9+/fM//7N+9rOfBfU5HI5238MYE9R+6RjztwvkO/pcu/gm83Q5fXWerkZH59tXz/Wb+Cbz0xfnMDc3VydOnNBrr73Wrq+/z9Gtt96q48eP6/Dhw5o3b55mzZqlDz/80Orv7/NTWVmpBQsW6OWXX9aAAQM6Hdff5yki1AUgWG5urqZPn37ZMTfeeKP1cXV1tbKysjR69Ght2LAhaJzb7dYf/vCHoLa6ujq1tLRYv6G43e52v3XU1tZKav9bjJ10dZ4upy/P0zeRkJCg8PDwDs+3r53rN+F2uyUFfpNPSkqy2r86P263W83Nzaqrqwv6Tb+2tlZjxozp3YJ7UF5ennbu3KmSkhIlJydb7cxRQFRUlG655RZJ0h133KEjR47oP//zP/Xkk09KYn5KS0tVW1urjIwMq621tVUlJSVau3atdSdxf58nVtRsJiEhQd/5zncue1z8zePMmTPKzMzU97//fRUVFSksLPg/5+jRo1VeXq6amhqrbffu3XI6ndZfjNGjR6ukpCRoK4rdu3fL4/F87aATCl2Zpyvpy/P0TURFRSkjI0PFxcVB7cXFxX3mH76rkZqaKrfbHTQ/zc3N2r9/vzU/GRkZioyMDBpTU1Oj8vLyPjGHxhjl5uZq69at2rt3r1JTU4P6maOOGWPU1NTE/PxNdna2ysrKdPz4ceu444479PDDD+v48eO66aabmCeJ7TmuVWfOnDG33HKLue+++0xVVZWpqamxjosubjuRnZ1tjh49avbs2WOSk5ODtp04d+6cSUxMNDNmzDBlZWVm69atJi4urk9tO/Hpp5+aY8eOmZ///Odm4MCB5tixY+bYsWOmvr7eGMM8deTi9hwvvPCC+fDDD01+fr6JiYkxFRUVoS6tV9TX11s/J5LM6tWrzbFjx6ztSVauXGlcLpfZunWrKSsrMzNmzOhwy4Dk5GSzZ88ec/ToUXPffff1mS0D5s2bZ1wul3n77beD/u354osvrDH9fY6WLl1qSkpKzOnTp82JEyfMsmXLTFhYmNm9e7cxhvnpzFfv+jSGeTKG7TmuWUVFRUZSh8dXffrpp2bixIkmOjraxMfHm9zc3KAtJowx5sSJE+YHP/iBcTqdxu12mxUrVvSpLSdmzZrV4Tzt27fPGsM8tffrX//aDB061ERFRZnvf//71tYL/cG+ffs6/JmZNWuWMSawbcBTTz1l3G63cTqd5t577zVlZWVBX6OxsdHk5uaa+Ph4Ex0dbSZNmmT+/Oc/h+Bsul9n//YUFRVZY/r7HD3yyCPW35/Bgweb7OxsK6QZw/x05tKgxjwZ4zCmD2+tDgAAcA3jGjUAAACbIqgBAADYFEENAADApghqAAAANkVQAwAAsCmCGgAAgE0R1AAAAGyKoAYAAGBTBDUAAACbIqgBwFfk5OTI4XDI4XAoMjJSN910kxYvXqzz589bY7Zs2aLMzEy5XC4NHDhQt912m37xi1/or3/9q6TAQ6FnzpypW2+9VWFhYcrPzw/R2QC41hHUAOAS999/v2pqavSnP/1JTz/9tNatW6fFixdLkpYvX65p06Zp5MiRevPNN1VeXq5Vq1bpj3/8ozZt2iRJampq0uDBg7V8+XKNGDEilKcC4BrHsz4B4CtycnJ07tw5bd++3Wp79NFH9fvf/147duzQXXfdpeeff14LFixo97nnzp3Tt771raC2zMxM3X777Xr++ed7tnAAfRIragBwBdHR0WppadErr7yigQMH6vHHH+9w3KUhDQCuFkENAC7jvffe06uvvqrs7Gx9/PHHuummmxQZGRnqsgD0EwQ1ALjE73//ew0cOFADBgzQ6NGjde+992rNmjUyxsjhcIS6PAD9SESoCwAAu8nKytL69esVGRkpj8djraANGzZMBw4cUEtLC6tqAHoFK2oAcImYmBjdcsstGjp0aFAgmzlzphoaGrRu3boOP+/cuXO9VCGA/oIVNQD4mu666y4tWbJEixYt0pkzZ/Tggw/K4/Hok08+0W9+8xvdc8891t2gx48flyQ1NDTo7NmzOn78uKKiovTd7343hGcA4FrD9hwA8BUdbc9xqddff12//vWvdezYMbW1tenmm2/WT37yE+Xl5Vl3fnZ0LdvQoUNVUVHRM4UD6JMIagAAADbFNWoAAAA2RVADAACwKYIaAACATRHUAAAAbIqgBgAAYFMENQAAAJsiqAEAANgUQQ0AAMCmCGoAAAA2RVADAACwKYIaAACATf1/mrX0dRppatIAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 700x275 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "marker = {\n",
    "    \"linestyle\": \"none\",\n",
    "    \"marker\": \"o\",\n",
    "    \"markersize\": 7,\n",
    "    \"color\": \"blue\",\n",
    "    \"alpha\": 0.5,\n",
    "}\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(7, 2.75))\n",
    "ax.plot(PCs[0], PCs[1], label=\"Scores\", **marker)\n",
    "\n",
    "ax.set_xlabel(\"PC1\")\n",
    "ax.set_ylabel(\"PC2\")\n",
    "\n",
    "text = [ax.text(x, y, t) for x, y, t in zip(PCs[0], PCs[1] + 0.5, RGB.columns)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "67cbf486",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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kyZP1m9/8Rtddd53+7d/+TZ9++qnLNQXfZ7PZ9MEHH+jmm2/W1KlTde211+q+++7ToUOHFBoaqm3btikjI0OvvPKKAgMD5eXlpVdeeUU7d+50eT+VPn36KCEhQXfddZfi4uIUExOjF154odHH9PLy0uuvv678/HzFxMRo9uzZ+u1vf3vJX78Luf322/Xee+8pJydHQ4YM0U9/+lOlp6frmmuucT7uW2+9paqqKg0dOlTTpk1zuT6kKfr376/09HQtXbpUMTExevXVV5WWluayzYgRIzRjxgxNmDBBV199dYMLVqX//+6qV111lW6++WaNGTNGvXr10vr165s116WyWY2dhHKjsrIyBQUFqbS09LIOK5rAb7u0DH7bpf2qrKxUUVGRoqKiGlxACM935swZde/eXStWrGhwJMKklJQUvf3220beCh0X/r5tys9vrvkAAFySzz77TH/72980dOhQlZaWatGiRZKk8ePHu3kytDbEBwDgki1fvlwHDhxQx44dNWjQIO3YsaNV//0TuAfxAQC4JAMGDFB+fr67x2ggJSXF+dbhaB244BQAABhFfABwOw+77h3ARbTE9yvxAcBt6t8tsrH3HwDgmeq/X3/4TrpNwTUfANzG29tbwcHBLu9jcSXf0hlA81mWpYqKCpWUlCg4OLjBW+g3BfEBwK3q34GyPkAAeLbg4OCL/qXcS0F8AHArm82m8PBwhYSENOkPYgEwr0OHDpd1xKMe8QHAI3h7e7fI/9QAeD4uOAUAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo5oUHzU1NXrqqacUFRUlPz8/9erVS4sWLVJdXZ1zG8uylJKSooiICPn5+Sk2Nlb79u1r8cEBAEDr1KT4WLp0qV588UWtWrVKBQUFWrZsmX77299q5cqVzm2WLVum9PR0rVq1Snl5eQoLC9PYsWNVXl7e4sMDAIDWp0nx8fHHH2v8+PGKj49XZGSk/vM//1NxcXHas2ePpPNHPTIyMjR//nwlJCQoJiZGWVlZqqioUHZ29hV5AgAAoHVpUnyMGjVKmzdv1tdffy1J+uKLL7Rz507dddddkqSioiIVFxcrLi7OeRu73a7Ro0dr165djd5nVVWVysrKXD4AAEDb5dOUjZ988kmVlpbq+uuvl7e3t2pra7V48WL94he/kCQVFxdLkkJDQ11uFxoaqsOHDzd6n2lpaVq4cGFzZgcAAK1Qk458rF+/Xv/7v/+r7Oxs7d27V1lZWVq+fLmysrJctrPZbC6fW5bVYFm9efPmqbS01Plx9OjRJj4FAADQmjTpyMcTTzyhuXPn6r777pMk3XTTTTp8+LDS0tI0ZcoUhYWFSTp/BCQ8PNx5u5KSkgZHQ+rZ7XbZ7fbmzg8AAFqZJh35qKiokJeX6028vb2dv2obFRWlsLAw5eTkONdXV1crNzdXI0aMaIFxAQBAa9ekIx8///nPtXjxYvXs2VM33nijPvvsM6Wnp2vq1KmSzp9uSUpKUmpqqqKjoxUdHa3U1FT5+/tr4sSJV+QJAACA1qVJ8bFy5UotWLBAM2fOVElJiSIiIjR9+nQ9/fTTzm2Sk5N19uxZzZw5U6dOndKwYcO0adMmBQQEtPjwAACg9bFZlmW5e4jvKysrU1BQkEpLSxUYGOjucS4qcu777h6hTTi0JN7dIwAALlNTfn7zt10AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRTY6PY8eOadKkSeratav8/f3Vv39/5efnO9dblqWUlBRFRETIz89PsbGx2rdvX4sODQAAWq8mxcepU6c0cuRIdejQQX/+85+1f/9+rVixQsHBwc5tli1bpvT0dK1atUp5eXkKCwvT2LFjVV5e3tKzAwCAVsinKRsvXbpUDodDmZmZzmWRkZHO/7YsSxkZGZo/f74SEhIkSVlZWQoNDVV2dramT5/eMlMDAIBWq0lHPt555x0NHjxY99xzj0JCQjRgwAC99NJLzvVFRUUqLi5WXFycc5ndbtfo0aO1a9euRu+zqqpKZWVlLh8AAKDtalJ8fPvtt1q9erWio6P14YcfasaMGXrsscf08ssvS5KKi4slSaGhoS63Cw0Nda77obS0NAUFBTk/HA5Hc54HAABoJZoUH3V1dRo4cKBSU1M1YMAATZ8+XQ899JBWr17tsp3NZnP53LKsBsvqzZs3T6Wlpc6Po0ePNvEpAACA1qRJ8REeHq4bbrjBZVnfvn115MgRSVJYWJgkNTjKUVJS0uBoSD273a7AwECXDwAA0HY1KT5GjhypAwcOuCz7+uuvdc0110iSoqKiFBYWppycHOf66upq5ebmasSIES0wLgAAaO2a9Nsus2fP1ogRI5Samqp7771Xu3fv1tq1a7V27VpJ50+3JCUlKTU1VdHR0YqOjlZqaqr8/f01ceLEK/IEAABA69Kk+BgyZIjeeustzZs3T4sWLVJUVJQyMjKUmJjo3CY5OVlnz57VzJkzderUKQ0bNkybNm1SQEBAiw8PAABaH5tlWZa7h/i+srIyBQUFqbS01OOv/4ic+767R2gTDi2Jd/cIAIDL1JSf3/xtFwAAYBTxAQAAjCI+AACAUcQHAAAwivgAAABGER8AAMAo4gMAABhFfAAAAKOIDwAAYBTxAQAAjCI+AACAUcQHAAAwivgAAABGER8AAMAo4gMAABhFfAAAAKOIDwAAYBTxAQAAjCI+AACAUcQHAAAwivgAAABGER8AAMAo4gMAABhFfAAAAKOIDwAAYBTxAQAAjCI+AACAUcQHAAAwivgAAABGER8AAMAo4gMAABhFfAAAAKOIDwAAYBTxAQAAjCI+AACAUcQHAAAwivgAAABGER8AAMAo4gMAABhFfAAAAKOIDwAAYBTxAQAAjCI+AACAUcQHAAAwivgAAABGER8AAMAo4gMAABhFfAAAAKOIDwAAYBTxAQAAjCI+AACAUcQHAAAwivgAAABGER8AAMAo4gMAABhFfAAAAKOIDwAAYBTxAQAAjCI+AACAUcQHAAAwivgAAABGER8AAMAo4gMAABhFfAAAAKOIDwAAYNRlxUdaWppsNpuSkpKcyyzLUkpKiiIiIuTn56fY2Fjt27fvcucEAABtRLPjIy8vT2vXrlW/fv1cli9btkzp6elatWqV8vLyFBYWprFjx6q8vPyyhwUAAK1fs+Lj9OnTSkxM1EsvvaSrrrrKudyyLGVkZGj+/PlKSEhQTEyMsrKyVFFRoezs7Ebvq6qqSmVlZS4fAACg7WpWfMyaNUvx8fEaM2aMy/KioiIVFxcrLi7Oucxut2v06NHatWtXo/eVlpamoKAg54fD4WjOSAAAoJVocny8/vrr2rt3r9LS0hqsKy4uliSFhoa6LA8NDXWu+6F58+aptLTU+XH06NGmjgQAAFoRn6ZsfPToUf3617/Wpk2b5Ovre8HtbDaby+eWZTVYVs9ut8tutzdlDAAA0Io16chHfn6+SkpKNGjQIPn4+MjHx0e5ubl6/vnn5ePj4zzi8cOjHCUlJQ2OhgAAgPapSfFx22236auvvtLnn3/u/Bg8eLASExP1+eefq1evXgoLC1NOTo7zNtXV1crNzdWIESNafHgAAND6NOm0S0BAgGJiYlyWderUSV27dnUuT0pKUmpqqqKjoxUdHa3U1FT5+/tr4sSJLTc1AABotZoUH5ciOTlZZ8+e1cyZM3Xq1CkNGzZMmzZtUkBAQEs/FAAAaIVslmVZ7h7i+8rKyhQUFKTS0lIFBga6e5yLipz7vrtHaBMOLYl39wgAgMvUlJ/f/G0XAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo5oUH2lpaRoyZIgCAgIUEhKiu+++WwcOHHDZxrIspaSkKCIiQn5+foqNjdW+fftadGgAANB6NSk+cnNzNWvWLH3yySfKyclRTU2N4uLidObMGec2y5YtU3p6ulatWqW8vDyFhYVp7NixKi8vb/HhAQBA6+PTlI03btzo8nlmZqZCQkKUn5+vm2++WZZlKSMjQ/Pnz1dCQoIkKSsrS6GhocrOztb06dNbbnIAANAqXdY1H6WlpZKkLl26SJKKiopUXFysuLg45zZ2u12jR4/Wrl27Gr2PqqoqlZWVuXwAAIC2q9nxYVmW5syZo1GjRikmJkaSVFxcLEkKDQ112TY0NNS57ofS0tIUFBTk/HA4HM0dCQAAtALNjo9HH31UX375pV577bUG62w2m8vnlmU1WFZv3rx5Ki0tdX4cPXq0uSMBAIBWoEnXfNT71a9+pXfeeUfbt29Xjx49nMvDwsIknT8CEh4e7lxeUlLS4GhIPbvdLrvd3pwxAABAK9SkIx+WZenRRx/Vhg0btGXLFkVFRbmsj4qKUlhYmHJycpzLqqurlZubqxEjRrTMxAAAoFVr0pGPWbNmKTs7W3/6058UEBDgvI4jKChIfn5+stlsSkpKUmpqqqKjoxUdHa3U1FT5+/tr4sSJV+QJAACA1qVJ8bF69WpJUmxsrMvyzMxMPfDAA5Kk5ORknT17VjNnztSpU6c0bNgwbdq0SQEBAS0yMAAAaN2aFB+WZf3oNjabTSkpKUpJSWnuTAAAoA3jb7sAAACjiA8AAGAU8QEAAIwiPgAAgFHEBwAAMIr4AAAARhEfAADAKOIDAAAYRXwAAACjiA8AAGAU8QEAAIwiPgAAgFHEBwAAMIr4AAAARhEfAADAKOIDAAAYRXwAAACjiA8AAGAU8QEAAIwiPgAAgFHEBwAAMIr4AAAARhEfAADAKOIDAAAYRXwAAACjiA8AAGAU8QEAAIwiPgAAgFHEBwAAMIr4AAAARhEfAADAKOIDAAAYRXwAAACjiA8AAGAU8QEAAIwiPgAAgFHEBwAAMIr4AAAARhEfAADAKOIDAAAYRXwAAACjiA8AAGCUj7sHANByIue+7+4R2oxDS+LdPQLQZnHkAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADCK+AAAAEYRHwAAwCjiAwAAGEV8AAAAo4gPAABgFPEBAACMIj4AAIBRxAcAADDqisXHCy+8oKioKPn6+mrQoEHasWPHlXooAADQilyR+Fi/fr2SkpI0f/58ffbZZ/rZz36mO++8U0eOHLkSDwcAAFqRKxIf6enpevDBBzVt2jT17dtXGRkZcjgcWr169ZV4OAAA0Ir4tPQdVldXKz8/X3PnznVZHhcXp127djXYvqqqSlVVVc7PS0tLJUllZWUtPVqLq6uqcPcIbUJreK1bC/bJlsN+CTRN/feMZVk/um2Lx8fJkydVW1ur0NBQl+WhoaEqLi5usH1aWpoWLlzYYLnD4Wjp0eChgjLcPQHQEPsl0Dzl5eUKCgq66DYtHh/1bDaby+eWZTVYJknz5s3TnDlznJ/X1dXpu+++U9euXRvdHpeurKxMDodDR48eVWBgoLvHAdgn4ZHYL1uGZVkqLy9XRETEj27b4vHRrVs3eXt7NzjKUVJS0uBoiCTZ7XbZ7XaXZcHBwS09VrsWGBjINxQ8CvskPBH75eX7sSMe9Vr8gtOOHTtq0KBBysnJcVmek5OjESNGtPTDAQCAVuaKnHaZM2eO7r//fg0ePFjDhw/X2rVrdeTIEc2YMeNKPBwAAGhFrkh8TJgwQf/85z+1aNEinThxQjExMfrggw90zTXXXImHwwXY7XY988wzDU5rAe7CPglPxH5pns26lN+JAQAAaCH8bRcAAGAU8QEAAIwiPgAAgFHEBwAAMIr4AAAARhEf7cCZM2e0fft2d48BAB6htrbW5fNPP/1U27dv17lz59w0UftDfLQDBw8e1C233OLuMdCOnDt3TsnJyerTp4+GDh2qzMxMl/X/+Mc/5O3t7abp0F6dOHFCo0aNkt1u1+jRo3Xq1CmNGzdOw4cPV2xsrGJiYnTixAl3j9kuEB8AWtzixYv18ssva8aMGYqLi9Ps2bM1ffp0l214iyGY9uSTT8qyLL311lsKDw/XuHHjVFZWpqNHj+rw4cMKDQ3V4sWL3T1mu8CbjLUBXbp0uej62tpanT59usGhRuBKiY6O1nPPPadx48ZJkgoLC3XnnXdq5MiR+v3vf6+SkhJFRESwT8KoiIgIbdiwQT/96U/13XffqVu3bsrJydFtt90mSdq6daumTZumwsJCN0/a9l2Rt1eHWVVVVXrkkUd00003Nbr+8OHDWrhwoeGp0J4dO3ZMMTExzs979+6tbdu26dZbb9X999+vZcuWuXE6tFenTp1S9+7dJZ3/R5u/v7/Ln/3o3bs3p10MIT7agP79+8vhcGjKlCmNrv/iiy+IDxgVFhamwsJCRUZGOpdFRERoy5YtuuWWWy64rwJXUkhIiE6cOCGHwyFJevTRR12OHJ86dUqdOnVy13jtCtd8tAHx8fH617/+dcH1Xbp00eTJk80NhHbv1ltvVXZ2doPl9QFy6NAh80Oh3evfv78+/vhj5+dLlixxiY+dO3eqX79+7hit3eGaDwAt7vDhw/rb3/6m22+/vdH1J06c0KZNmzgCAo+Sl5cnPz8/l1OGuDKIDwAAYBSnXQAAgFHEBwAAMIr4AAAARhEfAADAKOKjDTh16pRWrlypsrKyButKS0svuA64Utgn4YnYLz0H8dEGrFq1Stu3b1dgYGCDdUFBQdqxY4dWrlzphsnQXrFPwhOxX3oO4qMN+OMf/6gZM2ZccP306dP15ptvGpwI7R37JDwR+6XnID7agMLCQkVHR19wfXR0NH8oCUaxT8ITsV96DuKjDfD29tbx48cvuP748ePy8uKlhjnsk/BE7Jeeg69yGzBgwAC9/fbbF1z/1ltvacCAAeYGQrvHPglPxH7pQSy0em+++abl4+NjrVy50qqpqXEur6mpsZ5//nmrQ4cO1h/+8Ac3Toj2hn0Snoj90nPwt13aiPnz5ystLU0BAQHq1auXbDabCgsLdfr0aT3xxBNasmSJu0dEO8M+CU/EfukZiI82ZPfu3Xr11Vd18OBBWZala6+9VhMnTtTQoUPdPRraKfZJeCL2S/cjPgAAgFFccNoGVFRUaNasWerevbtCQkI0ceJEnTx50t1joR1jn4QnYr/0HMRHG/DMM89o3bp1io+P13333aecnBw98sgj7h4L7Rj7JDwR+6Xn4LRLG9C7d28tXrxY9913n6Tz5zNHjhypyspKeXt7u3k6tEfsk/BE7Jeeg/hoAzp27KiioiJ1797duczPz09ff/21HA6HGydDe8U+CU/Efuk5OO3SBtTW1qpjx44uy3x8fFRTU+OmidDesU/CE7Ffeg4fdw+Ay2dZlh544AHZ7XbnssrKSs2YMUOdOnVyLtuwYYM7xkM7xD4JT8R+6TmIjzZgypQpDZZNmjTJDZMA57FPwhOxX3oOrvkAAABGcc0HAAAwivgAAABGER8AAMAo4gMAABhFfAAAAKOIDwAAYBTxAQAAjCI+AACAUf8PwyQXF0y31KAAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "perc = pca.explained_variance_ratio_ * 100\n",
    "perc = pd.DataFrame(\n",
    "    perc,\n",
    "    columns=[\"Percentage explained ratio\"],\n",
    "    index=[\"PC %s\" % pc for pc in np.arange(len(perc)) + 1],\n",
    ")\n",
    "ax = perc.plot(kind=\"bar\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0461500",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The non-projected loadings plot can help us see if the data has some sort of aggregation that we can use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "bbabd98c",
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "common = {\"linestyle\": \"none\", \"markersize\": 7, \"alpha\": 0.5}\n",
    "\n",
    "markers = {\n",
    "    0: {\"color\": \"black\", \"marker\": \"o\", \"label\": \"no yellowing\"},\n",
    "    1: {\"color\": \"red\", \"marker\": \"^\", \"label\": \"low\"},\n",
    "    2: {\"color\": \"blue\", \"marker\": \"*\", \"label\": \"moderate\"},\n",
    "    3: {\"color\": \"khaki\", \"marker\": \"s\", \"label\": \"high\"},\n",
    "    4: {\"color\": \"darkgoldenrod\", \"marker\": \"d\", \"label\": \"very high\"},\n",
    "}\n",
    "\n",
    "\n",
    "def unprojected_loadings():\n",
    "    fig, ax = plt.subplots(figsize=(7, 7))\n",
    "    for x, y, idx in zip(\n",
    "        loadings.iloc[:, 0], loadings.iloc[:, 1], df[\"yellowing index\"]\n",
    "    ):\n",
    "        ax.plot(x, y, **common, **markers.get(idx))\n",
    "\n",
    "    ax.set_xlabel(\"non-projected PC1\")\n",
    "    ax.set_ylabel(\"non-projected PC2\")\n",
    "    ax.axis([-1, 1, -1, 1])\n",
    "    ax.axis([-0.25, 0.25, -0.4, 0.4])\n",
    "\n",
    "    # Trick to remove duplicate labels from the for-loop.\n",
    "    handles, labels = ax.get_legend_handles_labels()\n",
    "    by_label = dict(zip(labels, handles))\n",
    "    ax.legend(by_label.values(), by_label.keys())\n",
    "    return fig, ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ab85edba",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "unprojected_loadings();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e33ab2a8",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Summary\n",
    "\n",
    "- PCA is probably be most robust, and easy to perform, non-supervised ML technique (it has been a common technique in ocean sciences since before the ML hype);\n",
    "- We learned that a single RGB value does not have enough predictive power to be used alone, we'll need at least a combination of Reds and Greens;\n",
    "- The loading plot show that the moderate and the low yellowing have some overlaps. That can be troublesome when using this model for predictions."
   ]
  }
 ],
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