notebooks/01-eda.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c75ebfc4-d6ae-4d63-b200-4c7fdd865b74",
   "metadata": {},
   "source": [
    "# Antarctica: EDA\n",
    "\n",
    "Goal of this notebook is to explore basic descriptive statistics about the original probes data. The expectation is the probe locations are distributed randomly. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2dca46c3-971a-486e-b0d8-2e9750cb28f0",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "# Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "48026ee6-1ee5-4a1a-a035-f7a9031d4133",
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "from typing import Mapping, NamedTuple, Sequence\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "from matplotlib import patches as patches\n",
    "from matplotlib import pyplot as plt\n",
    "from pandas import DataFrame\n",
    "from tqdm import tqdm\n",
    "\n",
    "import antarctica as aa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "da2740a2-3c66-4d36-8263-679713691c52",
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.set_style(\"whitegrid\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6d4e643-79af-4d77-9b7b-a3fdac711dad",
   "metadata": {},
   "source": [
    "# Dataset\n",
    "\n",
    "First, we read and prep the raw data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5d5ad67c-72e7-4d18-a977-8f711d9447d8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .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>x</th>\n",
       "      <th>y</th>\n",
       "      <th>distance_expected</th>\n",
       "      <th>distance_expected_err</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>probe_id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.472751</td>\n",
       "      <td>1.302734</td>\n",
       "      <td>0.428625</td>\n",
       "      <td>0.021431</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.944659</td>\n",
       "      <td>11.519452</td>\n",
       "      <td>2.392850</td>\n",
       "      <td>0.119642</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12.623399</td>\n",
       "      <td>15.411657</td>\n",
       "      <td>1.264116</td>\n",
       "      <td>0.063206</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8.340580</td>\n",
       "      <td>3.964348</td>\n",
       "      <td>2.261914</td>\n",
       "      <td>0.113096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9.833046</td>\n",
       "      <td>14.837630</td>\n",
       "      <td>2.668234</td>\n",
       "      <td>0.133412</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  x          y  distance_expected  distance_expected_err\n",
       "probe_id                                                                \n",
       "0          0.472751   1.302734           0.428625               0.021431\n",
       "1          5.944659  11.519452           2.392850               0.119642\n",
       "2         12.623399  15.411657           1.264116               0.063206\n",
       "3          8.340580   3.964348           2.261914               0.113096\n",
       "4          9.833046  14.837630           2.668234               0.133412"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probes = aa.create_probes(\"data/probes.csv\")\n",
    "probes.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a85f0df9-c333-43cc-b8f5-5df6b8e772de",
   "metadata": {},
   "source": [
    "# Count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ff439ec9-3180-4be1-862d-66a304da059f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = len(probes)\n",
    "n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1b1d885-eb45-4cc8-9c16-1ffb57d148a2",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "There are 50 probes total."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "658a494c-deaa-4840-9698-1e3bb3c7f081",
   "metadata": {},
   "source": [
    "# Coordinates"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a800d58a-ad1b-4bb5-884d-e858d355ab10",
   "metadata": {},
   "source": [
    "## X and Y Distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "db1de666-cf5f-409f-9559-bd5f6114f2d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Y')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Independent distributions\n",
    "_, axs = plt.subplots(ncols=2, figsize=(10,4))\n",
    "\n",
    "sns.histplot(data=probes, x=\"x\", ax=axs[0])\n",
    "axs[0].set_title(\"X\")\n",
    "\n",
    "sns.histplot(data=probes, x=\"y\", ax=axs[1])\n",
    "axs[1].set_title(\"Y\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0e12e692-2fc9-435a-810b-c4ca464077aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.JointGrid at 0x14f797da0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Joint distribution\n",
    "sns.jointplot(data=probes, x=\"x\", y=\"y\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5aab082b-e0a6-457c-a185-d880b7b97ea1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Vector Length')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Vector length\n",
    "df = np.sqrt(probes.x**2 + probes.y**2)\n",
    "sns.histplot(x=df)\n",
    "plt.gca().set_xlabel(\"Vector Length\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "197484be-cbd7-4ccf-90de-a533790951c4",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "No obvious patterns in the coordinates. Probe locations appear to be fairly random which matches our expectation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "158c61f4-a78a-4f87-b1ba-e53a20e161ac",
   "metadata": {},
   "source": [
    "# Expected Distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "9e53d232-5d6b-496e-8523-bff67ab0754b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='distance_expected', ylabel='Count'>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.histplot(data=probes, x=\"distance_expected\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "562ebf10-56ad-49c2-8b0c-dc02ba33b010",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='distance_expected_err', ylabel='Count'>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.histplot(data=probes, x=\"distance_expected_err\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7de462c-fef3-44c6-8d0a-8974eecdc8dc",
   "metadata": {},
   "source": [
    "The fact that these distributions are identical suggests the distance error is a function of distance. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "db42cf50-5599-4974-8bdd-02928bb62cff",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "probe_id\n",
       "0     0.05\n",
       "1     0.05\n",
       "2     0.05\n",
       "3     0.05\n",
       "4     0.05\n",
       "5     0.05\n",
       "6     0.05\n",
       "7     0.05\n",
       "8     0.05\n",
       "9     0.05\n",
       "10    0.05\n",
       "11    0.05\n",
       "12    0.05\n",
       "13    0.05\n",
       "14    0.05\n",
       "15    0.05\n",
       "16    0.05\n",
       "17    0.05\n",
       "18    0.05\n",
       "19    0.05\n",
       "20    0.05\n",
       "21    0.05\n",
       "22    0.05\n",
       "23    0.05\n",
       "24    0.05\n",
       "25    0.05\n",
       "26    0.05\n",
       "27    0.05\n",
       "28    0.05\n",
       "29    0.05\n",
       "30    0.05\n",
       "31    0.05\n",
       "32    0.05\n",
       "33    0.05\n",
       "34    0.05\n",
       "35    0.05\n",
       "36    0.05\n",
       "37    0.05\n",
       "38    0.05\n",
       "39    0.05\n",
       "40    0.05\n",
       "41    0.05\n",
       "42    0.05\n",
       "43    0.05\n",
       "44    0.05\n",
       "45    0.05\n",
       "46    0.05\n",
       "47    0.05\n",
       "48    0.05\n",
       "49    0.05\n",
       "dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probes.distance_expected_err / probes.distance_expected"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43406def-dc7c-4fc2-8833-bd5f521d814b",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "The expected distance error is 5% of the expected distance. This suggests that we should consider normalizing the distance errors since we should expect the locations to be less precise when 2 probes are further away from each other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "221520cc-71f3-4596-8f69-95b866ddbf11",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}