diff --git a/TDA_Explore.ipynb b/TDA_Explore.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..ed7d2aed77b9f3ac44c91e8dcce0d64e045b10c8
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+++ b/TDA_Explore.ipynb
@@ -0,0 +1,486307 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<h1><center>US Presidential Election Results</center></h1>\n",
+ "<img src=\"https://d3n8a8pro7vhmx.cloudfront.net/fairvote/pages/98/meta_images/original/iStock_000005814659_Large-cropped.jpg?1450044496\" width=\"70%\">\n",
+ "<p style=\"text-align: center;\">Image from: https://www.fairvote.org/rcv#where_is_ranked_choice_voting_used</p>"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The United States election results have been analyzed through several machine learning methods. In this notebook, we will use TDA to determine whether there is a natural pattern in pressidential elections results."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "from sklearn import preprocessing\n",
+ "\n",
+ "from ripser import ripser\n",
+ "from ripser import Rips\n",
+ "from persim import plot_diagrams\n",
+ "\n",
+ "%matplotlib inline"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "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>year</th>\n",
+ " <th>state</th>\n",
+ " <th>state_po</th>\n",
+ " <th>county</th>\n",
+ " <th>FIPS</th>\n",
+ " <th>office</th>\n",
+ " <th>candidate</th>\n",
+ " <th>party</th>\n",
+ " <th>candidatevotes</th>\n",
+ " <th>totalvotes</th>\n",
+ " <th>version</th>\n",
+ " </tr>\n",
+ " </thead>\n",
+ " <tbody>\n",
+ " <tr>\n",
+ " <th>0</th>\n",
+ " <td>2000</td>\n",
+ " <td>Alabama</td>\n",
+ " <td>AL</td>\n",
+ " <td>Autauga</td>\n",
+ " <td>1001.0</td>\n",
+ " <td>President</td>\n",
+ " <td>Al Gore</td>\n",
+ " <td>democrat</td>\n",
+ " <td>4942.0</td>\n",
+ " <td>17208</td>\n",
+ " <td>20191203</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1</th>\n",
+ " <td>2000</td>\n",
+ " <td>Alabama</td>\n",
+ " <td>AL</td>\n",
+ " <td>Autauga</td>\n",
+ " <td>1001.0</td>\n",
+ " <td>President</td>\n",
+ " <td>George W. Bush</td>\n",
+ " <td>republican</td>\n",
+ " <td>11993.0</td>\n",
+ " <td>17208</td>\n",
+ " <td>20191203</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2</th>\n",
+ " <td>2000</td>\n",
+ " <td>Alabama</td>\n",
+ " <td>AL</td>\n",
+ " <td>Autauga</td>\n",
+ " <td>1001.0</td>\n",
+ " <td>President</td>\n",
+ " <td>Ralph Nader</td>\n",
+ " <td>green</td>\n",
+ " <td>160.0</td>\n",
+ " <td>17208</td>\n",
+ " <td>20191203</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3</th>\n",
+ " <td>2000</td>\n",
+ " <td>Alabama</td>\n",
+ " <td>AL</td>\n",
+ " <td>Autauga</td>\n",
+ " <td>1001.0</td>\n",
+ " <td>President</td>\n",
+ " <td>Other</td>\n",
+ " <td>NaN</td>\n",
+ " <td>113.0</td>\n",
+ " <td>17208</td>\n",
+ " <td>20191203</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>4</th>\n",
+ " <td>2000</td>\n",
+ " <td>Alabama</td>\n",
+ " <td>AL</td>\n",
+ " <td>Baldwin</td>\n",
+ " <td>1003.0</td>\n",
+ " <td>President</td>\n",
+ " <td>Al Gore</td>\n",
+ " <td>democrat</td>\n",
+ " <td>13997.0</td>\n",
+ " <td>56480</td>\n",
+ " <td>20191203</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>5</th>\n",
+ " <td>2000</td>\n",
+ " <td>Alabama</td>\n",
+ " <td>AL</td>\n",
+ " <td>Baldwin</td>\n",
+ " <td>1003.0</td>\n",
+ " <td>President</td>\n",
+ " <td>George W. Bush</td>\n",
+ " <td>republican</td>\n",
+ " <td>40872.0</td>\n",
+ " <td>56480</td>\n",
+ " <td>20191203</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>6</th>\n",
+ " <td>2000</td>\n",
+ " <td>Alabama</td>\n",
+ " <td>AL</td>\n",
+ " <td>Baldwin</td>\n",
+ " <td>1003.0</td>\n",
+ " <td>President</td>\n",
+ " <td>Ralph Nader</td>\n",
+ " <td>green</td>\n",
+ " <td>1033.0</td>\n",
+ " <td>56480</td>\n",
+ " <td>20191203</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>7</th>\n",
+ " <td>2000</td>\n",
+ " <td>Alabama</td>\n",
+ " <td>AL</td>\n",
+ " <td>Baldwin</td>\n",
+ " <td>1003.0</td>\n",
+ " <td>President</td>\n",
+ " <td>Other</td>\n",
+ " <td>NaN</td>\n",
+ " <td>578.0</td>\n",
+ " <td>56480</td>\n",
+ " <td>20191203</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>8</th>\n",
+ " <td>2000</td>\n",
+ " <td>Alabama</td>\n",
+ " <td>AL</td>\n",
+ " <td>Barbour</td>\n",
+ " <td>1005.0</td>\n",
+ " <td>President</td>\n",
+ " <td>Al Gore</td>\n",
+ " <td>democrat</td>\n",
+ " <td>5188.0</td>\n",
+ " <td>10395</td>\n",
+ " <td>20191203</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>9</th>\n",
+ " <td>2000</td>\n",
+ " <td>Alabama</td>\n",
+ " <td>AL</td>\n",
+ " <td>Barbour</td>\n",
+ " <td>1005.0</td>\n",
+ " <td>President</td>\n",
+ " <td>George W. Bush</td>\n",
+ " <td>republican</td>\n",
+ " <td>5096.0</td>\n",
+ " <td>10395</td>\n",
+ " <td>20191203</td>\n",
+ " </tr>\n",
+ " </tbody>\n",
+ "</table>\n",
+ "</div>"
+ ],
+ "text/plain": [
+ " year state state_po county FIPS office candidate \\\n",
+ "0 2000 Alabama AL Autauga 1001.0 President Al Gore \n",
+ "1 2000 Alabama AL Autauga 1001.0 President George W. Bush \n",
+ "2 2000 Alabama AL Autauga 1001.0 President Ralph Nader \n",
+ "3 2000 Alabama AL Autauga 1001.0 President Other \n",
+ "4 2000 Alabama AL Baldwin 1003.0 President Al Gore \n",
+ "5 2000 Alabama AL Baldwin 1003.0 President George W. Bush \n",
+ "6 2000 Alabama AL Baldwin 1003.0 President Ralph Nader \n",
+ "7 2000 Alabama AL Baldwin 1003.0 President Other \n",
+ "8 2000 Alabama AL Barbour 1005.0 President Al Gore \n",
+ "9 2000 Alabama AL Barbour 1005.0 President George W. Bush \n",
+ "\n",
+ " party candidatevotes totalvotes version \n",
+ "0 democrat 4942.0 17208 20191203 \n",
+ "1 republican 11993.0 17208 20191203 \n",
+ "2 green 160.0 17208 20191203 \n",
+ "3 NaN 113.0 17208 20191203 \n",
+ "4 democrat 13997.0 56480 20191203 \n",
+ "5 republican 40872.0 56480 20191203 \n",
+ "6 green 1033.0 56480 20191203 \n",
+ "7 NaN 578.0 56480 20191203 \n",
+ "8 democrat 5188.0 10395 20191203 \n",
+ "9 republican 5096.0 10395 20191203 "
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# import dataframe\n",
+ "df = df = pd.read_csv('~/Desktop/topological_machine_learning/Data/countypres_2000_2016.csv')\n",
+ "# print first 10 rows\n",
+ "df.head(10)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def county_crosstab(County, Year, Index, Columns):\n",
+ " subset_df = df[df.year == Year]\n",
+ " sub_df = subset_df[subset_df.county == County]\n",
+ " crosstab = pd.crosstab(index = sub_df[Index], columns = sub_df[Columns])\n",
+ " return crosstab"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "party democrat green republican\n",
+ "candidate \n",
+ "Al Gore 1 0 0\n",
+ "George W. Bush 0 0 1\n",
+ "Ralph Nader 0 1 0\n"
+ ]
+ }
+ ],
+ "source": [
+ "ct=county_crosstab('Autauga', 2000, 'candidate', 'party')\n",
+ "print(ct)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "{'type': 'Feature',\n",
+ " 'properties': {'GEO_ID': '0500000US01001',\n",
+ " 'STATE': '01',\n",
+ " 'COUNTY': '001',\n",
+ " 'NAME': 'Autauga',\n",
+ " 'LSAD': 'County',\n",
+ " 'CENSUSAREA': 594.436},\n",
+ " 'geometry': {'type': 'Polygon',\n",
+ " 'coordinates': [[[-86.496774, 32.344437],\n",
+ " [-86.717897, 32.402814],\n",
+ " [-86.814912, 32.340803],\n",
+ " [-86.890581, 32.502974],\n",
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+ ]
+ },
+ "execution_count": 30,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from urllib.request import urlopen\n",
+ "import json\n",
+ "with urlopen('https://raw.githubusercontent.com/plotly/datasets/master/geojson-counties-fips.json') as response:\n",
+ " counties = json.load(response)\n",
+ "\n",
+ "counties[\"features\"][0]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 33,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "application/vnd.plotly.v1+json": {
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+ "plotlyServerURL": "https://plot.ly"
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