Add EM vs GS Results

EMvsGS/EMvsGS-Results.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "b361579d",
+   "metadata": {},
+   "source": [
+    "# EM vs Gibbs Sampler - Results\n",
+    "\n",
+    "This is an experiment to compare performance of Expectation Maximization (EM) and Gibbs Sampler (GS) in the context of Gaussian Mixture Models.\n",
+    "\n",
+    "- 500 runs each for K = 3 and K = 6 clusters\n",
+    "- 1000 data points in each\n",
+    "- Univariate\n",
+    "\n",
+    "During Data Generation, Means were generated from a Uniform [-10, 10] distribution. Standard Deviations were generated from a Uniform [0.25, 5] distribution."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a82ede1a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import pandas as pd\n",
+    "import plotly.express as px\n",
+    "import plotly.graph_objects as go\n",
+    "import matplotlib.pyplot as plt\n",
+    "import seaborn as sns"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "253f623f",
+   "metadata": {
+    "lines_to_next_cell": 0
+   },
+   "outputs": [],
+   "source": [
+    "# Load Data\n",
+    "gs3 = pd.read_csv(\"gs-k-3.csv\")\n",
+    "gs6 = pd.read_csv(\"gs-k-6.csv\")\n",
+    "\n",
+    "em3 = pd.read_csv(\"em-k-3.csv\")\n",
+    "em6 = pd.read_csv(\"em-k-6.csv\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "61a41812",
+   "metadata": {},
+   "source": [
+    "## The Data\n",
+    "\n",
+    "Gibbs Sampler Results have the following data\n",
+    "\n",
+    "- RS: Rand Score\n",
+    "- ARS: Adjusted Rand Score\n",
+    "- SS: Silhouette Score\n",
+    "\n",
+    "for each of the three methods\n",
+    "\n",
+    "- Base GS\n",
+    "- GS with Multiple Initializations\n",
+    "- GS with Burn In\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "6fd66639",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# GS with K = 3\n",
+    "gs3"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f536009d",
+   "metadata": {},
+   "source": [
+    "The dataframe for EM has the Adjusted Rand Score (ARS) results for EM in 2 modes:\n",
+    "\n",
+    "- EM with Many Random Initializations (`gmm_mri_ars`)\n",
+    "- EM with K-Means Initialization (`gmm_kmeans_ars`)\n",
+    "\n",
+    "And the final column is the standard K-Means Clustering results (`kmeans_ars`)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c605b756",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# EM with K = 3\n",
+    "em3"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1f0f9611",
+   "metadata": {},
+   "source": [
+    "## Results\n",
+    "\n",
+    "The plots are interactive.\n",
+    "\n",
+    "### K = 3"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ca13161d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "fig = go.Figure()\n",
+    "fig.add_trace(go.Box(y=gs3['gs_base_ars'], name=\"GS Base\"))\n",
+    "fig.add_trace(go.Box(y=gs3['gs_burnin_ars'], name=\"GS Burn In\"))\n",
+    "fig.add_trace(go.Box(y=gs3['gs_multi_ars'], name=\"GS Multi\"))\n",
+    "fig.add_trace(go.Box(y=em3['gmm_mri_ars'], name=\"EM Multi Init\"))\n",
+    "fig.add_trace(go.Box(y=em3['gmm_kmeans_ars'], name=\"EM K-Means Init\"))\n",
+    "fig.add_trace(go.Box(y=em3['kmeans_ars'], name=\"Standard K-Means\"))\n",
+    "fig.update_layout(title_text=\"K = 3\")\n",
+    "fig.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c9ad9d65",
+   "metadata": {},
+   "source": [
+    "### K = 6"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "d4435abe",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "fig = go.Figure()\n",
+    "fig.add_trace(go.Box(y=gs6['gs_base_ars'], name=\"GS Base\"))\n",
+    "fig.add_trace(go.Box(y=gs6['gs_burnin_ars'], name=\"GS Burn In\"))\n",
+    "fig.add_trace(go.Box(y=gs6['gs_multi_ars'], name=\"GS Multi\"))\n",
+    "fig.add_trace(go.Box(y=em6['gmm_mri_ars'], name=\"EM Multi Init\"))\n",
+    "fig.add_trace(go.Box(y=em6['gmm_kmeans_ars'], name=\"EM K-Means Init\"))\n",
+    "fig.add_trace(go.Box(y=em6['kmeans_ars'], name=\"Standard K-Means\"))\n",
+    "fig.update_layout(title_text=\"K = 6\")\n",
+    "fig.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "434a31f7",
+   "metadata": {},
+   "source": [
+    "## Conclusions\n",
+    "\n",
+    "Gibbs Sampler with Multi Init, and both of the EM versions perform better than the standard K-Means.\n",
+    "\n",
+    "Between GS and EM, GS with Multi Init seems to be performing the best, by a slight margin over EM."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c85e8401",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
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+   "notebook_metadata_filter": "-all",
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+ "nbformat_minor": 5
+}