diff --git a/EMvsGS/EMvsGS-Results.ipynb b/EMvsGS/EMvsGS-Results.ipynb new file mode 100644 index 0000000..5640356 --- /dev/null +++ b/EMvsGS/EMvsGS-Results.ipynb @@ -0,0 +1,196 @@ +{ + "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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