{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# SVD" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook illustrates the embedding of a graph through the [singular value decomposition](https://en.wikipedia.org/wiki/Singular_value_decomposition) of the adjacency matrix. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from IPython.display import SVG" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from sknetwork.data import karate_club, painters, movie_actor\n", "from sknetwork.embedding import SVD\n", "from sknetwork.visualization import visualize_graph, visualize_bigraph" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Graphs" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "graph = karate_club(metadata=True)\n", "adjacency = graph.adjacency\n", "labels = graph.labels" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "svd = SVD(2)\n", "embedding = svd.fit_transform(adjacency)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "image = visualize_graph(adjacency, embedding, labels=labels)\n", "SVG(image)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Directed graphs" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "graph = painters(metadata=True)\n", "adjacency = graph.adjacency\n", "names = graph.names" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "svd = SVD(2)\n", "embedding = svd.fit_transform(adjacency)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "image = visualize_graph(adjacency, embedding, names=names)\n", "SVG(image)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bipartite graphs" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "graph = movie_actor(metadata=True)\n", "biadjacency = graph.biadjacency\n", "names_row = graph.names_row\n", "names_col = graph.names_col" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "svd = SVD(2, normalized=False)\n", "svd.fit(biadjacency)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "embedding_row = svd.embedding_row_\n", "embedding_col = svd.embedding_col_" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "pycharm": { "is_executing": false, "name": "#%%\n" } }, "outputs": [], "source": [ "image = visualize_bigraph(biadjacency, names_row, names_col, \n", " position_row=embedding_row, position_col=embedding_col,\n", " color_row='blue', color_col='red', scale=1.5)\n", "SVG(image)" ] } ], "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": "3.9.13" }, "pycharm": { "stem_cell": { "cell_type": "raw", "metadata": { "collapsed": false }, "source": [] } }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false }, 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