| { |
| "cells": [ |
| { |
| "cell_type": "markdown", |
| "metadata": {}, |
| "source": [ |
| "# PageRank\n", |
| "The PageRank algorithm produces a probability distribution representing the likelihood that a person randomly traversing a graph will arrive at any particular vertex. PageRank was added in MADlib 1.11.\n", |
| "\n", |
| "We also implement personalized PageRank, in which a notion of importance provides personalization to a query. This was added in 1.14" |
| ] |
| }, |
| { |
| "cell_type": "code", |
| "execution_count": 1, |
| "metadata": {}, |
| "outputs": [], |
| "source": [ |
| "%load_ext sql" |
| ] |
| }, |
| { |
| "cell_type": "code", |
| "execution_count": 2, |
| "metadata": {}, |
| "outputs": [], |
| "source": [ |
| "# Greenplum Database 5.x on GCP (PM demo machine) - via tunnel\n", |
| "%sql postgresql://gpadmin@localhost:8000/madlib\n", |
| " \n", |
| "# PostgreSQL local\n", |
| "#%sql postgresql://fmcquillan@localhost:5432/madlib" |
| ] |
| }, |
| { |
| "cell_type": "code", |
| "execution_count": 3, |
| "metadata": {}, |
| "outputs": [ |
| { |
| "name": "stdout", |
| "output_type": "stream", |
| "text": [ |
| "1 rows affected.\n" |
| ] |
| }, |
| { |
| "data": { |
| "text/html": [ |
| "<table>\n", |
| " <tr>\n", |
| " <th>version</th>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>MADlib version: 1.18.0-dev, git revision: rel/v1.17.0-100-g4987e8f, cmake configuration time: Wed Mar 24 23:51:47 UTC 2021, build type: release, build system: Linux-3.10.0-1160.21.1.el7.x86_64, C compiler: gcc 4.8.5, C++ compiler: g++ 4.8.5</td>\n", |
| " </tr>\n", |
| "</table>" |
| ], |
| "text/plain": [ |
| "[(u'MADlib version: 1.18.0-dev, git revision: rel/v1.17.0-100-g4987e8f, cmake configuration time: Wed Mar 24 23:51:47 UTC 2021, build type: release, build system: Linux-3.10.0-1160.21.1.el7.x86_64, C compiler: gcc 4.8.5, C++ compiler: g++ 4.8.5',)]" |
| ] |
| }, |
| "execution_count": 3, |
| "metadata": {}, |
| "output_type": "execute_result" |
| } |
| ], |
| "source": [ |
| "%sql select madlib.version();\n", |
| "#%sql select version();" |
| ] |
| }, |
| { |
| "cell_type": "markdown", |
| "metadata": {}, |
| "source": [ |
| "# 1. Create vertex and edge tables" |
| ] |
| }, |
| { |
| "cell_type": "code", |
| "execution_count": 4, |
| "metadata": {}, |
| "outputs": [ |
| { |
| "name": "stdout", |
| "output_type": "stream", |
| "text": [ |
| "Done.\n", |
| "Done.\n", |
| "Done.\n", |
| "7 rows affected.\n", |
| "22 rows affected.\n", |
| "22 rows affected.\n" |
| ] |
| }, |
| { |
| "data": { |
| "text/html": [ |
| "<table>\n", |
| " <tr>\n", |
| " <th>src</th>\n", |
| " <th>dest</th>\n", |
| " <th>user_id</th>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>0</td>\n", |
| " <td>1</td>\n", |
| " <td>1</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>0</td>\n", |
| " <td>2</td>\n", |
| " <td>2</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>0</td>\n", |
| " <td>2</td>\n", |
| " <td>1</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>0</td>\n", |
| " <td>4</td>\n", |
| " <td>2</td>\n", |
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| " <tr>\n", |
| " <td>0</td>\n", |
| " <td>4</td>\n", |
| " <td>1</td>\n", |
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| " <tr>\n", |
| " <td>0</td>\n", |
| " <td>1</td>\n", |
| " <td>2</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>1</td>\n", |
| " <td>3</td>\n", |
| " <td>1</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>1</td>\n", |
| " <td>3</td>\n", |
| " <td>2</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>1</td>\n", |
| " <td>2</td>\n", |
| " <td>2</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>1</td>\n", |
| " <td>2</td>\n", |
| " <td>1</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>2</td>\n", |
| " <td>5</td>\n", |
| " <td>1</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>2</td>\n", |
| " <td>3</td>\n", |
| " <td>1</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>2</td>\n", |
| " <td>3</td>\n", |
| " <td>2</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>2</td>\n", |
| " <td>6</td>\n", |
| " <td>1</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>3</td>\n", |
| " <td>0</td>\n", |
| " <td>2</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>3</td>\n", |
| " <td>0</td>\n", |
| " <td>1</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>4</td>\n", |
| " <td>0</td>\n", |
| " <td>1</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>4</td>\n", |
| " <td>0</td>\n", |
| " <td>2</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>5</td>\n", |
| " <td>6</td>\n", |
| " <td>2</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>5</td>\n", |
| " <td>6</td>\n", |
| " <td>1</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>6</td>\n", |
| " <td>3</td>\n", |
| " <td>1</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>6</td>\n", |
| " <td>3</td>\n", |
| " <td>2</td>\n", |
| " </tr>\n", |
| "</table>" |
| ], |
| "text/plain": [ |
| "[(0, 1, 1),\n", |
| " (0, 2, 2),\n", |
| " (0, 2, 1),\n", |
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| " (0, 1, 2),\n", |
| " (1, 3, 1),\n", |
| " (1, 3, 2),\n", |
| " (1, 2, 2),\n", |
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| " (2, 6, 1),\n", |
| " (3, 0, 2),\n", |
| " (3, 0, 1),\n", |
| " (4, 0, 1),\n", |
| " (4, 0, 2),\n", |
| " (5, 6, 2),\n", |
| " (5, 6, 1),\n", |
| " (6, 3, 1),\n", |
| " (6, 3, 2)]" |
| ] |
| }, |
| "execution_count": 4, |
| "metadata": {}, |
| "output_type": "execute_result" |
| } |
| ], |
| "source": [ |
| "%%sql \n", |
| "DROP TABLE IF EXISTS vertex, edge;\n", |
| "\n", |
| "CREATE TABLE vertex(\n", |
| " id INTEGER\n", |
| " );\n", |
| "\n", |
| "CREATE TABLE edge(\n", |
| " src INTEGER,\n", |
| " dest INTEGER,\n", |
| " user_id INTEGER\n", |
| " );\n", |
| "\n", |
| "INSERT INTO vertex VALUES\n", |
| "(0),\n", |
| "(1),\n", |
| "(2),\n", |
| "(3),\n", |
| "(4),\n", |
| "(5),\n", |
| "(6);\n", |
| "\n", |
| "INSERT INTO edge VALUES\n", |
| "(0, 1, 1),\n", |
| "(0, 2, 1),\n", |
| "(0, 4, 1),\n", |
| "(1, 2, 1),\n", |
| "(1, 3, 1),\n", |
| "(2, 3, 1),\n", |
| "(2, 5, 1),\n", |
| "(2, 6, 1),\n", |
| "(3, 0, 1),\n", |
| "(4, 0, 1),\n", |
| "(5, 6, 1),\n", |
| "(6, 3, 1),\n", |
| "(0, 1, 2),\n", |
| "(0, 2, 2),\n", |
| "(0, 4, 2),\n", |
| "(1, 2, 2),\n", |
| "(1, 3, 2),\n", |
| "(2, 3, 2),\n", |
| "(3, 0, 2),\n", |
| "(4, 0, 2),\n", |
| "(5, 6, 2),\n", |
| "(6, 3, 2);\n", |
| "\n", |
| "SELECT * from edge ORDER BY src;" |
| ] |
| }, |
| { |
| "cell_type": "markdown", |
| "metadata": {}, |
| "source": [ |
| "# 2. Calculate PageRank" |
| ] |
| }, |
| { |
| "cell_type": "code", |
| "execution_count": 5, |
| "metadata": {}, |
| "outputs": [ |
| { |
| "name": "stdout", |
| "output_type": "stream", |
| "text": [ |
| "Done.\n", |
| "1 rows affected.\n", |
| "7 rows affected.\n" |
| ] |
| }, |
| { |
| "data": { |
| "text/html": [ |
| "<table>\n", |
| " <tr>\n", |
| " <th>id</th>\n", |
| " <th>pagerank</th>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>0</td>\n", |
| " <td>0.287518161212</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>3</td>\n", |
| " <td>0.210171199451</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>2</td>\n", |
| " <td>0.146637377532</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>4</td>\n", |
| " <td>0.102910437211</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>1</td>\n", |
| " <td>0.102910437211</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>6</td>\n", |
| " <td>0.0972746644343</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>5</td>\n", |
| " <td>0.0525777229482</td>\n", |
| " </tr>\n", |
| "</table>" |
| ], |
| "text/plain": [ |
| "[(0, 0.287518161212111),\n", |
| " (3, 0.210171199451415),\n", |
| " (2, 0.146637377532288),\n", |
| " (4, 0.102910437211324),\n", |
| " (1, 0.102910437211324),\n", |
| " (6, 0.0972746644343418),\n", |
| " (5, 0.0525777229481976)]" |
| ] |
| }, |
| "execution_count": 5, |
| "metadata": {}, |
| "output_type": "execute_result" |
| } |
| ], |
| "source": [ |
| "%%sql\n", |
| "DROP TABLE IF EXISTS pagerank_out, pagerank_out_summary;\n", |
| "\n", |
| "SELECT madlib.pagerank(\n", |
| " 'vertex', -- Vertex table\n", |
| " 'id', -- Vertix id column\n", |
| " 'edge', -- Edge table\n", |
| " 'src=src, dest=dest', -- Comma delimted string of edge arguments\n", |
| " 'pagerank_out'); -- Output table of PageRank\n", |
| "\n", |
| "SELECT * FROM pagerank_out ORDER BY pagerank DESC;" |
| ] |
| }, |
| { |
| "cell_type": "markdown", |
| "metadata": {}, |
| "source": [ |
| "Look at the summary table:" |
| ] |
| }, |
| { |
| "cell_type": "code", |
| "execution_count": 7, |
| "metadata": {}, |
| "outputs": [ |
| { |
| "name": "stdout", |
| "output_type": "stream", |
| "text": [ |
| "1 rows affected.\n" |
| ] |
| }, |
| { |
| "data": { |
| "text/html": [ |
| "<table>\n", |
| " <tr>\n", |
| " <th>__iterations__</th>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>12</td>\n", |
| " </tr>\n", |
| "</table>" |
| ], |
| "text/plain": [ |
| "[(12,)]" |
| ] |
| }, |
| "execution_count": 7, |
| "metadata": {}, |
| "output_type": "execute_result" |
| } |
| ], |
| "source": [ |
| "%%sql\n", |
| "SELECT * FROM pagerank_out_summary;" |
| ] |
| }, |
| { |
| "cell_type": "markdown", |
| "metadata": {}, |
| "source": [ |
| "Now run PageRank with a damping factor of 0.5 which results in different final values:" |
| ] |
| }, |
| { |
| "cell_type": "markdown", |
| "metadata": {}, |
| "source": [ |
| "# 3. Calculate PageRank with optional params" |
| ] |
| }, |
| { |
| "cell_type": "code", |
| "execution_count": 6, |
| "metadata": {}, |
| "outputs": [ |
| { |
| "name": "stdout", |
| "output_type": "stream", |
| "text": [ |
| "Done.\n", |
| "1 rows affected.\n", |
| "7 rows affected.\n" |
| ] |
| }, |
| { |
| "data": { |
| "text/html": [ |
| "<table>\n", |
| " <tr>\n", |
| " <th>id</th>\n", |
| " <th>pagerank</th>\n", |
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| " <td>0</td>\n", |
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| " </tr>\n", |
| "</table>" |
| ], |
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| " (3, 0.199105076058278),\n", |
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| " (4, 0.109006420855422),\n", |
| " (1, 0.109006420855422),\n", |
| " (5, 0.0884570570850217)]" |
| ] |
| }, |
| "execution_count": 6, |
| "metadata": {}, |
| "output_type": "execute_result" |
| } |
| ], |
| "source": [ |
| "%%sql\n", |
| "DROP TABLE IF EXISTS pagerank_out, pagerank_out_summary;\n", |
| "SELECT madlib.pagerank(\n", |
| " 'vertex', -- Vertex table\n", |
| " 'id', -- Vertix id column\n", |
| " 'edge', -- Edge table\n", |
| " 'src=src, dest=dest', -- Comma delimted string of edge arguments\n", |
| " 'pagerank_out', -- Output table of PageRank\n", |
| " 0.5); -- Damping factor\n", |
| "SELECT * FROM pagerank_out ORDER BY pagerank DESC;" |
| ] |
| }, |
| { |
| "cell_type": "markdown", |
| "metadata": {}, |
| "source": [ |
| "# 4. Grouping\n", |
| "Now compute the PageRank distribution separately for each user using the grouping feature:" |
| ] |
| }, |
| { |
| "cell_type": "code", |
| "execution_count": 7, |
| "metadata": {}, |
| "outputs": [ |
| { |
| "name": "stdout", |
| "output_type": "stream", |
| "text": [ |
| "Done.\n", |
| "1 rows affected.\n", |
| "14 rows affected.\n" |
| ] |
| }, |
| { |
| "data": { |
| "text/html": [ |
| "<table>\n", |
| " <tr>\n", |
| " <th>user_id</th>\n", |
| " <th>id</th>\n", |
| " <th>pagerank</th>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>1</td>\n", |
| " <td>0</td>\n", |
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| " <tr>\n", |
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| " <td>0.201881146671</td>\n", |
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| " <td>0.237866867733</td>\n", |
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| " <td>2</td>\n", |
| " <td>2</td>\n", |
| " <td>0.159148764894</td>\n", |
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| " <td>2</td>\n", |
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| " <td>0.11168334438</td>\n", |
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| " <td>2</td>\n", |
| " <td>6</td>\n", |
| " <td>0.0396428571429</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>2</td>\n", |
| " <td>5</td>\n", |
| " <td>0.0214285714286</td>\n", |
| " </tr>\n", |
| "</table>" |
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| " (1, 6L, 0.114536378321472),\n", |
| " (1, 4L, 0.10026745615438),\n", |
| " (1, 1L, 0.10026745615438),\n", |
| " (1, 5L, 0.0619115553528898),\n", |
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| " (2, 3L, 0.237866867733431),\n", |
| " (2, 2L, 0.159148764893974),\n", |
| " (2, 1L, 0.111683344379718),\n", |
| " (2, 4L, 0.111683344379718),\n", |
| " (2, 6L, 0.0396428571428571),\n", |
| " (2, 5L, 0.0214285714285714)]" |
| ] |
| }, |
| "execution_count": 7, |
| "metadata": {}, |
| "output_type": "execute_result" |
| } |
| ], |
| "source": [ |
| "%%sql\n", |
| "DROP TABLE IF EXISTS pagerank_out, pagerank_out_summary;\n", |
| "\n", |
| "SELECT madlib.pagerank(\n", |
| " 'vertex', -- Vertex table\n", |
| " 'id', -- Vertix id column\n", |
| " 'edge', -- Edge table\n", |
| " 'src=src, dest=dest', -- Comma delimted string of edge arguments\n", |
| " 'pagerank_out', -- Output table of PageRank\n", |
| " NULL, -- Default damping factor (0.85)\n", |
| " NULL, -- Default max iters (100)\n", |
| " 0.00000001, -- Threshold\n", |
| " 'user_id'); -- Grouping column name\n", |
| "\n", |
| "SELECT * FROM pagerank_out ORDER BY user_id, pagerank DESC;" |
| ] |
| }, |
| { |
| "cell_type": "code", |
| "execution_count": 11, |
| "metadata": {}, |
| "outputs": [ |
| { |
| "name": "stdout", |
| "output_type": "stream", |
| "text": [ |
| "2 rows affected.\n" |
| ] |
| }, |
| { |
| "data": { |
| "text/html": [ |
| "<table>\n", |
| " <tr>\n", |
| " <th>user_id</th>\n", |
| " <th>__iterations__</th>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>1</td>\n", |
| " <td>27</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>2</td>\n", |
| " <td>31</td>\n", |
| " </tr>\n", |
| "</table>" |
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| "text/plain": [ |
| "[(1, 27), (2, 31)]" |
| ] |
| }, |
| "execution_count": 11, |
| "metadata": {}, |
| "output_type": "execute_result" |
| } |
| ], |
| "source": [ |
| "%%sql\n", |
| "SELECT * FROM pagerank_out_summary ORDER BY user_id;" |
| ] |
| }, |
| { |
| "cell_type": "markdown", |
| "metadata": {}, |
| "source": [ |
| "# 5. Personalized PageRank\n", |
| "Here we specify {2,4} as the personalization vertices. This parameter could be specified as ARRAY[2,4] as well:" |
| ] |
| }, |
| { |
| "cell_type": "code", |
| "execution_count": 12, |
| "metadata": {}, |
| "outputs": [ |
| { |
| "name": "stdout", |
| "output_type": "stream", |
| "text": [ |
| "Done.\n", |
| "1 rows affected.\n", |
| "7 rows affected.\n" |
| ] |
| }, |
| { |
| "data": { |
| "text/html": [ |
| "<table>\n", |
| " <tr>\n", |
| " <th>id</th>\n", |
| " <th>pagerank</th>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>0</td>\n", |
| " <td>0.282616480981</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>2</td>\n", |
| " <td>0.189069710497</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>3</td>\n", |
| " <td>0.177501646133</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>4</td>\n", |
| " <td>0.15505560795</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>1</td>\n", |
| " <td>0.0800556079496</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>6</td>\n", |
| " <td>0.0743076577868</td>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>5</td>\n", |
| " <td>0.0401701653568</td>\n", |
| " </tr>\n", |
| "</table>" |
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| "text/plain": [ |
| "[(0, 0.282616480980651),\n", |
| " (2, 0.18906971049691),\n", |
| " (3, 0.177501646133459),\n", |
| " (4, 0.155055607949638),\n", |
| " (1, 0.0800556079496381),\n", |
| " (6, 0.0743076577867786),\n", |
| " (5, 0.0401701653567887)]" |
| ] |
| }, |
| "execution_count": 12, |
| "metadata": {}, |
| "output_type": "execute_result" |
| } |
| ], |
| "source": [ |
| "%%sql\n", |
| "DROP TABLE IF EXISTS pagerank_out, pagerank_out_summary;\n", |
| "SELECT madlib.pagerank(\n", |
| " 'vertex', -- Vertex table\n", |
| " 'id', -- Vertix id column\n", |
| " 'edge', -- Edge table\n", |
| " 'src=src, dest=dest', -- Comma delimted string of edge arguments\n", |
| " 'pagerank_out', -- Output table of PageRank\n", |
| " NULL, -- Default damping factor (0.85)\n", |
| " NULL, -- Default max iters (100)\n", |
| " NULL, -- Default Threshold\n", |
| " NULL, -- No Grouping\n", |
| " '{2,4}'); -- Personalization vertices\n", |
| "SELECT * FROM pagerank_out ORDER BY pagerank DESC;" |
| ] |
| }, |
| { |
| "cell_type": "code", |
| "execution_count": 14, |
| "metadata": {}, |
| "outputs": [ |
| { |
| "name": "stdout", |
| "output_type": "stream", |
| "text": [ |
| "1 rows affected.\n" |
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| "<table>\n", |
| " <tr>\n", |
| " <th>__iterations__</th>\n", |
| " </tr>\n", |
| " <tr>\n", |
| " <td>37</td>\n", |
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| "[(37,)]" |
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| "execution_count": 14, |
| "metadata": {}, |
| "output_type": "execute_result" |
| } |
| ], |
| "source": [ |
| "%%sql\n", |
| "SELECT * FROM pagerank_out_summary;" |
| ] |
| } |
| ], |
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| "display_name": "Python 2", |
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