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[10/51] [partial] incubator-hivemall-site git commit: Updated
userguide for dimsum and general classifier/regressor
http://git-wip-us.apache.org/repos/asf/incubator-hivemall-site/blob/f103c424/userguide/recommend/movielens_cf.html
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+
+<!DOCTYPE HTML>
+<html lang="" >
+ <head>
+ <meta charset="UTF-8">
+ <meta content="text/html; charset=utf-8" http-equiv="Content-Type">
+ <title>Item-based Collaborative Filtering ยท Hivemall User Manual</title>
+ <meta http-equiv="X-UA-Compatible" content="IE=edge" />
+ <meta name="description" content="">
+ <meta name="generator" content="GitBook 3.2.2">
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+ <link rel="next" href="movielens_mf.html" />
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+ <link rel="prev" href="movielens_dataset.html" />
+
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+ </head>
+ <body>
+
+<div class="book">
+ <div class="book-summary">
+
+
+<div id="book-search-input" role="search">
+ <input type="text" placeholder="Type to search" />
+</div>
+
+
+ <nav role="navigation">
+
+
+
+<ul class="summary">
+
+
+
+
+ <li>
+ <a href="http://hivemall.incubator.apache.org/" target="_blank" class="custom-link"><i class="fa fa-home"></i> Home</a>
+ </li>
+
+
+
+
+ <li class="divider"></li>
+
+
+
+
+ <li class="header">TABLE OF CONTENTS</li>
+
+
+
+ <li class="chapter " data-level="1.1" data-path="../">
+
+ <a href="../">
+
+
+ <b>1.1.</b>
+
+ Introduction
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.2" data-path="../getting_started/">
+
+ <a href="../getting_started/">
+
+
+ <b>1.2.</b>
+
+ Getting Started
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="1.2.1" data-path="../getting_started/installation.html">
+
+ <a href="../getting_started/installation.html">
+
+
+ <b>1.2.1.</b>
+
+ Installation
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.2.2" data-path="../getting_started/permanent-functions.html">
+
+ <a href="../getting_started/permanent-functions.html">
+
+
+ <b>1.2.2.</b>
+
+ Install as permanent functions
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.2.3" data-path="../getting_started/input-format.html">
+
+ <a href="../getting_started/input-format.html">
+
+
+ <b>1.2.3.</b>
+
+ Input Format
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="1.3" data-path="../tips/">
+
+ <a href="../tips/">
+
+
+ <b>1.3.</b>
+
+ Tips for Effective Hivemall
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="1.3.1" data-path="../tips/addbias.html">
+
+ <a href="../tips/addbias.html">
+
+
+ <b>1.3.1.</b>
+
+ Explicit addBias() for better prediction
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.3.2" data-path="../tips/rand_amplify.html">
+
+ <a href="../tips/rand_amplify.html">
+
+
+ <b>1.3.2.</b>
+
+ Use rand_amplify() to better prediction results
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.3.3" data-path="../tips/rt_prediction.html">
+
+ <a href="../tips/rt_prediction.html">
+
+
+ <b>1.3.3.</b>
+
+ Real-time Prediction on RDBMS
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.3.4" data-path="../tips/ensemble_learning.html">
+
+ <a href="../tips/ensemble_learning.html">
+
+
+ <b>1.3.4.</b>
+
+ Ensemble learning for stable prediction
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.3.5" data-path="../tips/mixserver.html">
+
+ <a href="../tips/mixserver.html">
+
+
+ <b>1.3.5.</b>
+
+ Mixing models for a better prediction convergence (MIX server)
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.3.6" data-path="../tips/emr.html">
+
+ <a href="../tips/emr.html">
+
+
+ <b>1.3.6.</b>
+
+ Run Hivemall on Amazon Elastic MapReduce
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="1.4" data-path="../tips/general_tips.html">
+
+ <a href="../tips/general_tips.html">
+
+
+ <b>1.4.</b>
+
+ General Hive/Hadoop tips
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="1.4.1" data-path="../tips/rowid.html">
+
+ <a href="../tips/rowid.html">
+
+
+ <b>1.4.1.</b>
+
+ Adding rowid for each row
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.4.2" data-path="../tips/hadoop_tuning.html">
+
+ <a href="../tips/hadoop_tuning.html">
+
+
+ <b>1.4.2.</b>
+
+ Hadoop tuning for Hivemall
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="1.5" data-path="../troubleshooting/">
+
+ <a href="../troubleshooting/">
+
+
+ <b>1.5.</b>
+
+ Troubleshooting
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="1.5.1" data-path="../troubleshooting/oom.html">
+
+ <a href="../troubleshooting/oom.html">
+
+
+ <b>1.5.1.</b>
+
+ OutOfMemoryError in training
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.5.2" data-path="../troubleshooting/mapjoin_task_error.html">
+
+ <a href="../troubleshooting/mapjoin_task_error.html">
+
+
+ <b>1.5.2.</b>
+
+ SemanticException Generate Map Join Task Error: Cannot serialize object
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.5.3" data-path="../troubleshooting/asterisk.html">
+
+ <a href="../troubleshooting/asterisk.html">
+
+
+ <b>1.5.3.</b>
+
+ Asterisk argument for UDTF does not work
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.5.4" data-path="../troubleshooting/num_mappers.html">
+
+ <a href="../troubleshooting/num_mappers.html">
+
+
+ <b>1.5.4.</b>
+
+ The number of mappers is less than input splits in Hadoop 2.x
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.5.5" data-path="../troubleshooting/mapjoin_classcastex.html">
+
+ <a href="../troubleshooting/mapjoin_classcastex.html">
+
+
+ <b>1.5.5.</b>
+
+ Map-side Join causes ClassCastException on Tez
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+
+
+
+ <li class="header">Part II - Generic Features</li>
+
+
+
+ <li class="chapter " data-level="2.1" data-path="../misc/generic_funcs.html">
+
+ <a href="../misc/generic_funcs.html">
+
+
+ <b>2.1.</b>
+
+ List of generic Hivemall functions
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="2.2" data-path="../misc/topk.html">
+
+ <a href="../misc/topk.html">
+
+
+ <b>2.2.</b>
+
+ Efficient Top-K query processing
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="2.3" data-path="../misc/tokenizer.html">
+
+ <a href="../misc/tokenizer.html">
+
+
+ <b>2.3.</b>
+
+ English/Japanese Text Tokenizer
+
+ </a>
+
+
+
+ </li>
+
+
+
+
+ <li class="header">Part III - Feature Engineering</li>
+
+
+
+ <li class="chapter " data-level="3.1" data-path="../ft_engineering/scaling.html">
+
+ <a href="../ft_engineering/scaling.html">
+
+
+ <b>3.1.</b>
+
+ Feature Scaling
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="3.2" data-path="../ft_engineering/hashing.html">
+
+ <a href="../ft_engineering/hashing.html">
+
+
+ <b>3.2.</b>
+
+ Feature Hashing
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="3.3" data-path="../ft_engineering/selection.html">
+
+ <a href="../ft_engineering/selection.html">
+
+
+ <b>3.3.</b>
+
+ Feature Selection
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="3.4" data-path="../ft_engineering/binning.html">
+
+ <a href="../ft_engineering/binning.html">
+
+
+ <b>3.4.</b>
+
+ Feature Binning
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="3.5" data-path="../ft_engineering/tfidf.html">
+
+ <a href="../ft_engineering/tfidf.html">
+
+
+ <b>3.5.</b>
+
+ TF-IDF Calculation
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="3.6" data-path="../ft_engineering/ft_trans.html">
+
+ <a href="../ft_engineering/ft_trans.html">
+
+
+ <b>3.6.</b>
+
+ FEATURE TRANSFORMATION
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="3.6.1" data-path="../ft_engineering/vectorization.html">
+
+ <a href="../ft_engineering/vectorization.html">
+
+
+ <b>3.6.1.</b>
+
+ Feature Vectorization
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="3.6.2" data-path="../ft_engineering/quantify.html">
+
+ <a href="../ft_engineering/quantify.html">
+
+
+ <b>3.6.2.</b>
+
+ Quantify non-number features
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+
+
+
+ <li class="header">Part IV - Evaluation</li>
+
+
+
+ <li class="chapter " data-level="4.1" data-path="../eval/stat_eval.html">
+
+ <a href="../eval/stat_eval.html">
+
+
+ <b>4.1.</b>
+
+ Statistical evaluation of a prediction model
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="4.1.1" data-path="../eval/auc.html">
+
+ <a href="../eval/auc.html">
+
+
+ <b>4.1.1.</b>
+
+ Area Under the ROC Curve
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="4.2" data-path="../eval/rank.html">
+
+ <a href="../eval/rank.html">
+
+
+ <b>4.2.</b>
+
+ Ranking Measures
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="4.3" data-path="../eval/datagen.html">
+
+ <a href="../eval/datagen.html">
+
+
+ <b>4.3.</b>
+
+ Data Generation
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="4.3.1" data-path="../eval/lr_datagen.html">
+
+ <a href="../eval/lr_datagen.html">
+
+
+ <b>4.3.1.</b>
+
+ Logistic Regression data generation
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+
+
+
+ <li class="header">Part V - Prediction</li>
+
+
+
+ <li class="chapter " data-level="5.1" data-path="../misc/prediction.html">
+
+ <a href="../misc/prediction.html">
+
+
+ <b>5.1.</b>
+
+ How Prediction Works
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="5.2" data-path="../regression/general.html">
+
+ <a href="../regression/general.html">
+
+
+ <b>5.2.</b>
+
+ Regression
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="5.3" data-path="../binaryclass/general.html">
+
+ <a href="../binaryclass/general.html">
+
+
+ <b>5.3.</b>
+
+ Binary Classification
+
+ </a>
+
+
+
+ </li>
+
+
+
+
+ <li class="header">Part VI - Binary classification tutorials</li>
+
+
+
+ <li class="chapter " data-level="6.1" data-path="../binaryclass/a9a.html">
+
+ <a href="../binaryclass/a9a.html">
+
+
+ <b>6.1.</b>
+
+ a9a
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="6.1.1" data-path="../binaryclass/a9a_dataset.html">
+
+ <a href="../binaryclass/a9a_dataset.html">
+
+
+ <b>6.1.1.</b>
+
+ Data preparation
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="6.1.2" data-path="../binaryclass/a9a_lr.html">
+
+ <a href="../binaryclass/a9a_lr.html">
+
+
+ <b>6.1.2.</b>
+
+ Logistic Regression
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="6.1.3" data-path="../binaryclass/a9a_minibatch.html">
+
+ <a href="../binaryclass/a9a_minibatch.html">
+
+
+ <b>6.1.3.</b>
+
+ Mini-batch Gradient Descent
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="6.2" data-path="../binaryclass/news20.html">
+
+ <a href="../binaryclass/news20.html">
+
+
+ <b>6.2.</b>
+
+ News20
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="6.2.1" data-path="../binaryclass/news20_dataset.html">
+
+ <a href="../binaryclass/news20_dataset.html">
+
+
+ <b>6.2.1.</b>
+
+ Data preparation
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="6.2.2" data-path="../binaryclass/news20_pa.html">
+
+ <a href="../binaryclass/news20_pa.html">
+
+
+ <b>6.2.2.</b>
+
+ Perceptron, Passive Aggressive
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="6.2.3" data-path="../binaryclass/news20_scw.html">
+
+ <a href="../binaryclass/news20_scw.html">
+
+
+ <b>6.2.3.</b>
+
+ CW, AROW, SCW
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="6.2.4" data-path="../binaryclass/news20_adagrad.html">
+
+ <a href="../binaryclass/news20_adagrad.html">
+
+
+ <b>6.2.4.</b>
+
+ AdaGradRDA, AdaGrad, AdaDelta
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="6.3" data-path="../binaryclass/kdd2010a.html">
+
+ <a href="../binaryclass/kdd2010a.html">
+
+
+ <b>6.3.</b>
+
+ KDD2010a
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="6.3.1" data-path="../binaryclass/kdd2010a_dataset.html">
+
+ <a href="../binaryclass/kdd2010a_dataset.html">
+
+
+ <b>6.3.1.</b>
+
+ Data preparation
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="6.3.2" data-path="../binaryclass/kdd2010a_scw.html">
+
+ <a href="../binaryclass/kdd2010a_scw.html">
+
+
+ <b>6.3.2.</b>
+
+ PA, CW, AROW, SCW
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="6.4" data-path="../binaryclass/kdd2010b.html">
+
+ <a href="../binaryclass/kdd2010b.html">
+
+
+ <b>6.4.</b>
+
+ KDD2010b
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="6.4.1" data-path="../binaryclass/kdd2010b_dataset.html">
+
+ <a href="../binaryclass/kdd2010b_dataset.html">
+
+
+ <b>6.4.1.</b>
+
+ Data preparation
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="6.4.2" data-path="../binaryclass/kdd2010b_arow.html">
+
+ <a href="../binaryclass/kdd2010b_arow.html">
+
+
+ <b>6.4.2.</b>
+
+ AROW
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="6.5" data-path="../binaryclass/webspam.html">
+
+ <a href="../binaryclass/webspam.html">
+
+
+ <b>6.5.</b>
+
+ Webspam
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="6.5.1" data-path="../binaryclass/webspam_dataset.html">
+
+ <a href="../binaryclass/webspam_dataset.html">
+
+
+ <b>6.5.1.</b>
+
+ Data pareparation
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="6.5.2" data-path="../binaryclass/webspam_scw.html">
+
+ <a href="../binaryclass/webspam_scw.html">
+
+
+ <b>6.5.2.</b>
+
+ PA1, AROW, SCW
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="6.6" data-path="../binaryclass/titanic_rf.html">
+
+ <a href="../binaryclass/titanic_rf.html">
+
+
+ <b>6.6.</b>
+
+ Kaggle Titanic
+
+ </a>
+
+
+
+ </li>
+
+
+
+
+ <li class="header">Part VII - Multiclass classification tutorials</li>
+
+
+
+ <li class="chapter " data-level="7.1" data-path="../multiclass/news20.html">
+
+ <a href="../multiclass/news20.html">
+
+
+ <b>7.1.</b>
+
+ News20 Multiclass
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="7.1.1" data-path="../multiclass/news20_dataset.html">
+
+ <a href="../multiclass/news20_dataset.html">
+
+
+ <b>7.1.1.</b>
+
+ Data preparation
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="7.1.2" data-path="../multiclass/news20_one-vs-the-rest_dataset.html">
+
+ <a href="../multiclass/news20_one-vs-the-rest_dataset.html">
+
+
+ <b>7.1.2.</b>
+
+ Data preparation for one-vs-the-rest classifiers
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="7.1.3" data-path="../multiclass/news20_pa.html">
+
+ <a href="../multiclass/news20_pa.html">
+
+
+ <b>7.1.3.</b>
+
+ PA
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="7.1.4" data-path="../multiclass/news20_scw.html">
+
+ <a href="../multiclass/news20_scw.html">
+
+
+ <b>7.1.4.</b>
+
+ CW, AROW, SCW
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="7.1.5" data-path="../multiclass/news20_ensemble.html">
+
+ <a href="../multiclass/news20_ensemble.html">
+
+
+ <b>7.1.5.</b>
+
+ Ensemble learning
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="7.1.6" data-path="../multiclass/news20_one-vs-the-rest.html">
+
+ <a href="../multiclass/news20_one-vs-the-rest.html">
+
+
+ <b>7.1.6.</b>
+
+ one-vs-the-rest classifier
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="7.2" data-path="../multiclass/iris.html">
+
+ <a href="../multiclass/iris.html">
+
+
+ <b>7.2.</b>
+
+ Iris
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="7.2.1" data-path="../multiclass/iris_dataset.html">
+
+ <a href="../multiclass/iris_dataset.html">
+
+
+ <b>7.2.1.</b>
+
+ Data preparation
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="7.2.2" data-path="../multiclass/iris_scw.html">
+
+ <a href="../multiclass/iris_scw.html">
+
+
+ <b>7.2.2.</b>
+
+ SCW
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="7.2.3" data-path="../multiclass/iris_randomforest.html">
+
+ <a href="../multiclass/iris_randomforest.html">
+
+
+ <b>7.2.3.</b>
+
+ RandomForest
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+
+
+
+ <li class="header">Part VIII - Regression tutorials</li>
+
+
+
+ <li class="chapter " data-level="8.1" data-path="../regression/e2006.html">
+
+ <a href="../regression/e2006.html">
+
+
+ <b>8.1.</b>
+
+ E2006-tfidf regression
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="8.1.1" data-path="../regression/e2006_dataset.html">
+
+ <a href="../regression/e2006_dataset.html">
+
+
+ <b>8.1.1.</b>
+
+ Data preparation
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="8.1.2" data-path="../regression/e2006_arow.html">
+
+ <a href="../regression/e2006_arow.html">
+
+
+ <b>8.1.2.</b>
+
+ Passive Aggressive, AROW
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="8.2" data-path="../regression/kddcup12tr2.html">
+
+ <a href="../regression/kddcup12tr2.html">
+
+
+ <b>8.2.</b>
+
+ KDDCup 2012 track 2 CTR prediction
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="8.2.1" data-path="../regression/kddcup12tr2_dataset.html">
+
+ <a href="../regression/kddcup12tr2_dataset.html">
+
+
+ <b>8.2.1.</b>
+
+ Data preparation
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="8.2.2" data-path="../regression/kddcup12tr2_lr.html">
+
+ <a href="../regression/kddcup12tr2_lr.html">
+
+
+ <b>8.2.2.</b>
+
+ Logistic Regression, Passive Aggressive
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="8.2.3" data-path="../regression/kddcup12tr2_lr_amplify.html">
+
+ <a href="../regression/kddcup12tr2_lr_amplify.html">
+
+
+ <b>8.2.3.</b>
+
+ Logistic Regression with Amplifier
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="8.2.4" data-path="../regression/kddcup12tr2_adagrad.html">
+
+ <a href="../regression/kddcup12tr2_adagrad.html">
+
+
+ <b>8.2.4.</b>
+
+ AdaGrad, AdaDelta
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+
+
+
+ <li class="header">Part IX - Recommendation</li>
+
+
+
+ <li class="chapter " data-level="9.1" data-path="cf.html">
+
+ <a href="cf.html">
+
+
+ <b>9.1.</b>
+
+ Collaborative Filtering
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="9.1.1" data-path="item_based_cf.html">
+
+ <a href="item_based_cf.html">
+
+
+ <b>9.1.1.</b>
+
+ Item-based Collaborative Filtering
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="9.2" data-path="news20.html">
+
+ <a href="news20.html">
+
+
+ <b>9.2.</b>
+
+ News20 related article recommendation Tutorial
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="9.2.1" data-path="../multiclass/news20_dataset.html">
+
+ <a href="../multiclass/news20_dataset.html">
+
+
+ <b>9.2.1.</b>
+
+ Data preparation
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="9.2.2" data-path="news20_jaccard.html">
+
+ <a href="news20_jaccard.html">
+
+
+ <b>9.2.2.</b>
+
+ LSH/Minhash and Jaccard Similarity
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="9.2.3" data-path="news20_knn.html">
+
+ <a href="news20_knn.html">
+
+
+ <b>9.2.3.</b>
+
+ LSH/Minhash and Brute-Force Search
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="9.2.4" data-path="news20_bbit_minhash.html">
+
+ <a href="news20_bbit_minhash.html">
+
+
+ <b>9.2.4.</b>
+
+ kNN search using b-Bits Minhash
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="9.3" data-path="movielens.html">
+
+ <a href="movielens.html">
+
+
+ <b>9.3.</b>
+
+ MovieLens movie recommendation Tutorial
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="9.3.1" data-path="movielens_dataset.html">
+
+ <a href="movielens_dataset.html">
+
+
+ <b>9.3.1.</b>
+
+ Data preparation
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter active" data-level="9.3.2" data-path="movielens_cf.html">
+
+ <a href="movielens_cf.html">
+
+
+ <b>9.3.2.</b>
+
+ Item-based Collaborative Filtering
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="9.3.3" data-path="movielens_mf.html">
+
+ <a href="movielens_mf.html">
+
+
+ <b>9.3.3.</b>
+
+ Matrix Factorization
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="9.3.4" data-path="movielens_fm.html">
+
+ <a href="movielens_fm.html">
+
+
+ <b>9.3.4.</b>
+
+ Factorization Machine
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="9.3.5" data-path="movielens_cv.html">
+
+ <a href="movielens_cv.html">
+
+
+ <b>9.3.5.</b>
+
+ 10-fold Cross Validation (Matrix Factorization)
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+
+
+
+ <li class="header">Part X - Anomaly Detection</li>
+
+
+
+ <li class="chapter " data-level="10.1" data-path="../anomaly/lof.html">
+
+ <a href="../anomaly/lof.html">
+
+
+ <b>10.1.</b>
+
+ Outlier Detection using Local Outlier Factor (LOF)
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="10.2" data-path="../anomaly/sst.html">
+
+ <a href="../anomaly/sst.html">
+
+
+ <b>10.2.</b>
+
+ Change-Point Detection using Singular Spectrum Transformation (SST)
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="10.3" data-path="../anomaly/changefinder.html">
+
+ <a href="../anomaly/changefinder.html">
+
+
+ <b>10.3.</b>
+
+ ChangeFinder: Detecting Outlier and Change-Point Simultaneously
+
+ </a>
+
+
+
+ </li>
+
+
+
+
+ <li class="header">Part XI - Clustering</li>
+
+
+
+ <li class="chapter " data-level="11.1" data-path="../clustering/lda.html">
+
+ <a href="../clustering/lda.html">
+
+
+ <b>11.1.</b>
+
+ Latent Dirichlet Allocation
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="11.2" data-path="../clustering/plsa.html">
+
+ <a href="../clustering/plsa.html">
+
+
+ <b>11.2.</b>
+
+ Probabilistic Latent Semantic Analysis
+
+ </a>
+
+
+
+ </li>
+
+
+
+
+ <li class="header">Part XII - GeoSpatial functions</li>
+
+
+
+ <li class="chapter " data-level="12.1" data-path="../geospatial/latlon.html">
+
+ <a href="../geospatial/latlon.html">
+
+
+ <b>12.1.</b>
+
+ Lat/Lon functions
+
+ </a>
+
+
+
+ </li>
+
+
+
+
+ <li class="header">Part XIII - Hivemall on Spark</li>
+
+
+
+ <li class="chapter " data-level="13.1" data-path="../spark/getting_started/">
+
+ <a href="../spark/getting_started/">
+
+
+ <b>13.1.</b>
+
+ Getting Started
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="13.1.1" data-path="../spark/getting_started/installation.html">
+
+ <a href="../spark/getting_started/installation.html">
+
+
+ <b>13.1.1.</b>
+
+ Installation
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="13.2" data-path="../spark/binaryclass/">
+
+ <a href="../spark/binaryclass/">
+
+
+ <b>13.2.</b>
+
+ Binary Classification
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="13.2.1" data-path="../spark/binaryclass/a9a_df.html">
+
+ <a href="../spark/binaryclass/a9a_df.html">
+
+
+ <b>13.2.1.</b>
+
+ a9a Tutorial for DataFrame
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="13.3" data-path="../spark/binaryclass/">
+
+ <a href="../spark/binaryclass/">
+
+
+ <b>13.3.</b>
+
+ Regression
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="13.3.1" data-path="../spark/regression/e2006_df.html">
+
+ <a href="../spark/regression/e2006_df.html">
+
+
+ <b>13.3.1.</b>
+
+ E2006-tfidf regression Tutorial for DataFrame
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="13.4" data-path="../spark/misc/misc.html">
+
+ <a href="../spark/misc/misc.html">
+
+
+ <b>13.4.</b>
+
+ Generic features
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="13.4.1" data-path="../spark/misc/topk_join.html">
+
+ <a href="../spark/misc/topk_join.html">
+
+
+ <b>13.4.1.</b>
+
+ Top-k Join processing
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="13.4.2" data-path="../spark/misc/functions.html">
+
+ <a href="../spark/misc/functions.html">
+
+
+ <b>13.4.2.</b>
+
+ Other utility functions
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+
+
+
+ <li class="header">Part XIV - Hivemall on Docker</li>
+
+
+
+ <li class="chapter " data-level="14.1" data-path="../docker/getting_started.html">
+
+ <a href="../docker/getting_started.html">
+
+
+ <b>14.1.</b>
+
+ Getting Started
+
+ </a>
+
+
+
+ </li>
+
+
+
+
+ <li class="header">Part XIV - External References</li>
+
+
+
+ <li class="chapter " data-level="15.1" >
+
+ <a target="_blank" href="https://github.com/maropu/hivemall-spark">
+
+
+ <b>15.1.</b>
+
+ Hivemall on Apache Spark
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="15.2" >
+
+ <a target="_blank" href="https://github.com/daijyc/hivemall/wiki/PigHome">
+
+
+ <b>15.2.</b>
+
+ Hivemall on Apache Pig
+
+ </a>
+
+
+
+ </li>
+
+
+
+
+ <li class="divider"></li>
+
+ <li>
+ <a href="https://www.gitbook.com" target="blank" class="gitbook-link">
+ Published with GitBook
+ </a>
+ </li>
+</ul>
+
+
+ </nav>
+
+
+ </div>
+
+ <div class="book-body">
+
+ <div class="body-inner">
+
+
+
+<div class="book-header" role="navigation">
+
+
+ <!-- Title -->
+ <h1>
+ <i class="fa fa-circle-o-notch fa-spin"></i>
+ <a href=".." >Item-based Collaborative Filtering</a>
+ </h1>
+</div>
+
+
+
+
+ <div class="page-wrapper" tabindex="-1" role="main">
+ <div class="page-inner">
+
+<div id="book-search-results">
+ <div class="search-noresults">
+
+ <section class="normal markdown-section">
+
+ <!--
+ Licensed to the Apache Software Foundation (ASF) under one
+ or more contributor license agreements. See the NOTICE file
+ distributed with this work for additional information
+ regarding copyright ownership. The ASF licenses this file
+ to you under the Apache License, Version 2.0 (the
+ "License"); you may not use this file except in compliance
+ with the License. You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+ Unless required by applicable law or agreed to in writing,
+ software distributed under the License is distributed on an
+ "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ KIND, either express or implied. See the License for the
+ specific language governing permissions and limitations
+ under the License.
+-->
+<p><a href="item_based_cf.html">Our user guide for item-based collaborative filtering (CF)</a> introduced how to make recommendation based on item-item similarities. Here, we particularly focus on <a href="item_based_cf.html#dimsum-approximated-all-pairs-cosine-similarity-computation">DIMSUM</a>, an efficient and approximated similarity computation scheme, and try to make recommendation from the MovieLens data.</p>
+<!-- toc --><div id="toc" class="toc">
+
+<ul>
+<li><a href="#compute-movie-movie-similarity">Compute movie-movie similarity</a></li>
+<li><a href="#prediction">Prediction</a></li>
+<li><a href="#recommendation">Recommendation</a></li>
+<li><a href="#evaluation">Evaluation</a></li>
+</ul>
+
+</div><!-- tocstop -->
+<h1 id="compute-movie-movie-similarity">Compute movie-movie similarity</h1>
+<p><a href="item_based_cf.html#dimsum-approximated-all-pairs-cosine-similarity-computation.md">As we explained in the general introduction of item-based CF</a>, following query finds top-<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.69444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.03148em;">k</span></span></span></span> nearest-neighborhood movies for each movie:</p>
+<pre><code class="lang-sql"><span class="hljs-keyword">drop</span> <span class="hljs-keyword">table</span> <span class="hljs-keyword">if</span> <span class="hljs-keyword">exists</span> dimsum_movie_similarity;
+<span class="hljs-keyword">create</span> <span class="hljs-keyword">table</span> dimsum_movie_similarity
+<span class="hljs-keyword">as</span>
+<span class="hljs-keyword">with</span> movie_magnitude <span class="hljs-keyword">as</span> ( <span class="hljs-comment">-- compute magnitude of each movie vector</span>
+ <span class="hljs-keyword">select</span>
+ to_map(j, mag) <span class="hljs-keyword">as</span> mags
+ <span class="hljs-keyword">from</span> (
+ <span class="hljs-keyword">select</span>
+ movieid <span class="hljs-keyword">as</span> j,
+ l2_norm(rating) <span class="hljs-keyword">as</span> mag
+ <span class="hljs-keyword">from</span>
+ training
+ <span class="hljs-keyword">group</span> <span class="hljs-keyword">by</span>
+ movieid
+ ) t0
+),
+movie_features <span class="hljs-keyword">as</span> (
+ <span class="hljs-keyword">select</span>
+ userid <span class="hljs-keyword">as</span> i,
+ collect_list(
+ feature(movieid, rating)
+ ) <span class="hljs-keyword">as</span> feature_vector
+ <span class="hljs-keyword">from</span>
+ training
+ <span class="hljs-keyword">group</span> <span class="hljs-keyword">by</span>
+ userid
+),
+partial_result <span class="hljs-keyword">as</span> ( <span class="hljs-comment">-- launch DIMSUM in a MapReduce fashion</span>
+ <span class="hljs-keyword">select</span>
+ dimsum_mapper(f.feature_vector, m.mags, <span class="hljs-string">'-threshold 0.1 -disable_symmetric_output'</span>)
+ <span class="hljs-keyword">as</span> (movieid, other, s)
+ <span class="hljs-keyword">from</span>
+ movie_features f
+ <span class="hljs-keyword">left</span> <span class="hljs-keyword">outer</span> <span class="hljs-keyword">join</span> movie_magnitude m
+),
+similarity <span class="hljs-keyword">as</span> ( <span class="hljs-comment">-- reduce (i.e., sum up) mappers' partial results</span>
+ <span class="hljs-keyword">select</span>
+ movieid,
+ other,
+ <span class="hljs-keyword">sum</span>(s) <span class="hljs-keyword">as</span> similarity
+ <span class="hljs-keyword">from</span>
+ partial_result
+ <span class="hljs-keyword">group</span> <span class="hljs-keyword">by</span>
+ movieid, other
+),
+topk <span class="hljs-keyword">as</span> (
+ <span class="hljs-keyword">select</span>
+ each_top_k( <span class="hljs-comment">-- get top-10 nearest neighbors based on similarity score</span>
+ <span class="hljs-number">10</span>, movieid, similarity,
+ movieid, other <span class="hljs-comment">-- output items</span>
+ ) <span class="hljs-keyword">as</span> (<span class="hljs-keyword">rank</span>, similarity, movieid, other)
+ <span class="hljs-keyword">from</span> (
+ <span class="hljs-keyword">select</span> * <span class="hljs-keyword">from</span> similarity
+ CLUSTER <span class="hljs-keyword">BY</span> movieid
+ ) t
+)
+<span class="hljs-keyword">select</span>
+ movieid, other, similarity
+<span class="hljs-keyword">from</span>
+ topk
+;
+</code></pre>
+<table>
+<thead>
+<tr>
+<th style="text-align:center">movieid</th>
+<th style="text-align:center">other</th>
+<th style="text-align:left">similarity</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td style="text-align:center">1</td>
+<td style="text-align:center">2095</td>
+<td style="text-align:left">0.9377422722094696</td>
+</tr>
+<tr>
+<td style="text-align:center">1</td>
+<td style="text-align:center">231</td>
+<td style="text-align:left">0.9316530366756418</td>
+</tr>
+<tr>
+<td style="text-align:center">1</td>
+<td style="text-align:center">1407</td>
+<td style="text-align:left">0.9194745656079863</td>
+</tr>
+<tr>
+<td style="text-align:center">1</td>
+<td style="text-align:center">3442</td>
+<td style="text-align:left">0.9133853300741587</td>
+</tr>
+<tr>
+<td style="text-align:center">1</td>
+<td style="text-align:center">1792</td>
+<td style="text-align:left">0.9072960945403309</td>
+</tr>
+<tr>
+<td style="text-align:center">...</td>
+<td style="text-align:center">...</td>
+<td style="text-align:left">...</td>
+</tr>
+</tbody>
+</table>
+<p>Since we set <code>k=10</code>, output has 10 most-similar movies per <code>movieid</code>.</p>
+<div class="panel panel-primary"><div class="panel-heading"><h3 class="panel-title" id="note"><i class="fa fa-edit"></i> Note</h3></div><div class="panel-body"><p>Since we specified an option <code>-disable_symmetric_output</code>, output table does not contain inverted similarities such as <code><2095, 1></code>, <code><231, 1></code>, <code><1407, 1></code>, ...</p></div></div>
+<h1 id="prediction">Prediction</h1>
+<p>Next, we predict rating for unforeseen user-movie pairs based on the top-<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.69444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.03148em;">k</span></span></span></span> similarities:</p>
+<pre><code class="lang-sql"><span class="hljs-keyword">drop</span> <span class="hljs-keyword">table</span> <span class="hljs-keyword">if</span> <span class="hljs-keyword">exists</span> dimsum_prediction;
+<span class="hljs-keyword">create</span> <span class="hljs-keyword">table</span> dimsum_prediction
+<span class="hljs-keyword">as</span>
+<span class="hljs-keyword">with</span> similarity_all <span class="hljs-keyword">as</span> (
+ <span class="hljs-comment">-- copy (i1, i2)'s similarity as (i2, i1)'s one</span>
+ <span class="hljs-keyword">select</span> movieid, other, similarity <span class="hljs-keyword">from</span> dimsum_movie_similarity
+ <span class="hljs-keyword">union</span> all
+ <span class="hljs-keyword">select</span> other <span class="hljs-keyword">as</span> movieid, movieid <span class="hljs-keyword">as</span> other, similarity <span class="hljs-keyword">from</span> dimsum_movie_similarity
+)
+<span class="hljs-keyword">select</span>
+ <span class="hljs-comment">-- target user</span>
+ t1.userid,
+
+ <span class="hljs-comment">-- recommendation candidate</span>
+ t2.movieid,
+
+ <span class="hljs-comment">-- predicted rating: r_{u,i} = sum(s_{i,:} * r_{u,:}) / sum(s_{i,:})</span>
+ <span class="hljs-keyword">sum</span>(t1.rating * t2.similarity) / <span class="hljs-keyword">sum</span>(t2.similarity) <span class="hljs-keyword">as</span> rating
+<span class="hljs-keyword">from</span>
+ training t1 <span class="hljs-comment">-- r_{u,<movieid>}</span>
+<span class="hljs-keyword">left</span> <span class="hljs-keyword">join</span> <span class="hljs-comment">-- s_{i,<other>}</span>
+ similarity_all t2
+ <span class="hljs-keyword">on</span> t1.movieid = t2.other
+<span class="hljs-keyword">where</span>
+ <span class="hljs-comment">-- do not include movies that user already rated</span>
+ <span class="hljs-keyword">NOT</span> <span class="hljs-keyword">EXISTS</span> (
+ <span class="hljs-keyword">SELECT</span> a.movieid <span class="hljs-keyword">FROM</span> training a
+ <span class="hljs-keyword">WHERE</span> a.userid = t1.userid <span class="hljs-keyword">AND</span> a.movieid = t2.movieid
+ )
+<span class="hljs-keyword">group</span> <span class="hljs-keyword">by</span>
+ t1.userid, t2.movieid
+;
+</code></pre>
+<p>This query computes estimated rating as follows:</p>
+<table>
+<thead>
+<tr>
+<th style="text-align:center">userid</th>
+<th style="text-align:center">movieid</th>
+<th style="text-align:left">rating</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td style="text-align:center">1</td>
+<td style="text-align:center">1000</td>
+<td style="text-align:left">5.0</td>
+</tr>
+<tr>
+<td style="text-align:center">1</td>
+<td style="text-align:center">1010</td>
+<td style="text-align:left">5.0</td>
+</tr>
+<tr>
+<td style="text-align:center">1</td>
+<td style="text-align:center">1012</td>
+<td style="text-align:left">4.246349332667371</td>
+</tr>
+<tr>
+<td style="text-align:center">1</td>
+<td style="text-align:center">1013</td>
+<td style="text-align:left">5.0</td>
+</tr>
+<tr>
+<td style="text-align:center">1</td>
+<td style="text-align:center">1014</td>
+<td style="text-align:left">5.0</td>
+</tr>
+<tr>
+<td style="text-align:center">...</td>
+<td style="text-align:center">...</td>
+<td style="text-align:left">...</td>
+</tr>
+</tbody>
+</table>
+<p>Theoretically, for the <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>t</mi></mrow><annotation encoding="application/x-tex">t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.61508em;"></span><span class="strut bottom" style="height:0.61508em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">t</span></span></span></span>-th nearest-neighborhood item <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>τ</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">\tau(t)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.1132em;">τ</span><span class=
"mopen">(</span><span class="mord mathit">t</span><span class="mclose">)</span></span></span></span>, prediction can be done by top-<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.69444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.03148em;">k</span></span></span></span> weighted sum of target user's historical ratings:
+<span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>r</mi><mrow><mi>u</mi><mo separator="true">,</mo><mi>i</mi></mrow></msub><mo>=</mo><mfrac><mrow><msubsup><mo>∑</mo><mrow><mi>t</mi><mo>=</mo><mn>1</mn></mrow><mi>k</mi></msubsup><msub><mi>s</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>τ</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></msub><mo>⋅</mo><msub><mi>r</mi><mrow><mi>u</mi><mo separator="true">,</mo><mi>τ</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></msub></mrow><mrow><msubsup><mo>∑</mo><mrow><mi>t</mi><mo>=</mo><mn>1</mn></mrow><mi>k</mi></msubsup><msub><mi>s</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>τ</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></msub></mrow></mfrac><mo separator="true">,</mo></mrow><annotation encoding="application/x-tex">
+r_{u,i} = \frac{\sum^k_{t=1} s_{i,\tau(t)} \cdot r_{u,\tau(t)} }{ \sum^k_{t=1} s_{i,\tau(t)} },
+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:1.5953079999999997em;"></span><span class="strut bottom" style="height:2.6906159999999995em;vertical-align:-1.0953079999999997em;"></span><span class="base displaystyle textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">r</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">u</span><span class="mpunct mtight">,</span><span class="mord mathit mtight">i</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></s
pan></span><span class="mrel">=</span><span class="mord reset-textstyle displaystyle textstyle uncramped"><span class="mopen sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span><span class="mfrac"><span class="vlist"><span style="top:0.7401079999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle textstyle cramped"><span class="mord textstyle cramped"><span class="mop"><span class="mop op-symbol small-op" style="top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist"><span style="top:0.30001em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">t</span><span class="mrel mtight">=</span><span class="mord mathrm mti
ght">1</span></span></span></span><span style="top:-0.364em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.03148em;">k</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span><span class="mord"><span class="mord mathit">s</span><span class="msupsub"><span class="vlist"><span style="top:0.18019999999999992em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathit mtight" style="margin-right:0.1
132em;">τ</span><span class="mopen mtight">(</span><span class="mord mathit mtight">t</span><span class="mclose mtight">)</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span><span style="top:-0.22999999999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle textstyle uncramped frac-line"></span></span><span style="top:-0.7451999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle textstyle uncramped"><span class="mord textstyle uncramped"><span class="mop"><span class="mop op-symbol small-op" style="top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist"><span style="top:0.30001em;margin-left:0em;margin-right:0.0
5em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">t</span><span class="mrel mtight">=</span><span class="mord mathrm mtight">1</span></span></span></span><span style="top:-0.364em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathit mtight" style="margin-right:0.03148em;">k</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span><span class="mord"><span class="mord mathit">s</span><span class="msupsub"><span class="vlist"><span style="top:0.18019999999999992em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-
ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathit mtight" style="margin-right:0.1132em;">τ</span><span class="mopen mtight">(</span><span class="mord mathit mtight">t</span><span class="mclose mtight">)</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span><span class="mbin">⋅</span><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">r</span><span class="msupsub"><span class="vlist"><span style="top:0.18019999999999992em;margin-right:0.05em;margin-left:-0.02778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-t
extstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">u</span><span class="mpunct mtight">,</span><span class="mord mathit mtight" style="margin-right:0.1132em;">τ</span><span class="mopen mtight">(</span><span class="mord mathit mtight">t</span><span class="mclose mtight">)</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span><span class="mclose sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span></span><span class="mpunct">,</span></span></span></span></span>
+where <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>r</mi><mrow><mi>u</mi><mo separator="true">,</mo><mi>i</mi></mrow></msub></mrow><annotation encoding="application/x-tex">r_{u,i}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.716668em;vertical-align:-0.286108em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">r</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">u</span><span class="mpunct mtight">,</span><span class="mord mathit mtight">i</span></s
pan></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span> is user <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>u</mi></mrow><annotation encoding="application/x-tex">u</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.43056em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">u</span></span></span></span>'s rating for item (movie) <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.65952em;"></span><span class="strut bottom" style="height:0.65952em;
vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">i</span></span></span></span>, and <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>s</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi></mrow></msub></mrow><annotation encoding="application/x-tex">s_{i,j}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.716668em;vertical-align:-0.286108em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">s</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">i</sp
an><span class="mpunct mtight">,</span><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span> is similarity of <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.65952em;"></span><span class="strut bottom" style="height:0.65952em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">i</span></span></span></span>-<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class
="strut" style="height:0.65952em;"></span><span class="strut bottom" style="height:0.85396em;vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.05724em;">j</span></span></span></span> (<code>movieid</code>-<code>other</code>) pair.</p>
+<div class="panel panel-warning"><div class="panel-heading"><h3 class="panel-title" id="caution"><i class="fa fa-exclamation-triangle"></i> Caution</h3></div><div class="panel-body"><p>Since the number of similarities and users' past ratings are limited, we cannot say this output <strong>always</strong> contains prediction for <strong>every</strong> unforeseen user-item pairs; sometimes prediction for a specific user-item pair might be missing (i.e., <code>NULL</code>).</p></div></div>
+<p>In fact, our goal is to make recommendation, but we can evaluate the intermediate result as a rating prediction problem:</p>
+<pre><code class="lang-sql"><span class="hljs-keyword">select</span>
+ mae(t1.rating, t2.rating) <span class="hljs-keyword">as</span> mae,
+ rmse(t1.rating, t2.rating) <span class="hljs-keyword">as</span> rmse
+<span class="hljs-keyword">from</span>
+ testing t1
+<span class="hljs-keyword">left</span> <span class="hljs-keyword">join</span>
+ dimsum_prediction t2
+ <span class="hljs-keyword">on</span> t1.movieid = t2.movieid
+<span class="hljs-keyword">where</span>
+ t1.userid = t2.userid
+;
+</code></pre>
+<table>
+<thead>
+<tr>
+<th style="text-align:center">mae</th>
+<th style="text-align:center">rmse</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td style="text-align:center">0.7308365821230256</td>
+<td style="text-align:center">0.9594799959251938</td>
+</tr>
+</tbody>
+</table>
+<p>Rating of the MovieLens data is in <code>[1, 5]</code> range, so this average errors are reasonable as a predictor.</p>
+<h1 id="recommendation">Recommendation</h1>
+<p>By using the prediction table, making recommendation for each user is straightforward:</p>
+<pre><code class="lang-sql"><span class="hljs-keyword">drop</span> <span class="hljs-keyword">table</span> <span class="hljs-keyword">if</span> <span class="hljs-keyword">exists</span> dimsum_recommendation;
+<span class="hljs-keyword">create</span> <span class="hljs-keyword">table</span> dimsum_recommendation
+<span class="hljs-keyword">as</span>
+<span class="hljs-keyword">select</span>
+ userid,
+ map_values(to_ordered_map(rating, movieid, <span class="hljs-literal">true</span>)) <span class="hljs-keyword">as</span> rec_movies
+<span class="hljs-keyword">from</span>
+ dimsum_prediction
+<span class="hljs-keyword">group</span> <span class="hljs-keyword">by</span>
+ userid
+;
+</code></pre>
+<table>
+<thead>
+<tr>
+<th style="text-align:center">userid</th>
+<th style="text-align:left">rec_movies</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td style="text-align:center">1</td>
+<td style="text-align:left">["2590","999","372","1380","2078",...]</td>
+</tr>
+<tr>
+<td style="text-align:center">2</td>
+<td style="text-align:left">["580","945","43","36","1704",...]</td>
+</tr>
+<tr>
+<td style="text-align:center">3</td>
+<td style="text-align:left">["3744","852","1610","3740","2915",...]</td>
+</tr>
+<tr>
+<td style="text-align:center">4</td>
+<td style="text-align:left">["3379","923","1997","2194","2944",...]</td>
+</tr>
+<tr>
+<td style="text-align:center">5</td>
+<td style="text-align:left">["998","101","2696","2968","2275",...]</td>
+</tr>
+<tr>
+<td style="text-align:center">...</td>
+<td style="text-align:left">...</td>
+</tr>
+</tbody>
+</table>
+<div class="panel panel-primary"><div class="panel-heading"><h3 class="panel-title" id="note"><i class="fa fa-edit"></i> Note</h3></div><div class="panel-body"><p>Size of <code>rec_movies</code> varies depending on each user's <code>training</code> samples and what movies he/she already rated. </p></div></div>
+<h1 id="evaluation">Evaluation</h1>
+<p>Eventually, you can measure the quality of recommendation by using <a href="../eval/rank.html">ranking measures</a>:</p>
+<pre><code class="lang-sql">with truth as (
+ <span class="hljs-keyword">select</span>
+ userid,
+ map_values(to_ordered_map(rating, <span class="hljs-keyword">cast</span>(movieid <span class="hljs-keyword">as</span> <span class="hljs-keyword">string</span>), <span class="hljs-literal">true</span>)) <span class="hljs-keyword">as</span> truth
+ <span class="hljs-keyword">from</span>
+ testing
+ <span class="hljs-keyword">group</span> <span class="hljs-keyword">by</span>
+ userid
+)
+<span class="hljs-keyword">select</span>
+ recall(t1.rec_movies, t2.truth, <span class="hljs-number">10</span>) <span class="hljs-keyword">as</span> recall,
+ <span class="hljs-keyword">precision</span>(t1.rec_movies, t2.truth, <span class="hljs-number">10</span>) <span class="hljs-keyword">as</span> <span class="hljs-keyword">precision</span>,
+ average_precision(t1.rec_movies, t2.truth) <span class="hljs-keyword">as</span> average_precision,
+ auc(t1.rec_movies, t2.truth) <span class="hljs-keyword">as</span> auc,
+ mrr(t1.rec_movies, t2.truth) <span class="hljs-keyword">as</span> mrr,
+ ndcg(t1.rec_movies, t2.truth) <span class="hljs-keyword">as</span> ndcg
+<span class="hljs-keyword">from</span>
+ dimsum_recommendation t1
+<span class="hljs-keyword">join</span>
+ truth t2 <span class="hljs-keyword">on</span> t1.userid = t2.userid
+<span class="hljs-keyword">where</span> <span class="hljs-comment">-- at least 10 recommended items are necessary to compute recall@10 and precision@10</span>
+ <span class="hljs-keyword">size</span>(t1.rec_movies) >= <span class="hljs-number">10</span>
+;
+</code></pre>
+<table>
+<thead>
+<tr>
+<th style="text-align:center">measure</th>
+<th style="text-align:left">accuracy</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td style="text-align:center"><strong>Recall@10</strong></td>
+<td style="text-align:left">0.027033598585322713</td>
+</tr>
+<tr>
+<td style="text-align:center"><strong>Precision@10</strong></td>
+<td style="text-align:left">0.009001989389920506</td>
+</tr>
+<tr>
+<td style="text-align:center"><strong>Average Precision</strong></td>
+<td style="text-align:left">0.017363681149831108</td>
+</tr>
+<tr>
+<td style="text-align:center"><strong>AUC</strong></td>
+<td style="text-align:left">0.5264553136097863</td>
+</tr>
+<tr>
+<td style="text-align:center"><strong>MRR</strong></td>
+<td style="text-align:left">0.03507380742291146</td>
+</tr>
+<tr>
+<td style="text-align:center"><strong>NDCG</strong></td>
+<td style="text-align:left">0.15787655209987522</td>
+</tr>
+</tbody>
+</table>
+<p>If you set larger value to the DIMSUM's <code>-threshold</code> option, similarity will be more aggressively approximated. Consequently, while efficiency is improved, the accuracy is likely to be decreased.
+<div id="page-footer" class="localized-footer"><hr><!--
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