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+ + + + <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 add_bias() 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> + + 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/pairing.html"> + + <a href="../ft_engineering/pairing.html"> + + + <b>3.5.</b> + + FEATURE PAIRING + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="3.5.1" data-path="../ft_engineering/polynomial.html"> + + <a href="../ft_engineering/polynomial.html"> + + + <b>3.5.1.</b> + + Polynomial Features + + </a> + + + + </li> + + + </ul> + + </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="chapter " data-level="3.7" data-path="../ft_engineering/tfidf.html"> + + <a href="../ft_engineering/tfidf.html"> + + + <b>3.7.</b> + + TF-IDF Calculation + + </a> + + + + </li> + + + + + <li class="header">Part IV - Evaluation</li> + + + + <li class="chapter " data-level="4.1" data-path="../eval/binary_classification_measures.html"> + + <a href="../eval/binary_classification_measures.html"> + + + <b>4.1.</b> + + Binary Classification Metrics + + </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/multilabel_classification_measures.html"> + + <a href="../eval/multilabel_classification_measures.html"> + + + <b>4.2.</b> + + Multi-label Classification Metrics + + </a> + + + + </li> + + <li class="chapter " data-level="4.3" data-path="../eval/regression.html"> + + <a href="../eval/regression.html"> + + + <b>4.3.</b> + + Regression metrics + + </a> + + + + </li> + + <li class="chapter " data-level="4.4" data-path="../eval/rank.html"> + + <a href="../eval/rank.html"> + + + <b>4.4.</b> + + Ranking Measures + + </a> + + + + </li> + + <li class="chapter " data-level="4.5" data-path="../eval/datagen.html"> + + <a href="../eval/datagen.html"> + + + <b>4.5.</b> + + Data Generation + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="4.5.1" data-path="../eval/lr_datagen.html"> + + <a href="../eval/lr_datagen.html"> + + + <b>4.5.1.</b> + + Logistic Regression data generation + + </a> + + + + </li> + + + </ul> + + </li> + + + + + <li class="header">Part V - Supervised Learning</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="header">Part VI - Binary classification</li> + + + + <li class="chapter " data-level="6.1" data-path="../binaryclass/general.html"> + + <a href="../binaryclass/general.html"> + + + <b>6.1.</b> + + Binary Classification + + </a> + + + + </li> + + <li class="chapter " data-level="6.2" data-path="../binaryclass/a9a.html"> + + <a href="../binaryclass/a9a.html"> + + + <b>6.2.</b> + + a9a tutorial + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="6.2.1" data-path="../binaryclass/a9a_dataset.html"> + + <a href="../binaryclass/a9a_dataset.html"> + + + <b>6.2.1.</b> + + Data preparation + + </a> + + + + </li> + + <li class="chapter " data-level="6.2.2" data-path="../binaryclass/a9a_lr.html"> + + <a href="../binaryclass/a9a_lr.html"> + + + <b>6.2.2.</b> + + Logistic Regression + + </a> + + + + </li> + + <li class="chapter " data-level="6.2.3" data-path="../binaryclass/a9a_minibatch.html"> + + <a href="../binaryclass/a9a_minibatch.html"> + + + <b>6.2.3.</b> + + Mini-batch Gradient Descent + + </a> + + + + </li> + + + </ul> + + </li> + + <li class="chapter " data-level="6.3" data-path="../binaryclass/news20.html"> + + <a href="../binaryclass/news20.html"> + + + <b>6.3.</b> + + News20 tutorial + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="6.3.1" data-path="../binaryclass/news20_dataset.html"> + + <a href="../binaryclass/news20_dataset.html"> + + + <b>6.3.1.</b> + + Data preparation + + </a> + + + + </li> + + <li class="chapter " data-level="6.3.2" data-path="../binaryclass/news20_pa.html"> + + <a href="../binaryclass/news20_pa.html"> + + + <b>6.3.2.</b> + + Perceptron, Passive Aggressive + + </a> + + + + </li> + + <li class="chapter " data-level="6.3.3" data-path="../binaryclass/news20_scw.html"> + + <a href="../binaryclass/news20_scw.html"> + + + <b>6.3.3.</b> + + CW, AROW, SCW + + </a> + + + + </li> + + <li class="chapter " data-level="6.3.4" data-path="../binaryclass/news20_adagrad.html"> + + <a href="../binaryclass/news20_adagrad.html"> + + + <b>6.3.4.</b> + + AdaGradRDA, AdaGrad, AdaDelta + + </a> + + + + </li> + + <li class="chapter " data-level="6.3.5" data-path="../binaryclass/news20_rf.html"> + + <a href="../binaryclass/news20_rf.html"> + + + <b>6.3.5.</b> + + Random Forest + + </a> + + + + </li> + + + </ul> + + </li> + + <li class="chapter " data-level="6.4" data-path="../binaryclass/kdd2010a.html"> + + <a href="../binaryclass/kdd2010a.html"> + + + <b>6.4.</b> + + KDD2010a tutorial + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="6.4.1" data-path="../binaryclass/kdd2010a_dataset.html"> + + <a href="../binaryclass/kdd2010a_dataset.html"> + + + <b>6.4.1.</b> + + Data preparation + + </a> + + + + </li> + + <li class="chapter " data-level="6.4.2" data-path="../binaryclass/kdd2010a_scw.html"> + + <a href="../binaryclass/kdd2010a_scw.html"> + + + <b>6.4.2.</b> + + PA, CW, AROW, SCW + + </a> + + + + </li> + + + </ul> + + </li> + + <li class="chapter " data-level="6.5" data-path="../binaryclass/kdd2010b.html"> + + <a href="../binaryclass/kdd2010b.html"> + + + <b>6.5.</b> + + KDD2010b tutorial + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="6.5.1" data-path="../binaryclass/kdd2010b_dataset.html"> + + <a href="../binaryclass/kdd2010b_dataset.html"> + + + <b>6.5.1.</b> + + Data preparation + + </a> + + + + </li> + + <li class="chapter " data-level="6.5.2" data-path="../binaryclass/kdd2010b_arow.html"> + + <a href="../binaryclass/kdd2010b_arow.html"> + + + <b>6.5.2.</b> + + AROW + + </a> + + + + </li> + + + </ul> + + </li> + + <li class="chapter " data-level="6.6" data-path="../binaryclass/webspam.html"> + + <a href="../binaryclass/webspam.html"> + + + <b>6.6.</b> + + Webspam tutorial + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="6.6.1" data-path="../binaryclass/webspam_dataset.html"> + + <a href="../binaryclass/webspam_dataset.html"> + + + <b>6.6.1.</b> + + Data pareparation + + </a> + + + + </li> + + <li class="chapter " data-level="6.6.2" data-path="../binaryclass/webspam_scw.html"> + + <a href="../binaryclass/webspam_scw.html"> + + + <b>6.6.2.</b> + + PA1, AROW, SCW + + </a> + + + + </li> + + + </ul> + + </li> + + <li class="chapter " data-level="6.7" data-path="../binaryclass/titanic_rf.html"> + + <a href="../binaryclass/titanic_rf.html"> + + + <b>6.7.</b> + + Kaggle Titanic tutorial + + </a> + + + + </li> + + + + + <li class="header">Part VII - Multiclass classification</li> + + + + <li class="chapter " data-level="7.1" data-path="../multiclass/news20.html"> + + <a href="../multiclass/news20.html"> + + + <b>7.1.</b> + + News20 Multiclass tutorial + + </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 tutorial + + </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> + + Random Forest + + </a> + + + + </li> + + + </ul> + + </li> + + + + + <li class="header">Part VIII - Regression</li> + + + + <li class="chapter " data-level="8.1" data-path="../regression/general.html"> + + <a href="../regression/general.html"> + + + <b>8.1.</b> + + Regression + + </a> + + + + </li> + + <li class="chapter " data-level="8.2" data-path="../regression/e2006.html"> + + <a href="../regression/e2006.html"> + + + <b>8.2.</b> + + E2006-tfidf regression tutorial + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="8.2.1" data-path="../regression/e2006_dataset.html"> + + <a href="../regression/e2006_dataset.html"> + + + <b>8.2.1.</b> + + Data preparation + + </a> + + + + </li> + + <li class="chapter " data-level="8.2.2" data-path="../regression/e2006_arow.html"> + + <a href="../regression/e2006_arow.html"> + + + <b>8.2.2.</b> + + Passive Aggressive, AROW + + </a> + + + + </li> + + + </ul> + + </li> + + <li class="chapter " data-level="8.3" data-path="../regression/kddcup12tr2.html"> + + <a href="../regression/kddcup12tr2.html"> + + + <b>8.3.</b> + + KDDCup 2012 track 2 CTR prediction tutorial + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="8.3.1" data-path="../regression/kddcup12tr2_dataset.html"> + + <a href="../regression/kddcup12tr2_dataset.html"> + + + <b>8.3.1.</b> + + Data preparation + + </a> + + + + </li> + + <li class="chapter " data-level="8.3.2" data-path="../regression/kddcup12tr2_lr.html"> + + <a href="../regression/kddcup12tr2_lr.html"> + + + <b>8.3.2.</b> + + Logistic Regression, Passive Aggressive + + </a> + + + + </li> + + <li class="chapter " data-level="8.3.3" data-path="../regression/kddcup12tr2_lr_amplify.html"> + + <a href="../regression/kddcup12tr2_lr_amplify.html"> + + + <b>8.3.3.</b> + + Logistic Regression with Amplifier + + </a> + + + + </li> + + <li class="chapter " data-level="8.3.4" data-path="../regression/kddcup12tr2_adagrad.html"> + + <a href="../regression/kddcup12tr2_adagrad.html"> + + + <b>8.3.4.</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 " 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 active" data-level="9.3.5" data-path="movielens_slim.html"> + + <a href="movielens_slim.html"> + + + <b>9.3.5.</b> + + SLIM for Fast Top-K Recommendation + + </a> + + + + </li> + + <li class="chapter " data-level="9.3.6" data-path="movielens_cv.html"> + + <a href="movielens_cv.html"> + + + <b>9.3.6.</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> + + <li class="chapter " data-level="13.2.2" data-path="../spark/binaryclass/a9a_sql.html"> + + <a href="../spark/binaryclass/a9a_sql.html"> + + + <b>13.2.2.</b> + + a9a Tutorial for SQL + + </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> + + <li class="chapter " data-level="13.3.2" data-path="../spark/regression/e2006_sql.html"> + + <a href="../spark/regression/e2006_sql.html"> + + + <b>13.3.2.</b> + + E2006-tfidf regression Tutorial for SQL + + </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=".." >SLIM for Fast Top-K Recommendation</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>Hivemall supports a neighborhood-learning scheme using SLIM. +SLIM is a representative of neighborhood-learning recommendation algorithm introduced in the following paper:</p> +<ul> +<li>Xia Ning and George Karypis, <a href="https://dl.acm.org/citation.cfm?id=2118303"; target="_blank">SLIM: Sparse Linear Methods for Top-N Recommender Systems</a>, Proc. ICDM, 2011.</li> +</ul> +<p><em>Caution: SLIM is supported from Hivemall v0.5-rc.1 or later.</em></p> +<!-- toc --><div id="toc" class="toc"> + +<ul> +<li><a href="#slim-optimization-objective">SLIM optimization objective</a></li> +<li><a href="#data-preparation">Data preparation</a><ul> +<li><a href="#rating-binarization">Rating binarization</a></li> +<li><a href="#splitting-dataset">Splitting dataset</a><ul> +<li><a href="#leave-one-out-cross-validation">Leave-one-out cross validation</a></li> +<li><a href="#k-hold-corss-validation"><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:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.07153em;">K</span></span></span></span>-hold corss validation</a></li> +</ul> +</li> +<li><a href="#precompute-movie-movie-similarity">Precompute movie-movie similarity</a></li> +<li><a href="#create-training-input-tables">Create training input tables</a></li> +</ul> +</li> +<li><a href="#training">Training</a><ul> +<li><a href="#build-a-prediction-model-by-slim">Build a prediction model by SLIM</a></li> +<li><a href="#usage-of-trainslim">Usage of <code>train_slim</code></a></li> +</ul> +</li> +<li><a href="#prediction-and-recommendation">Prediction and recommendation</a><ul> +<li><a href="#predict-unknown-value-of-user-item-matrix">Predict unknown value of user-item matrix</a></li> +</ul> +</li> +<li><a href="#evaluation">Evaluation</a><ul> +<li><a href="#top-k-ranking-measures-hit-ratek-mrrk-and-precisionk">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:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.07153em;">K</span></span></span></span> ranking measures: Hit-Rate@K, MRR@K, and Precision@K</a><ul> +<li><a href="#leave-one-out-result">Leave-one-out result</a></li> +<li><a href="#k-hold-result"><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:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.07153em;">K</span></span></span></span>-hold result</a></li> +</ul> +</li> +<li><a href="#ranking-measures-mrr">Ranking measures: MRR</a><ul> +<li><a href="#leave-one-out-result-1">Leave-one-out result</a></li> +</ul> +</li> +</ul> +</li> +</ul> + +</div><!-- tocstop --> +<h1 id="slim-optimization-objective">SLIM optimization objective</h1> +<p>The optimization objective of <a href="(http:/glaros.dtc.umn.edu/gkhome/fetch/papers/SLIM2011icdm.pdf">SLIM</a>) is similar to Elastic Net (L1+L2 regularization) with additional constraints as follows:</p> +<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtable><mtr><mtd><mrow></mrow></mtd><mtd><mrow><mrow></mrow><mspace width="0.277778em"></mspace><mrow><mstyle mathsize="0.5em"><mtable><mtr><mtd><mrow></mrow></mtd></mtr><mtr><mtd><mrow><mstyle mathsize="1em"><mtext><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">z</mi><mi mathvariant="normal">e</mi></mtext></mstyle></mrow></mtd></mtr><mtr><mtd><mrow><msup><mrow></mrow><mrow><mstyle mathsize="0.7em"><msub><mi>w</mi><mrow><mi>j</mi></mrow></msub></mstyle></mrow></msup></mrow></mtd></mtr></mtable></mstyle></mrow><mspace width="0.277778em"></mspace></mrow></mtd><mtd><mrow></mrow></mtd><mtd><mrow><mrow></mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mi mathvariant="normal">∥</mi><msub><mi>r</mi><mro w><mi>j</mi></mrow></msub><mo>−</mo><mi>R</mi><msub><mi>w</mi><mrow><mi>j</mi></mrow></msub><msubsup><mi mathvariant="normal">∥</mi><mn>2</mn><mn>2</mn></msubsup><mo>+</mo><mfrac><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mi mathvariant="normal">∥</mi><msub><mi>w</mi><mrow><mi>j</mi></mrow></msub><msubsup><mi mathvariant="normal">∥</mi><mn>2</mn><mn>2</mn></msubsup><mo>+</mo><mi>λ</mi><mi mathvariant="normal">∥</mi><msub><mi>w</mi><mrow><mi>j</mi></mrow></msub><msub><mi mathvariant="normal">∥</mi><mn>1</mn></msub></mrow></mtd></mtr><mtr><mtd><mrow></mrow></mtd><mtd><mrow><mrow></mrow><mtext><mi mathvariant="normal">s</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">b</mi><mi mathvariant="normal">j</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">t</mi><mtext> </mtext><mi mathvariant="normal">t</mi><mi mathvariant="normal">o</mi></mtext></mrow></mtd><mtd><mrow>< /mrow></mtd><mtd><mrow><mrow></mrow><msub><mi>w</mi><mrow><mi>j</mi></mrow></msub><mo>≥</mo><mn>0</mn></mrow></mtd></mtr><mtr><mtd><mrow></mrow></mtd><mtd><mrow><mrow></mrow></mrow></mtd><mtd><mrow></mrow></mtd><mtd><mrow><mrow></mrow><mi>d</mi><mi>i</mi><mi>a</mi><mi>g</mi><mo>(</mo><mi>W</mi><mo>)</mo><mo>=</mo><mn>0</mn></mrow></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex"> +\begin{aligned} +& \;{\tiny\begin{matrix}\\ \normalsize \text{minimize} \\ ^{\scriptsize w_{j}}\end{matrix}}\; +&& \frac{1}{2}\Vert r_{j} - Rw_{j} \Vert_2^2 + \frac{\beta}{2} \Vert w_{j} \Vert_2^2 + \lambda \Vert w_{j} \Vert_1 \\ +& \text{subject to} +&& w_{j} \geq 0 \\ +&&& diag(W)= 0 +\end{aligned} +</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:2.5232200000000002em;"></span><span class="strut bottom" style="height:4.5464400000000005em;vertical-align:-2.02322em;"></span><span class="base displaystyle textstyle uncramped"><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist"><span style="top:-1.1517800000000002em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="mord displaystyle textstyle uncramped"></span></span><span style="top:0.4632199999999996em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="mord displaystyle 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style="font-size:1em;">​</span></span><span class="mord displaystyle textstyle uncramped"></span></span><span style="top:-0.00999999999999951em;"><span class="fontsize-ensurer reset-size1 size5"><spa n style="font-size:1em;">​</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord text displaystyle textstyle uncramped sizing reset-size1 size5 displaystyle textstyle uncramped"><span class="mord mathrm">minimize</span></span></span></span><span style="top:1.1900000000000006em;"><span class="fontsize-ensurer reset-size1 size5"><span style="font-size:1em;">​</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord"><span></span><span class="msupsub"><span class="vlist"><span style="top:-0.413em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size1 size5"><span style="font-size:0.48999999999999994em;">​</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord scriptstyle uncramped mtight"><span class="mord mtight sizing reset-size1 size2 scriptstyle uncramped"><span class="mord mathit mtight" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="v list"><span style="top:0.14300000000000002em;margin-right:0.07142857142857144em;margin-left:-0.02691em;"><span class="fontsize-ensurer reset-size2 size5"><span style="font-size:0em;">​</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord scriptscriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size2 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size1 size5"><span style="font-size:0.48999999999999994em;">​</span></span>​</span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size1 size5"><span style="font-size:1em;">​</span></span>​</span></span></span></span></span></span><span class="mspace thick space"></span></span></span><span style="top:0.4632199999999996em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0.5em;">​</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord displaystyle textstyle uncramped"></span><span class="mord text displaystyle textstyle uncramped"><span class="mord mathrm">subject to</span></span></span></span><span style="top:1.6632199999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0.5em;">​</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord displaystyle textstyle uncramped"></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0.5em;">​</span></span>​</span></span></span><span class="arraycolsep" style="width:2em;"></span><span class="col-align-r"><span class="vlist"><span style="top:-1.1517800000000002em;"><span class="fontsize-ensu rer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="mord displaystyle textstyle uncramped"></span></span><span style="top:0.4632199999999996em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="mord displaystyle textstyle uncramped"></span></span><span style="top:1.6632199999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="mord displaystyle textstyle uncramped"></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="col-align-l"><span class="vlist"><span style="top:-1.1517800000000002em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord displaystyle textstyle uncramped "></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:0.686em;"><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="mord mathrm">2</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:-0.677em;"><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="mord mathrm">1</span></span></span></span><span class="baseline-f ix"><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="mord mathrm">∥</span><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">r</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;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" 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 class="mbin">−</span><span class="mord mathi t" style="margin-right:0.00773em;">R</span><span class="mord"><span class="mord mathit" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02691em;"><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" 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 class="mord"><span class="mord mathrm">∥</span><span class="msupsub"><span class="vlist"><span style="top:0.247em;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 scri ptstyle cramped mtight"><span class="mord mathrm mtight">2</span></span></span><span style="top:-0.4129999999999999em;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 mathrm mtight">2</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 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:0.686em;"><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="mord mathrm">2</sp an></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:-0.677em;"><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="mord mathit" style="margin-right:0.05278em;">β</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="mord mathrm">∥</span><span class="mord"><span class="mord mathit" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist"><span style=" top:0.15em;margin-right:0.05em;margin-left:-0.02691em;"><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" 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 class="mord"><span class="mord mathrm">∥</span><span class="msupsub"><span class="vlist"><span style="top:0.247em;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 mathrm mtight">2</span></span></span><span style="top:-0.4129999999999999em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 s ize5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathrm mtight">2</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 mathit">λ</span><span class="mord mathrm">∥</span><span class="mord"><span class="mord mathit" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02691em;"><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" 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 class="mord"><span class="mord mathrm">∥</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 mathrm mtight">1</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 style="top:0.4632199999999996em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord displaystyle textstyle uncramped"></span><span class="mord"><span class="mord mathit" style="margin-right:0.02691em;">w</span><span c lass="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02691em;"><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" 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 class="mrel">≥</span><span class="mord mathrm">0</span></span></span><span style="top:1.6632199999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="mord displaystyle textstyle uncramped"><span class="mord displaystyle textstyle uncramped"></span><span class="mord mathit">d</span><span class="mord mathit">i</span><span class="mord mathit">a</spa n><span class="mord mathit" style="margin-right:0.03588em;">g</span><span class="mopen">(</span><span class="mord mathit" style="margin-right:0.13889em;">W</span><span class="mclose">)</span><span class="mrel">=</span><span class="mord mathrm">0</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></span></p> +<h1 id="data-preparation">Data preparation</h1> +<h2 id="rating-binarization">Rating binarization</h2> +<p>In this article, each user-movie matrix element is binarized to reduce training samples and consider only high rated movies whose rating is 4 or 5. So, every matrix element having a lower rating than 4 is not used for training.</p> +<pre><code class="lang-sql"><span class="hljs-keyword">SET</span> hivevar:<span class="hljs-keyword">seed</span>=<span class="hljs-number">31</span>; + +<span class="hljs-keyword">DROP</span> <span class="hljs-keyword">TABLE</span> ratings2; +<span class="hljs-keyword">CREATE</span> <span class="hljs-keyword">TABLE</span> ratings2 <span class="hljs-keyword">as</span> +<span class="hljs-keyword">select</span> + <span class="hljs-keyword">rand</span>(${<span class="hljs-keyword">seed</span>}) <span class="hljs-keyword">as</span> rnd, + userid, + movieid <span class="hljs-keyword">as</span> itemid, + <span class="hljs-keyword">cast</span>(<span class="hljs-number">1.0</span> <span class="hljs-keyword">as</span> <span class="hljs-built_in">float</span>) <span class="hljs-keyword">as</span> rating <span class="hljs-comment">-- double is also accepted</span> +<span class="hljs-keyword">from</span> + ratings +<span class="hljs-keyword">where</span> rating >= <span class="hljs-number">4.</span> +; +</code></pre> +<p><code>rnd</code> field is appended for each record to split <code>ratings2</code> into training and testing data later.</p> +<p>Binarization is an optional step, and you can use raw rating values to train a SLIM model.</p> +<h2 id="splitting-dataset">Splitting dataset</h2> +<p>To evaluate a recommendation model, this tutorial uses two type cross validations:</p> +<ul> +<li>Leave-one-out cross validation</li> +<li><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:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.07153em;">K</span></span></span></span>-hold cross validation</li> +</ul> +<p>The former is used in the <a href="http://glaros.dtc.umn.edu/gkhome/fetch/papers/SLIM2011icdm.pdf"; target="_blank">SLIM's paper</a> and the latter is used in <a href="http://slideshare.net/MarkLevy/efficient-slides/"; target="_blank">Mendeley's slide</a>.</p> +<h3 id="leave-one-out-cross-validation">Leave-one-out cross validation</h3> +<p>For leave-one-out cross validation, the dataset is split into a training set and a testing set by randomly selecting one of the non-zero entries of each user and placing it into the testing set. +In the following query, the movie has the smallest <code>rnd</code> value is used as test data (<code>testing</code> table) per a user. +And, the others are used as training data (<code>training</code> table).</p> +<p>When we select slim's best hyperparameters, different test data is used in <a href="#evaluation">evaluation section</a> several times.</p> +<pre><code class="lang-sql"><span class="hljs-keyword">DROP</span> <span class="hljs-keyword">TABLE</span> testing; +<span class="hljs-keyword">CREATE</span> <span class="hljs-keyword">TABLE</span> testing +<span class="hljs-keyword">as</span> +<span class="hljs-keyword">WITH</span> top_k <span class="hljs-keyword">as</span> ( + <span class="hljs-keyword">select</span> + each_top_k(<span class="hljs-number">1</span>, userid, rnd, userid, itemid, rating) + <span class="hljs-keyword">as</span> (<span class="hljs-keyword">rank</span>, rnd, userid, itemid, rating) + <span class="hljs-keyword">from</span> ( + <span class="hljs-keyword">select</span> * <span class="hljs-keyword">from</span> ratings2 + CLUSTER <span class="hljs-keyword">BY</span> userid + ) t +) +<span class="hljs-keyword">select</span> + userid, itemid, rating +<span class="hljs-keyword">from</span> + top_k +; + +<span class="hljs-keyword">DROP</span> <span class="hljs-keyword">TABLE</span> training; +<span class="hljs-keyword">CREATE</span> <span class="hljs-keyword">TABLE</span> training <span class="hljs-keyword">as</span> +<span class="hljs-keyword">select</span> + l.* +<span class="hljs-keyword">from</span> + ratings2 l + <span class="hljs-keyword">LEFT</span> <span class="hljs-keyword">OUTER</span> <span class="hljs-keyword">JOIN</span> testing r <span class="hljs-keyword">ON</span> (l.userid=r.userid <span class="hljs-keyword">and</span> l.itemid=r.itemid) +<span class="hljs-keyword">where</span> + r.itemid <span class="hljs-keyword">IS</span> <span class="hljs-literal">NULL</span> <span class="hljs-comment">-- anti join</span> +; +</code></pre> +<h3 id="kkk-hold-corss-validation"><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:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.07153em;">K</span></span></span></span>-hold corss validation</h3> +<p>When <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>K</mi><mo>=</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">K=2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.07153em;">K</span><span class="mrel">=</span><span class="mord mathrm">2</span></span></span></span>, the dataset is divided into training data and testing dataset. +The numbers of training and testing samples roughly equal.</p> +<p>When we select slim's best hyperparameters, you'll first train a SLIM prediction model from training data and evaluate the prediction model by testing data.</p> +<p>Optionally, you can switch training data with testing data and evaluate again.</p> +<pre><code class="lang-sql"><span class="hljs-keyword">DROP</span> <span class="hljs-keyword">TABLE</span> testing; +<span class="hljs-keyword">CREATE</span> <span class="hljs-keyword">TABLE</span> testing +<span class="hljs-keyword">as</span> +<span class="hljs-keyword">select</span> * <span class="hljs-keyword">from</span> ratings2 +<span class="hljs-keyword">where</span> rnd >= <span class="hljs-number">0.5</span> +; + +<span class="hljs-keyword">DROP</span> <span class="hljs-keyword">TABLE</span> training; +<span class="hljs-keyword">CREATE</span> <span class="hljs-keyword">TABLE</span> training +<span class="hljs-keyword">as</span> +<span class="hljs-keyword">select</span> * <span class="hljs-keyword">from</span> ratings2 +<span class="hljs-keyword">where</span> rnd < <span class="hljs-number">0.5</span> +; +</code></pre> +<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>In the following section excluding evaluation section, +we will show the example of queries and its results based on <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:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.07153em;">K</span></span></span></span>-hold cross validation case. +But, this article's queries are valid for leave-one-out cross validation.</p></div></div> +<h2 id="precompute-movie-movie-similarity">Precompute movie-movie similarity</h2> +<p>SLIM needs 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> most similar movies for each movie to the approximate user-item matrix. +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.</p> +<p>Because we set <code>k=20</code>, the output has 20 most-similar movies per <code>itemid</code>. +We can adjust trade-off between training and prediction time and precision of matrix approximation by varying <code>k</code>. +Larger <code>k</code> is the better approximation for raw user-item matrix, but training time and memory usage tend to increase.</p> +<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">set</span> hivevar:k=<span class="hljs-number">20</span>; + +<span class="hljs-keyword">DROP</span> <span class="hljs-keyword">TABLE</span> knn_train; +<span class="hljs-keyword">CREATE</span> <span class="hljs-keyword">TABLE</span> knn_train +<span class="hljs-keyword">as</span> +<span class="hljs-keyword">with</span> item_magnitude <span class="hljs-keyword">as</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> + itemid <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> + itemid + ) t0 +), +item_features <span class="hljs-keyword">as</span> ( + <span class="hljs-keyword">select</span> + userid <span class="hljs-keyword">as</span> i, + collect_list( + feature(itemid, 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-keyword">select</span> + dimsum_mapper(f.feature_vector, m.mags, <span class="hljs-string">'-threshold 0.1 -int_feature'</span>) + <span class="hljs-keyword">as</span> (itemid, other, s) + <span class="hljs-keyword">from</span> + item_features f + <span class="hljs-keyword">CROSS</span> <span class="hljs-keyword">JOIN</span> item_magnitude m +), +similarity <span class="hljs-keyword">as</span> ( + <span class="hljs-keyword">select</span> + itemid, + other, + <span class="hljs-keyword">sum</span>(s) <span class="hljs-keyword">as</span> similarity + <span class="hljs-keyword">from</span> +
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