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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 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><!-- + 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. 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