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Posted to commits@hivemall.apache.org by my...@apache.org on 2017/09/13 14:10:29 UTC
[17/23] incubator-hivemall-site git commit: Updated userguide for
evaluation section
http://git-wip-us.apache.org/repos/asf/incubator-hivemall-site/blob/a98b42f8/userguide/eval/multilabel_classification_measures.html
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+<!DOCTYPE HTML>
+<html lang="" >
+ <head>
+ <meta charset="UTF-8">
+ <meta content="text/html; charset=utf-8" http-equiv="Content-Type">
+ <title>Multi-label Classification Metrics ยท Hivemall User Manual</title>
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+ <meta name="description" content="">
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+ <link rel="shortcut icon" href="../gitbook/images/favicon.ico" type="image/x-icon">
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+ <link rel="next" href="regression.html" />
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+ <link rel="prev" href="auc.html" />
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+ </head>
+ <body>
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+<div class="book">
+ <div class="book-summary">
+
+
+<div id="book-search-input" role="search">
+ <input type="text" placeholder="Type to search" />
+</div>
+
+
+ <nav role="navigation">
+
+
+
+<ul class="summary">
+
+
+
+
+ <li>
+ <a href="http://hivemall.incubator.apache.org/" target="_blank" class="custom-link"><i class="fa fa-home"></i> Home</a>
+ </li>
+
+
+
+
+ <li class="divider"></li>
+
+
+
+
+ <li class="header">TABLE OF CONTENTS</li>
+
+
+
+ <li class="chapter " data-level="1.1" data-path="../">
+
+ <a href="../">
+
+
+ <b>1.1.</b>
+
+ Introduction
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.2" data-path="../getting_started/">
+
+ <a href="../getting_started/">
+
+
+ <b>1.2.</b>
+
+ Getting Started
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="1.2.1" data-path="../getting_started/installation.html">
+
+ <a href="../getting_started/installation.html">
+
+
+ <b>1.2.1.</b>
+
+ Installation
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.2.2" data-path="../getting_started/permanent-functions.html">
+
+ <a href="../getting_started/permanent-functions.html">
+
+
+ <b>1.2.2.</b>
+
+ Install as permanent functions
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.2.3" data-path="../getting_started/input-format.html">
+
+ <a href="../getting_started/input-format.html">
+
+
+ <b>1.2.3.</b>
+
+ Input Format
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="1.3" data-path="../tips/">
+
+ <a href="../tips/">
+
+
+ <b>1.3.</b>
+
+ Tips for Effective Hivemall
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="1.3.1" data-path="../tips/addbias.html">
+
+ <a href="../tips/addbias.html">
+
+
+ <b>1.3.1.</b>
+
+ Explicit 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="binary_classification_measures.html">
+
+ <a href="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="auc.html">
+
+ <a href="auc.html">
+
+
+ <b>4.1.1.</b>
+
+ Area Under the ROC Curve
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter active" data-level="4.2" data-path="multilabel_classification_measures.html">
+
+ <a href="multilabel_classification_measures.html">
+
+
+ <b>4.2.</b>
+
+ Multi-label Classification Metrics
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="4.3" data-path="regression.html">
+
+ <a href="regression.html">
+
+
+ <b>4.3.</b>
+
+ Regression metrics
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="4.4" data-path="rank.html">
+
+ <a href="rank.html">
+
+
+ <b>4.4.</b>
+
+ Ranking Measures
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="4.5" data-path="datagen.html">
+
+ <a href="datagen.html">
+
+
+ <b>4.5.</b>
+
+ Data Generation
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="4.5.1" data-path="lr_datagen.html">
+
+ <a href="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="../recommend/cf.html">
+
+ <a href="../recommend/cf.html">
+
+
+ <b>9.1.</b>
+
+ Collaborative Filtering
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="9.1.1" data-path="../recommend/item_based_cf.html">
+
+ <a href="../recommend/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="../recommend/news20.html">
+
+ <a href="../recommend/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="../recommend/news20_jaccard.html">
+
+ <a href="../recommend/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="../recommend/news20_knn.html">
+
+ <a href="../recommend/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="../recommend/news20_bbit_minhash.html">
+
+ <a href="../recommend/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="../recommend/movielens.html">
+
+ <a href="../recommend/movielens.html">
+
+
+ <b>9.3.</b>
+
+ MovieLens movie recommendation Tutorial
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="9.3.1" data-path="../recommend/movielens_dataset.html">
+
+ <a href="../recommend/movielens_dataset.html">
+
+
+ <b>9.3.1.</b>
+
+ Data preparation
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="9.3.2" data-path="../recommend/movielens_cf.html">
+
+ <a href="../recommend/movielens_cf.html">
+
+
+ <b>9.3.2.</b>
+
+ Item-based Collaborative Filtering
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="9.3.3" data-path="../recommend/movielens_mf.html">
+
+ <a href="../recommend/movielens_mf.html">
+
+
+ <b>9.3.3.</b>
+
+ Matrix Factorization
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="9.3.4" data-path="../recommend/movielens_fm.html">
+
+ <a href="../recommend/movielens_fm.html">
+
+
+ <b>9.3.4.</b>
+
+ Factorization Machine
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="9.3.5" data-path="../recommend/movielens_cv.html">
+
+ <a href="../recommend/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>
+
+ <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=".." >Multi-label Classification Metrics</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.
+-->
+<!-- toc --><div id="toc" class="toc">
+
+<ul>
+<li><a href="#multi-label-classification">Multi-label classification</a></li>
+<li><a href="#example">Example</a><ul>
+<li><a href="#data">Data</a></li>
+</ul>
+</li>
+<li><a href="#evaluation-metrics-for-multi-label-classification">Evaluation metrics for multi-label classification</a><ul>
+<li><a href="#micro-f1-score">Micro F1-score</a></li>
+<li><a href="#micro-f-measure">Micro F-measure</a></li>
+</ul>
+</li>
+</ul>
+
+</div><!-- tocstop -->
+<h1 id="multi-label-classification">Multi-label classification</h1>
+<p>Multi-label classification problem is a task to predict labels given two or more categories.</p>
+<p>Each sample <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> has <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>l</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">l_i</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:0.84444em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.01968em;">l</span><span class="msupsub"><span class="vlist">
<span style="top:0.15em;margin-right:0.05em;margin-left:-0.01968em;"><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">i</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> labels, where <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>L</mi></mrow><annotation encoding="application/x-tex">L</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">L</span></span></span></span> is a set of unique labels in the dataset, and <span class="katex"><span class=
"katex-mathml"><math><semantics><mrow><mn>0</mn><mo>≤</mo><msub><mi>l</mi><mi>i</mi></msub><mo>≤</mo><mi mathvariant="normal">∣</mi><mi>L</mi><mi mathvariant="normal">∣</mi></mrow><annotation encoding="application/x-tex">0 \leq l_i \leq |L|</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 mathrm">0</span><span class="mrel">≤</span><span class="mord"><span class="mord mathit" style="margin-right:0.01968em;">l</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.01968em;"><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">i</span></span></span><sp
an 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">∣</span><span class="mord mathit">L</span><span class="mord mathrm">∣</span></span></span></span>.
+This page focuses on evaluation of such multi-label classification problems.</p>
+<h1 id="example">Example</h1>
+<p>This page introduces toy example dataset for explanation.</p>
+<h2 id="data">Data</h2>
+<p>The following table shows examples of multi-label classification's prediction.</p>
+<p>Suppose that animal names represent tags of blog posts and the given task is to predict tags for blog posts.
+The left column shows the ground truth labels and the right column shows predicted labels by a multi-label classifier.</p>
+<table>
+<thead>
+<tr>
+<th style="text-align:center">truth labels</th>
+<th style="text-align:center">predicted labels</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td style="text-align:center">cat, bird</td>
+<td style="text-align:center">cat, dog</td>
+</tr>
+<tr>
+<td style="text-align:center">cat, dog</td>
+<td style="text-align:center">cat, bird</td>
+</tr>
+<tr>
+<td style="text-align:center">cat</td>
+<td style="text-align:center">(<em>no truth label</em>)</td>
+</tr>
+<tr>
+<td style="text-align:center">bird</td>
+<td style="text-align:center">bird</td>
+</tr>
+<tr>
+<td style="text-align:center">bird, cat</td>
+<td style="text-align:center">bird, cat</td>
+</tr>
+<tr>
+<td style="text-align:center">cat, dog</td>
+<td style="text-align:center">cat, dog, bird</td>
+</tr>
+<tr>
+<td style="text-align:center">dog, bird</td>
+<td style="text-align:center">dog</td>
+</tr>
+</tbody>
+</table>
+<h1 id="evaluation-metrics-for-multi-label-classification">Evaluation metrics for multi-label classification</h1>
+<p>Hivemall provides micro F1-score and micro F-measure.</p>
+<p>Define <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>L</mi></mrow><annotation encoding="application/x-tex">L</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">L</span></span></span></span> is the set of the tag of blog posts, and <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>l</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">l_i</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:0.84444em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.01968em;">l</span><span clas
s="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.01968em;"><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">i</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 a tag set 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>-th document.
+In the same manner, <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>p</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">p_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:0.625em;vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">p</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 mathit mtight">i</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 a predi
cted tag set 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>-th document.</p>
+<h2 id="micro-f1-score">Micro F1-score</h2>
+<p>F1-score is the harmonic mean of recall and precision.</p>
+<p>The value is computed by the following equation:</p>
+<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mrow><mi mathvariant="normal">F</mi></mrow><mn>1</mn></msub><mo>=</mo><mn>2</mn><mfrac><mrow><msub><mo>∑</mo><mi>i</mi></msub><mi mathvariant="normal">∣</mi><msub><mi>l</mi><mi>i</mi></msub><mo>∩</mo><msub><mi>p</mi><mi>i</mi></msub><mi mathvariant="normal">∣</mi></mrow><mrow><mn>2</mn><mo>∗</mo><msub><mo>∑</mo><mi>i</mi></msub><mi mathvariant="normal">∣</mi><msub><mi>l</mi><mi>i</mi></msub><mo>∩</mo><msub><mi>p</mi><mi>i</mi></msub><mi mathvariant="normal">∣</mi><mo>+</mo><msub><mo>∑</mo><mi>i</mi></msub><mi mathvariant="normal">∣</mi><msub><mi>l</mi><mi>i</mi></msub><mo>−</mo><msub><mi>p</mi><mi>i</mi></msub><mi mathvariant="normal">∣</mi><mo>+</mo><msub><mo>∑</mo><mi>i</mi></msub><mi mathvariant="normal">∣</mi><msub><mi>p</mi><mi>i</mi></msub><mo>−</mo><msub><mi>l
</mi><mi>i</mi></msub><mi mathvariant="normal">∣</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">
+\mathrm{F}_1 = 2 \frac
+{\sum_i |l_i \cap p_i |}
+{ 2* \sum_i |l_i \cap p_i | + \sum_i |l_i - p_i| + \sum_i |p_i - l_i| }
+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:1.44001em;"></span><span class="strut bottom" style="height:2.4260200000000003em;vertical-align:-0.98601em;"></span><span class="base displaystyle textstyle uncramped"><span class="mord"><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">F</span></span><span class="msupsub"><span class="vlist"><span style="top:0.15em;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">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 class="mrel">=</span><span class="mord mathrm">2</span><span class="mord reset-textstyle displaystyle textstyle uncramped"><span cl
ass="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 class="mbin">∗</span><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-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 mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></sp
an></span><span class="mord mathrm">∣</span><span class="mord"><span class="mord mathit" style="margin-right:0.01968em;">l</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.01968em;"><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">i</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">p</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 mathit mt
ight">i</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 mathrm">∣</span><span class="mbin">+</span><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-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 mathit mtight">i</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 mathrm">∣</span><span class="mord"><span class="mord mathit" style="margin-right:0.01968em;">l</span><span class="msupsu
b"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.01968em;"><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">i</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">p</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 mathit mtight">i</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 mathrm">∣</span><span class="mbin">+</span><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-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 mathit mtight">i</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 mathrm">∣</span><span class="mord"><span class="mord mathit">p</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><s
pan class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight">i</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:0.01968em;">l</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.01968em;"><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">i</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 mathrm">∣</span></span></span></span><span style="top:-0.22999999999999998em;"><span class="fo
ntsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle textstyle uncramped frac-line"></span></span><span style="top:-0.69001em;"><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-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 mathit mtight">i</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 mathrm">
∣</span><span class="mord"><span class="mord mathit" style="margin-right:0.01968em;">l</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.01968em;"><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">i</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">p</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 mathit mtight">i</span></span></span><span cl
ass="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span><span class="mord mathrm">∣</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></span></span></span></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>Hivemall also provides <code>f1score</code> function, but it is old function to obtain F1-score. The value of <code>f1score</code> is based on set operation. So, we recommend to use <code>fmeasure</code> function to get F1-score based on this article.</p></div></div>
+<p>The following query shows the example to obtain F1-score.</p>
+<pre><code class="lang-sql">WITH data as (
+ <span class="hljs-keyword">select</span> <span class="hljs-built_in">array</span>(<span class="hljs-string">"cat"</span>, <span class="hljs-string">"bird"</span>) <span class="hljs-keyword">as</span> actual, <span class="hljs-built_in">array</span>(<span class="hljs-string">"cat"</span>, <span class="hljs-string">"dog"</span>) <span class="hljs-keyword">as</span> predicted
+<span class="hljs-keyword">union</span> all
+ <span class="hljs-keyword">select</span> <span class="hljs-built_in">array</span>(<span class="hljs-string">"cat"</span>, <span class="hljs-string">"dog"</span>) <span class="hljs-keyword">as</span> actual, <span class="hljs-built_in">array</span>(<span class="hljs-string">"cat"</span>, <span class="hljs-string">"bird"</span>) <span class="hljs-keyword">as</span> predicted
+<span class="hljs-keyword">union</span> all
+ <span class="hljs-keyword">select</span> <span class="hljs-built_in">array</span>(<span class="hljs-string">"cat"</span>) <span class="hljs-keyword">as</span> actual, <span class="hljs-built_in">array</span>() <span class="hljs-keyword">as</span> predicted
+<span class="hljs-keyword">union</span> all
+ <span class="hljs-keyword">select</span> <span class="hljs-built_in">array</span>(<span class="hljs-string">"bird"</span>) <span class="hljs-keyword">as</span> actual, <span class="hljs-built_in">array</span>(<span class="hljs-string">"bird"</span>) <span class="hljs-keyword">as</span> predicted
+<span class="hljs-keyword">union</span> all
+ <span class="hljs-keyword">select</span> <span class="hljs-built_in">array</span>(<span class="hljs-string">"bird"</span>, <span class="hljs-string">"cat"</span>) <span class="hljs-keyword">as</span> actual, <span class="hljs-built_in">array</span>(<span class="hljs-string">"bird"</span>, <span class="hljs-string">"cat"</span>) <span class="hljs-keyword">as</span> predicted
+<span class="hljs-keyword">union</span> all
+ <span class="hljs-keyword">select</span> <span class="hljs-built_in">array</span>(<span class="hljs-string">"cat"</span>, <span class="hljs-string">"dog"</span>) <span class="hljs-keyword">as</span> actual, <span class="hljs-built_in">array</span>(<span class="hljs-string">"cat"</span>, <span class="hljs-string">"dog"</span>, <span class="hljs-string">"bird"</span>) <span class="hljs-keyword">as</span> predicted
+<span class="hljs-keyword">union</span> all
+ <span class="hljs-keyword">select</span> <span class="hljs-built_in">array</span>(<span class="hljs-string">"dog"</span>, <span class="hljs-string">"bird"</span>) <span class="hljs-keyword">as</span> actual, <span class="hljs-built_in">array</span>(<span class="hljs-string">"dog"</span>) <span class="hljs-keyword">as</span> predicted
+)
+<span class="hljs-keyword">select</span>
+ fmeasure(actual, predicted)
+<span class="hljs-keyword">from</span> <span class="hljs-keyword">data</span>
+;
+</code></pre>
+<blockquote>
+<p>0.6956521739130435</p>
+</blockquote>
+<h2 id="micro-f-measure">Micro F-measure</h2>
+<p>F-measure is generalized F1-score and the weighted harmonic mean of recall and precision.</p>
+<p>The value is computed by the following equation:
+<span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mrow><mi mathvariant="normal">F</mi></mrow><mrow><mi>β</mi></mrow></msub><mo>=</mo><mo>(</mo><mn>1</mn><mo>+</mo><msup><mi>β</mi><mn>2</mn></msup><mo>)</mo><mfrac><mrow><msub><mo>∑</mo><mi>i</mi></msub><mi mathvariant="normal">∣</mi><msub><mi>l</mi><mi>i</mi></msub><mo>∩</mo><msub><mi>p</mi><mi>i</mi></msub><mi mathvariant="normal">∣</mi></mrow><mrow><msup><mi>β</mi><mn>2</mn></msup><mo>(</mo><msub><mo>∑</mo><mi>i</mi></msub><mi mathvariant="normal">∣</mi><msub><mi>l</mi><mi>i</mi></msub><mo>∩</mo><msub><mi>p</mi><mi>i</mi></msub><mi mathvariant="normal">∣</mi><mo>+</mo><msub><mo>∑</mo><mi>i</mi></msub><mi mathvariant="normal">∣</mi><msub><mi>l</mi><mi>i</mi></msub><mo>−</mo><msub><mi>p</mi><mi>i</mi></msub><mi mathvariant="normal">∣</mi><mo>)</mo><mo>+</mo><msub><mo>∑</mo
><mi>i</mi></msub><mi mathvariant="normal">∣</mi><msub><mi>l</mi><mi>i</mi></msub><mo>∩</mo><msub><mi>p</mi><mi>i</mi></msub><mi mathvariant="normal">∣</mi><mo>+</mo><msub><mo>∑</mo><mi>i</mi></msub><mi mathvariant="normal">∣</mi><msub><mi>p</mi><mi>i</mi></msub><mo>−</mo><msub><mi>l</mi><mi>i</mi></msub><mi mathvariant="normal">∣</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">
+\mathrm{F}_{\beta} = (1+\beta^2) \frac
+{\sum_i |l_i \cap p_i |}
+{ \beta^2 (\sum_i |l_i \cap p_i | + \sum_i |l_i - p_i|) + \sum_i |l_i \cap p_i | + \sum_i |p_i - l_i|}
+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:1.44001em;"></span><span class="strut bottom" style="height:2.4260200000000003em;vertical-align:-0.98601em;"></span><span class="base displaystyle textstyle uncramped"><span class="mord"><span class="mord displaystyle textstyle uncramped"><span class="mord mathrm">F</span></span><span class="msupsub"><span class="vlist"><span style="top:0.15em;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" 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><span class="mrel">=</span><span class="mopen"
>(</span><span class="mord mathrm">1</span><span class="mbin">+</span><span class="mord"><span class="mord mathit" style="margin-right:0.05278em;">β</span><span class="msupsub"><span class="vlist"><span style="top:-0.413em;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="mclose">)</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><sp
an class="reset-textstyle textstyle cramped"><span class="mord textstyle cramped"><span class="mord"><span class="mord mathit" style="margin-right:0.05278em;">β</span><span class="msupsub"><span class="vlist"><span style="top:-0.289em;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 class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span><span class="mopen">(</span><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-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 mathit mtight">i</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 mathrm">∣</span><span class="mord"><span class="mord mathit" style="margin-right:0.01968em;">l</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.01968em;"><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">i</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">p</span><span class="msupsub"><span class="v
list"><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 mathit mtight">i</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 mathrm">∣</span><span class="mbin">+</span><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-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 mathit mtight">i</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 mathrm">∣</span><span class="mord"><span class="mord mathit" style="margin-right:0.01968em;">l</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.01968em;"><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">i</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">p</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 mathit mtight">i</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 mathrm">∣</span><span class="mclose">)</span><span class="mbin">+</span><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-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 mathit mtight">i</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 m
athrm">∣</span><span class="mord"><span class="mord mathit" style="margin-right:0.01968em;">l</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.01968em;"><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">i</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">p</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 mathit mtight">i</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 mathrm">∣</span><span class="mbin">+</span><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-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">Ȁ
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