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Posted to commits@hivemall.apache.org by my...@apache.org on 2018/11/06 04:09:50 UTC
[12/16] incubator-hivemall-site git commit: Update user guide for
term vector model and added a mentor to project team
http://git-wip-us.apache.org/repos/asf/incubator-hivemall-site/blob/0e287d3d/userguide/ft_engineering/bm25.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>Okapi BM25 Term Weighting 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="../eval/binary_classification_measures.html" />
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+ <link rel="prev" href="tfidf.html" />
+
+
+ </head>
+ <body>
+
+<div class="book">
+ <div class="book-summary">
+
+
+<div id="book-search-input" role="search">
+ <input type="text" placeholder="Type to search" />
+</div>
+
+
+ <nav role="navigation">
+
+
+
+<ul class="summary">
+
+
+
+
+ <li>
+ <a href="https://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="../misc/funcs.html">
+
+ <a href="../misc/funcs.html">
+
+
+ <b>1.3.</b>
+
+ List of Functions
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.4" data-path="../tips/">
+
+ <a href="../tips/">
+
+
+ <b>1.4.</b>
+
+ Tips for Effective Hivemall
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="1.4.1" data-path="../tips/addbias.html">
+
+ <a href="../tips/addbias.html">
+
+
+ <b>1.4.1.</b>
+
+ Explicit add_bias() for better prediction
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.4.2" data-path="../tips/rand_amplify.html">
+
+ <a href="../tips/rand_amplify.html">
+
+
+ <b>1.4.2.</b>
+
+ Use rand_amplify() to better prediction results
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.4.3" data-path="../tips/rt_prediction.html">
+
+ <a href="../tips/rt_prediction.html">
+
+
+ <b>1.4.3.</b>
+
+ Real-time prediction on RDBMS
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.4.4" data-path="../tips/ensemble_learning.html">
+
+ <a href="../tips/ensemble_learning.html">
+
+
+ <b>1.4.4.</b>
+
+ Ensemble learning for stable prediction
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.4.5" data-path="../tips/mixserver.html">
+
+ <a href="../tips/mixserver.html">
+
+
+ <b>1.4.5.</b>
+
+ Mixing models for a better prediction convergence (MIX server)
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.4.6" data-path="../tips/emr.html">
+
+ <a href="../tips/emr.html">
+
+
+ <b>1.4.6.</b>
+
+ Run Hivemall on Amazon Elastic MapReduce
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="1.5" data-path="../tips/general_tips.html">
+
+ <a href="../tips/general_tips.html">
+
+
+ <b>1.5.</b>
+
+ General Hive/Hadoop Tips
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="1.5.1" data-path="../tips/rowid.html">
+
+ <a href="../tips/rowid.html">
+
+
+ <b>1.5.1.</b>
+
+ Adding rowid for each row
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.5.2" data-path="../tips/hadoop_tuning.html">
+
+ <a href="../tips/hadoop_tuning.html">
+
+
+ <b>1.5.2.</b>
+
+ Hadoop tuning for Hivemall
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="1.6" data-path="../troubleshooting/">
+
+ <a href="../troubleshooting/">
+
+
+ <b>1.6.</b>
+
+ Troubleshooting
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="1.6.1" data-path="../troubleshooting/oom.html">
+
+ <a href="../troubleshooting/oom.html">
+
+
+ <b>1.6.1.</b>
+
+ OutOfMemoryError in training
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.6.2" data-path="../troubleshooting/mapjoin_task_error.html">
+
+ <a href="../troubleshooting/mapjoin_task_error.html">
+
+
+ <b>1.6.2.</b>
+
+ SemanticException generate map join task error: Cannot serialize object
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.6.3" data-path="../troubleshooting/asterisk.html">
+
+ <a href="../troubleshooting/asterisk.html">
+
+
+ <b>1.6.3.</b>
+
+ Asterisk argument for UDTF does not work
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.6.4" data-path="../troubleshooting/num_mappers.html">
+
+ <a href="../troubleshooting/num_mappers.html">
+
+
+ <b>1.6.4.</b>
+
+ The number of mappers is less than input splits in Hadoop 2.x
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="1.6.5" data-path="../troubleshooting/mapjoin_classcastex.html">
+
+ <a href="../troubleshooting/mapjoin_classcastex.html">
+
+
+ <b>1.6.5.</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="chapter " data-level="2.4" data-path="../misc/approx.html">
+
+ <a href="../misc/approx.html">
+
+
+ <b>2.4.</b>
+
+ Approximate Aggregate Functions
+
+ </a>
+
+
+
+ </li>
+
+
+
+
+ <li class="header">Part III - Feature Engineering</li>
+
+
+
+ <li class="chapter " data-level="3.1" data-path="scaling.html">
+
+ <a href="scaling.html">
+
+
+ <b>3.1.</b>
+
+ Feature Scaling
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="3.2" data-path="hashing.html">
+
+ <a href="hashing.html">
+
+
+ <b>3.2.</b>
+
+ Feature Hashing
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="3.3" data-path="selection.html">
+
+ <a href="selection.html">
+
+
+ <b>3.3.</b>
+
+ Feature Selection
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="3.4" data-path="binning.html">
+
+ <a href="binning.html">
+
+
+ <b>3.4.</b>
+
+ Feature Binning
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="3.5" data-path="pairing.html">
+
+ <a href="pairing.html">
+
+
+ <b>3.5.</b>
+
+ Feature Paring
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="3.5.1" data-path="polynomial.html">
+
+ <a href="polynomial.html">
+
+
+ <b>3.5.1.</b>
+
+ Polynomial features
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="3.6" data-path="ft_trans.html">
+
+ <a href="ft_trans.html">
+
+
+ <b>3.6.</b>
+
+ Feature Transformation
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="3.6.1" data-path="vectorization.html">
+
+ <a href="vectorization.html">
+
+
+ <b>3.6.1.</b>
+
+ Feature vectorization
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="3.6.2" data-path="quantify.html">
+
+ <a href="quantify.html">
+
+
+ <b>3.6.2.</b>
+
+ Quantify non-number features
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="3.7" data-path="term_vector.html">
+
+ <a href="term_vector.html">
+
+
+ <b>3.7.</b>
+
+ Term Vector Model
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="3.7.1" data-path="tfidf.html">
+
+ <a href="tfidf.html">
+
+
+ <b>3.7.1.</b>
+
+ TF-IDF Term Weighting
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter active" data-level="3.7.2" data-path="bm25.html">
+
+ <a href="bm25.html">
+
+
+ <b>3.7.2.</b>
+
+ Okapi BM25 Term Weighting
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+
+
+
+ <li class="header">Part IV - Evaluation</li>
+
+
+
+ <li class="chapter " data-level="4.1" data-path="../eval/binary_classification_measures.html">
+
+ <a href="../eval/binary_classification_measures.html">
+
+
+ <b>4.1.</b>
+
+ Binary Classification Metrics
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="4.1.1" data-path="../eval/auc.html">
+
+ <a href="../eval/auc.html">
+
+
+ <b>4.1.1.</b>
+
+ Area under the ROC curve
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="4.2" data-path="../eval/multilabel_classification_measures.html">
+
+ <a href="../eval/multilabel_classification_measures.html">
+
+
+ <b>4.2.</b>
+
+ Multi-label Classification Metrics
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="4.3" data-path="../eval/regression.html">
+
+ <a href="../eval/regression.html">
+
+
+ <b>4.3.</b>
+
+ Regression Metrics
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="4.4" data-path="../eval/rank.html">
+
+ <a href="../eval/rank.html">
+
+
+ <b>4.4.</b>
+
+ Ranking Measures
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="4.5" data-path="../eval/datagen.html">
+
+ <a href="../eval/datagen.html">
+
+
+ <b>4.5.</b>
+
+ Data Generation
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="4.5.1" data-path="../eval/lr_datagen.html">
+
+ <a href="../eval/lr_datagen.html">
+
+
+ <b>4.5.1.</b>
+
+ Logistic Regression data generation
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+
+
+
+ <li class="header">Part V - Supervised Learning</li>
+
+
+
+ <li class="chapter " data-level="5.1" data-path="../supervised_learning/prediction.html">
+
+ <a href="../supervised_learning/prediction.html">
+
+
+ <b>5.1.</b>
+
+ How Prediction Works
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="5.2" data-path="../supervised_learning/tutorial.html">
+
+ <a href="../supervised_learning/tutorial.html">
+
+
+ <b>5.2.</b>
+
+ Step-by-Step Tutorial on Supervised Learning
+
+ </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="chapter " data-level="6.8" data-path="../binaryclass/criteo.html">
+
+ <a href="../binaryclass/criteo.html">
+
+
+ <b>6.8.</b>
+
+ Criteo Tutorial
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="6.8.1" data-path="../binaryclass/criteo_dataset.html">
+
+ <a href="../binaryclass/criteo_dataset.html">
+
+
+ <b>6.8.1.</b>
+
+ Data preparation
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="6.8.2" data-path="../binaryclass/criteo_ffm.html">
+
+ <a href="../binaryclass/criteo_ffm.html">
+
+
+ <b>6.8.2.</b>
+
+ Field-Aware Factorization Machines
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </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_slim.html">
+
+ <a href="../recommend/movielens_slim.html">
+
+
+ <b>9.3.5.</b>
+
+ SLIM for fast top-k recommendation
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="9.3.6" data-path="../recommend/movielens_cv.html">
+
+ <a href="../recommend/movielens_cv.html">
+
+
+ <b>9.3.6.</b>
+
+ 10-fold cross validation (Matrix Factorization)
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+
+
+
+ <li class="header">Part X - Anomaly Detection</li>
+
+
+
+ <li class="chapter " data-level="10.1" data-path="../anomaly/lof.html">
+
+ <a href="../anomaly/lof.html">
+
+
+ <b>10.1.</b>
+
+ Outlier Detection using Local Outlier Factor (LOF)
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="10.2" data-path="../anomaly/sst.html">
+
+ <a href="../anomaly/sst.html">
+
+
+ <b>10.2.</b>
+
+ Change-Point Detection using Singular Spectrum Transformation (SST)
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="10.3" data-path="../anomaly/changefinder.html">
+
+ <a href="../anomaly/changefinder.html">
+
+
+ <b>10.3.</b>
+
+ ChangeFinder: Detecting Outlier and Change-Point Simultaneously
+
+ </a>
+
+
+
+ </li>
+
+
+
+
+ <li class="header">Part XI - Clustering</li>
+
+
+
+ <li class="chapter " data-level="11.1" data-path="../clustering/lda.html">
+
+ <a href="../clustering/lda.html">
+
+
+ <b>11.1.</b>
+
+ Latent Dirichlet Allocation
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="11.2" data-path="../clustering/plsa.html">
+
+ <a href="../clustering/plsa.html">
+
+
+ <b>11.2.</b>
+
+ Probabilistic Latent Semantic Analysis
+
+ </a>
+
+
+
+ </li>
+
+
+
+
+ <li class="header">Part XII - GeoSpatial Functions</li>
+
+
+
+ <li class="chapter " data-level="12.1" data-path="../geospatial/latlon.html">
+
+ <a href="../geospatial/latlon.html">
+
+
+ <b>12.1.</b>
+
+ Lat/Lon functions
+
+ </a>
+
+
+
+ </li>
+
+
+
+
+ <li class="header">Part XIII - Hivemall on Spark</li>
+
+
+
+ <li class="chapter " data-level="13.1" data-path="../spark/getting_started/">
+
+ <a href="../spark/getting_started/">
+
+
+ <b>13.1.</b>
+
+ Getting Started
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="13.1.1" data-path="../spark/getting_started/installation.html">
+
+ <a href="../spark/getting_started/installation.html">
+
+
+ <b>13.1.1.</b>
+
+ Installation
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="13.2" data-path="../spark/binaryclass/">
+
+ <a href="../spark/binaryclass/">
+
+
+ <b>13.2.</b>
+
+ Binary Classification
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="13.2.1" data-path="../spark/binaryclass/a9a_df.html">
+
+ <a href="../spark/binaryclass/a9a_df.html">
+
+
+ <b>13.2.1.</b>
+
+ a9a tutorial for DataFrame
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="13.2.2" data-path="../spark/binaryclass/a9a_sql.html">
+
+ <a href="../spark/binaryclass/a9a_sql.html">
+
+
+ <b>13.2.2.</b>
+
+ a9a tutorial for SQL
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="13.3" data-path="../spark/binaryclass/">
+
+ <a href="../spark/binaryclass/">
+
+
+ <b>13.3.</b>
+
+ Regression
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="13.3.1" data-path="../spark/regression/e2006_df.html">
+
+ <a href="../spark/regression/e2006_df.html">
+
+
+ <b>13.3.1.</b>
+
+ E2006-tfidf regression tutorial for DataFrame
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="13.3.2" data-path="../spark/regression/e2006_sql.html">
+
+ <a href="../spark/regression/e2006_sql.html">
+
+
+ <b>13.3.2.</b>
+
+ E2006-tfidf regression tutorial for SQL
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+ <li class="chapter " data-level="13.4" data-path="../spark/misc/misc.html">
+
+ <a href="../spark/misc/misc.html">
+
+
+ <b>13.4.</b>
+
+ Generic features
+
+ </a>
+
+
+
+ <ul class="articles">
+
+
+ <li class="chapter " data-level="13.4.1" data-path="../spark/misc/topk_join.html">
+
+ <a href="../spark/misc/topk_join.html">
+
+
+ <b>13.4.1.</b>
+
+ Top-k join processing
+
+ </a>
+
+
+
+ </li>
+
+ <li class="chapter " data-level="13.4.2" data-path="../spark/misc/functions.html">
+
+ <a href="../spark/misc/functions.html">
+
+
+ <b>13.4.2.</b>
+
+ Other utility functions
+
+ </a>
+
+
+
+ </li>
+
+
+ </ul>
+
+ </li>
+
+
+
+
+ <li class="header">Part XIV - Hivemall on Docker</li>
+
+
+
+ <li class="chapter " data-level="14.1" data-path="../docker/getting_started.html">
+
+ <a href="../docker/getting_started.html">
+
+
+ <b>14.1.</b>
+
+ Getting Started
+
+ </a>
+
+
+
+ </li>
+
+
+
+
+ <li class="header">Part XIV - External References</li>
+
+
+
+ <li class="chapter " data-level="15.1" >
+
+ <a target="_blank" href="https://github.com/daijyc/hivemall/wiki/PigHome">
+
+
+ <b>15.1.</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>
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+ <a href=".." >Okapi BM25 Term Weighting</a>
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+<p><a href="https://en.wikipedia.org/wiki/Okapi_BM25" target="_blank">Okapi BM25</a> is a ranking function for documents for a given query.</p>
+<p>It can also be used for a better replacement of <a href="https://en.wikipedia.org/wiki/Tf%E2%80%93idf" target="_blank">TF-IDF</a> and can be used for term-weight for each document.</p>
+<!-- toc --><div id="toc" class="toc">
+
+<ul>
+<li><a href="#the-ranking-function">The ranking function</a></li>
+<li><a href="#data-preparation">Data preparation</a></li>
+<li><a href="#define-views-of-termdoc-frequency">Define views of term/doc frequency</a></li>
+<li><a href="#compute-okapi-bm25-score">Compute Okapi BM25 score</a><ul>
+<li><a href="#hyperparameters">Hyperparameters</a></li>
+<li><a href="#show-important-terms-for-each-document">Show important terms for each document</a></li>
+</ul>
+</li>
+<li><a href="#retrive-relevant-documents-for-a-given-search-terms">Retrive relevant documents for a given search terms</a></li>
+</ul>
+
+</div><!-- tocstop -->
+<h1 id="the-ranking-function">The ranking function</h1>
+<p>Given a query <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>Q</mi></mrow><annotation encoding="application/x-tex">Q</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:0.8777699999999999em;vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord mathit">Q</span></span></span></span>, containing keywords <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>q</mi><mn>1</mn><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo separator="true">,</mo><msub><mi>q</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">q1,....,q_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.64444em;"></span><span
class="strut bottom" style="height:0.8388800000000001em;vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.03588em;">q</span><span class="mord mathrm">1</span><span class="mpunct">,</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mpunct">,</span><span class="mord"><span class="mord mathit" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.03588em;"><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">n</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>, the BM25 score of a document <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.02778em;">D</span></span></span></span> is:</p>
+<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>s</mi><mi>c</mi><mi>o</mi><mi>r</mi><mi>e</mi><mo>(</mo><mi>Q</mi><mo separator="true">,</mo><mi>D</mi><mo>)</mo><mo>=</mo><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><mi>I</mi><mi>D</mi><mi>F</mi><mo>(</mo><msub><mi>q</mi><mrow><mi>i</mi></mrow></msub><mo>)</mo><mo>⋅</mo><mfrac><mrow><mi>t</mi><mi>f</mi><mo>(</mo><msub><mi>q</mi><mrow><mi>i</mi></mrow></msub><mo separator="true">,</mo><mi>D</mi><mo>)</mo><mo>⋅</mo><mo>(</mo><msub><mi>k</mi><mrow><mn>1</mn></mrow></msub><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>t</mi><mi>f</mi><mo>(</mo><msub><mi>q</mi><mrow><mi>i</mi></mrow></msub><mo separator="true">,</mo><mi>D</mi><mo>)</mo><mo>+</mo><msub><mi>k</mi><mrow><mn>1</mn></mrow></msub><mo>⋅</mo><mo>(</mo><mn>1</mn><mo>−</mo><mi>b</mi><mo>+</mo><mi>b</mi><mo>⋅</mo><mfrac><mrow><mi mathv
ariant="normal">∣</mi><mi>D</mi><mi mathvariant="normal">∣</mi></mrow><mrow><mi>a</mi><mi>v</mi><mi>g</mi><mi>d</mi><mi>l</mi></mrow></mfrac><mo>)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">
+score(Q, D) = \sum_{i=1}^{n}IDF(q_{i}) \cdot \frac{tf(q_{i},D) \cdot (k_{1}+1)}{tf(q_{i},D) + k_{1} \cdot (1 - b + b \cdot \frac{|D|}{avgdl})}
+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:1.6513970000000002em;"></span><span class="strut bottom" style="height:3.0325050000000005em;vertical-align:-1.381108em;"></span><span class="base displaystyle textstyle uncramped"><span class="mord mathit">s</span><span class="mord mathit">c</span><span class="mord mathit">o</span><span class="mord mathit" style="margin-right:0.02778em;">r</span><span class="mord mathit">e</span><span class="mopen">(</span><span class="mord mathit">Q</span><span class="mpunct">,</span><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="mclose">)</span><span class="mrel">=</span><span class="mop op-limits"><span class="vlist"><span style="top:1.1776689999999999em;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 script
style cramped mtight"><span class="mord mathit mtight">i</span><span class="mrel mtight">=</span><span class="mord mathrm mtight">1</span></span></span></span><span style="top:-0.000005000000000143778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-1.2500050000000003em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord scriptstyle uncramped mtight"><span class="mord mathit mtight">n</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="mord mathit" style="margin-right:0.07847em;">I</span><span class="mord mathit" style="margin-right:0.02778em;">D</span><span
class="mord mathit" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord"><span class="mord mathit" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.03588em;"><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></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="mbin">⋅</span><span class="mord reset-textstyle displaystyle textstyle uncramped"><span class="mopen sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span><span class="mfrac"><span class="vlist"><span style=
"top:0.9em;"><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 mathit">t</span><span class="mord mathit" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord"><span class="mord mathit" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.03588em;"><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></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="mpunct">,</span><span class="mord
mathit" style="margin-right:0.02778em;">D</span><span class="mclose">)</span><span class="mbin">+</span><span class="mord"><span class="mord mathit" style="margin-right:0.03148em;">k</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.03148em;"><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 mathrm mtight">1</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="mopen">(</span><span class="mord mathrm">1</span><span class="mbin">−</span><span class="mord mathit">b</span><span class="mbin">+</span><span class="mord mathit">b</span><span class="mbin">⋅</span><span clas
s="mord reset-textstyle textstyle cramped"><span class="mopen sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span><span class="mfrac"><span class="vlist"><span style="top:0.345em;"><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">a</span><span class="mord mathit mtight" style="margin-right:0.03588em;">v</span><span class="mord mathit mtight" style="margin-right:0.03588em;">g</span><span class="mord mathit mtight">d</span><span class="mord mathit mtight" style="margin-right:0.01968em;">l</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:-0.485em;"><span class="fon
tsize-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 mathrm mtight">∣</span><span class="mord mathit mtight" style="margin-right:0.02778em;">D</span><span class="mord mathrm 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 class="mclose sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span></span><span class="mclose">)</span></span></span></span><span style="top:-0.22999999999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle textstyle uncramped frac-line"></span></span><span style="top:-0.677em;"><span class="fontsize-ensurer reset-size5 size5"><span style
="font-size:0em;">​</span></span><span class="reset-textstyle textstyle uncramped"><span class="mord textstyle uncramped"><span class="mord mathit">t</span><span class="mord mathit" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord"><span class="mord mathit" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.03588em;"><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></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="mpunct">,</span><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="mclose">
)</span><span class="mbin">⋅</span><span class="mopen">(</span><span class="mord"><span class="mord mathit" style="margin-right:0.03148em;">k</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.03148em;"><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 mathrm mtight">1</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 mathrm">1</span><span class="mclose">)</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-siz
e5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span></span></span></span></span></span></p>
+<p>where <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>t</mi><mi>f</mi><mo>(</mo><msub><mi>q</mi><mrow><mi>i</mi></mrow></msub><mo separator="true">,</mo><mi>D</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">tf(q_{i}, D)</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">t</span><span class="mord mathit" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord"><span class="mord mathit" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.03588em;"><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></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="mpunct">,</span><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="mclose">)</span></span></span></span> is <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>q</mi><mrow><mi>i</mi></mrow></msub></mrow><annotation encoding="application/x-tex">q_{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" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;mar
gin-right:0.05em;margin-left:-0.03588em;"><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></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>'s term frequency in the document <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.02778em;">D</span></span></span></sp
an>, <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">∣</mi><mi>D</mi><mi mathvariant="normal">∣</mi></mrow><annotation encoding="application/x-tex">|D|</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">∣</span><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="mord mathrm">∣</span></span></span></span> is the length of the document <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"
></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.02778em;">D</span></span></span></span> in words, and <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>a</mi><mi>v</mi><mi>g</mi><mi>d</mi><mi>l</mi></mrow><annotation encoding="application/x-tex">avgdl</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:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord mathit">a</span><span class="mord mathit" style="margin-right:0.03588em;">v</span><span class="mord mathit" style="margin-right:0.03588em;">g</span><span class="mord mathit">d</span><span class="mord mathit" style="margin-right:0.01968em;">l</span></span></span></span> is the average document length in the text collection from which documents are drawn. <span class="katex"><span cla
ss="katex-mathml"><math><semantics><mrow><msub><mi>k</mi><mrow><mn>1</mn></mrow></msub></mrow><annotation encoding="application/x-tex">k_{1}</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:0.03148em;">k</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.03148em;"><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 mathrm mtight">1</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</s
pan></span></span></span></span></span></span> and <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>b</mi></mrow><annotation encoding="application/x-tex">b</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">b</span></span></span></span> are free parameters, usually chosen, in absence of an advanced optimization, as <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>k</mi><mrow><mn>1</mn></mrow></msub><mo>∈</mo><mo>[</mo><mn>1</mn><mi mathvariant="normal">.</mi><mn>2</mn><mo separator="true">,</mo><mn>2</mn><mi mathvariant="normal">.</mi><mn>0</mn><mo>]</mo></mrow><annotation encoding="application/x-tex">k_{1} \in [1.2,2.0]</annotation></semantics></math></span><span class="katex-html" aria-hidden="t
rue"><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"><span class="mord mathit" style="margin-right:0.03148em;">k</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.03148em;"><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 mathrm mtight">1</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="mord mathrm">.</span><span class="mord mathrm">2</span><span class="mpunct">,</span><span cla
ss="mord mathrm">2</span><span class="mord mathrm">.</span><span class="mord mathrm">0</span><span class="mclose">]</span></span></span></span> and <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>b</mi><mo>=</mo><mn>0</mn><mi mathvariant="normal">.</mi><mn>7</mn><mn>5</mn></mrow><annotation encoding="application/x-tex">b = 0.75</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">b</span><span class="mrel">=</span><span class="mord mathrm">0</span><span class="mord mathrm">.</span><span class="mord mathrm">7</span><span class="mord mathrm">5</span></span></span></span>.</p>
+<p>BM25 can also be applied for term weighing, showing how important a word is to a document in a collection or corpus, as follows:</p>
+<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>s</mi><mi>c</mi><mi>o</mi><mi>r</mi><mi>e</mi><mo>(</mo><msub><mi>t</mi><mrow><mi>i</mi></mrow></msub><mo separator="true">,</mo><mi>D</mi><mo>)</mo><mo>=</mo><mi>I</mi><mi>D</mi><mi>F</mi><mo>(</mo><msub><mi>t</mi><mrow><mi>i</mi></mrow></msub><mo>)</mo><mo>⋅</mo><mfrac><mrow><mi>t</mi><mi>f</mi><mo>(</mo><msub><mi>t</mi><mrow><mi>i</mi></mrow></msub><mo separator="true">,</mo><mi>D</mi><mo>)</mo><mo>⋅</mo><mo>(</mo><msub><mi>k</mi><mrow><mn>1</mn></mrow></msub><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>t</mi><mi>f</mi><mo>(</mo><msub><mi>t</mi><mrow><mi>i</mi></mrow></msub><mo separator="true">,</mo><mi>D</mi><mo>)</mo><mo>+</mo><msub><mi>k</mi><mrow><mn>1</mn></mrow></msub><mo>⋅</mo><mo>(</mo><mn>1</mn><mo>−</mo><mi>b</mi><mo>+</mo><mi>b</mi><mo>⋅</mo><mfrac><mrow><mi mathvariant="normal">∣</mi><mi>D</mi><mi mathvariant="normal">&#
x2223;</mi></mrow><mrow><mi>a</mi><mi>v</mi><mi>g</mi><mi>d</mi><mi>l</mi></mrow></mfrac><mo>)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">
+score(t_{i}, D) = IDF(t_{i}) \cdot \frac{tf(t_{i},D) \cdot (k_{1}+1)}{tf(t_{i},D) + k_{1} \cdot (1 - b + b \cdot \frac{|D|}{avgdl})}
+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:1.427em;"></span><span class="strut bottom" style="height:2.808108em;vertical-align:-1.381108em;"></span><span class="base displaystyle textstyle uncramped"><span class="mord mathit">s</span><span class="mord mathit">c</span><span class="mord mathit">o</span><span class="mord mathit" style="margin-right:0.02778em;">r</span><span class="mord mathit">e</span><span class="mopen">(</span><span class="mord"><span class="mord mathit">t</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</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 si
ze5"><span style="font-size:0em;">​</span></span>​</span></span></span></span><span class="mpunct">,</span><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="mclose">)</span><span class="mrel">=</span><span class="mord mathit" style="margin-right:0.07847em;">I</span><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="mord mathit" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord"><span class="mord mathit">t</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</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&
#x200B;</span></span>​</span></span></span></span><span class="mclose">)</span><span class="mbin">⋅</span><span class="mord reset-textstyle displaystyle textstyle uncramped"><span class="mopen sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span><span class="mfrac"><span class="vlist"><span style="top:0.9em;"><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 mathit">t</span><span class="mord mathit" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord"><span class="mord mathit">t</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="mo
rd scriptstyle cramped mtight"><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></span></span><span class="mpunct">,</span><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="mclose">)</span><span class="mbin">+</span><span class="mord"><span class="mord mathit" style="margin-right:0.03148em;">k</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.03148em;"><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 mathrm mtight">1</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>&#
x200B;</span></span></span></span><span class="mbin">⋅</span><span class="mopen">(</span><span class="mord mathrm">1</span><span class="mbin">−</span><span class="mord mathit">b</span><span class="mbin">+</span><span class="mord mathit">b</span><span class="mbin">⋅</span><span class="mord reset-textstyle textstyle cramped"><span class="mopen sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span><span class="mfrac"><span class="vlist"><span style="top:0.345em;"><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">a</span><span class="mord mathit mtight" style="margin-right:0.03588em;">v</span><span class="mord mathit mtight" style="margin-right:0.03588em;">g</span><span class="mord mathit mtight">d</span><span class="mord mathit mtight" style="margin-righ
t:0.01968em;">l</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:-0.485em;"><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 mathrm mtight">∣</span><span class="mord mathit mtight" style="margin-right:0.02778em;">D</span><span class="mord mathrm 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 class="mclose sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span></span><span class="mclose">)</span></span></span></span><
span style="top:-0.22999999999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle textstyle uncramped frac-line"></span></span><span style="top:-0.677em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle textstyle uncramped"><span class="mord textstyle uncramped"><span class="mord mathit">t</span><span class="mord mathit" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord"><span class="mord mathit">t</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-texts
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