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* 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.
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package org.apache.lucene.search.similarities;
import java.util.ArrayList;
import java.util.List;
import org.apache.lucene.index.FieldInvertState;
import org.apache.lucene.index.IndexOptions;
import org.apache.lucene.search.CollectionStatistics;
import org.apache.lucene.search.Explanation;
import org.apache.lucene.search.IndexSearcher;
import org.apache.lucene.search.TermStatistics;
import org.apache.lucene.util.SmallFloat;
/**
* Implementation of {@link Similarity} with the Vector Space Model.
* <p>
* Expert: Scoring API.
* <p>TFIDFSimilarity defines the components of Lucene scoring.
* Overriding computation of these components is a convenient
* way to alter Lucene scoring.
*
* <p>Suggested reading:
* <a href="http://nlp.stanford.edu/IR-book/html/htmledition/queries-as-vectors-1.html">
* Introduction To Information Retrieval, Chapter 6</a>.
*
* <p>The following describes how Lucene scoring evolves from
* underlying information retrieval models to (efficient) implementation.
* We first brief on <i>VSM Score</i>,
* then derive from it <i>Lucene's Conceptual Scoring Formula</i>,
* from which, finally, evolves <i>Lucene's Practical Scoring Function</i>
* (the latter is connected directly with Lucene classes and methods).
*
* <p>Lucene combines
* <a href="http://en.wikipedia.org/wiki/Standard_Boolean_model">
* Boolean model (BM) of Information Retrieval</a>
* with
* <a href="http://en.wikipedia.org/wiki/Vector_Space_Model">
* Vector Space Model (VSM) of Information Retrieval</a> -
* documents "approved" by BM are scored by VSM.
*
* <p>In VSM, documents and queries are represented as
* weighted vectors in a multi-dimensional space,
* where each distinct index term is a dimension,
* and weights are
* <a href="http://en.wikipedia.org/wiki/Tfidf">Tf-idf</a> values.
*
* <p>VSM does not require weights to be <i>Tf-idf</i> values,
* but <i>Tf-idf</i> values are believed to produce search results of high quality,
* and so Lucene is using <i>Tf-idf</i>.
* <i>Tf</i> and <i>Idf</i> are described in more detail below,
* but for now, for completion, let's just say that
* for given term <i>t</i> and document (or query) <i>x</i>,
* <i>Tf(t,x)</i> varies with the number of occurrences of term <i>t</i> in <i>x</i>
* (when one increases so does the other) and
* <i>idf(t)</i> similarly varies with the inverse of the
* number of index documents containing term <i>t</i>.
*
* <p><i>VSM score</i> of document <i>d</i> for query <i>q</i> is the
* <a href="http://en.wikipedia.org/wiki/Cosine_similarity">
* Cosine Similarity</a>
* of the weighted query vectors <i>V(q)</i> and <i>V(d)</i>:
*
* <br> <br>
* <table class="padding2" style="border-spacing: 2px; border-collapse: separate; border: 0; width:auto; margin-left:auto; margin-right:auto">
* <caption>formatting only</caption>
* <tr><td>
* <table class="padding1" style="border-spacing: 0px; border-collapse: separate; border: 1px solid; margin-left:auto; margin-right:auto">
* <caption>formatting only</caption>
* <tr><td>
* <table class="padding2" style="border-spacing: 2px; border-collapse: separate; border: 0; margin-left:auto; margin-right:auto">
* <caption>cosine similarity formula</caption>
* <tr>
* <td valign="middle" style="text-align: right" rowspan="1">
* cosine-similarity(q,d) =
* </td>
* <td valign="middle" style="text-align: center">
* <table>
* <caption>cosine similarity formula</caption>
* <tr><td style="text-align: center"><small>V(q) · V(d)</small></td></tr>
* <tr><td style="text-align: center">–––––––––</td></tr>
* <tr><td style="text-align: center"><small>|V(q)| |V(d)|</small></td></tr>
* </table>
* </td>
* </tr>
* </table>
* </td></tr>
* </table>
* </td></tr>
* <tr><td>
* <u style="text-align: center">VSM Score</u>
* </td></tr>
* </table>
* <br> <br>
*
*
* Where <i>V(q)</i> · <i>V(d)</i> is the
* <a href="http://en.wikipedia.org/wiki/Dot_product">dot product</a>
* of the weighted vectors,
* and <i>|V(q)|</i> and <i>|V(d)|</i> are their
* <a href="http://en.wikipedia.org/wiki/Euclidean_norm#Euclidean_norm">Euclidean norms</a>.
*
* <p>Note: the above equation can be viewed as the dot product of
* the normalized weighted vectors, in the sense that dividing
* <i>V(q)</i> by its euclidean norm is normalizing it to a unit vector.
*
* <p>Lucene refines <i>VSM score</i> for both search quality and usability:
* <ul>
* <li>Normalizing <i>V(d)</i> to the unit vector is known to be problematic in that
* it removes all document length information.
* For some documents removing this info is probably ok,
* e.g. a document made by duplicating a certain paragraph <i>10</i> times,
* especially if that paragraph is made of distinct terms.
* But for a document which contains no duplicated paragraphs,
* this might be wrong.
* To avoid this problem, a different document length normalization
* factor is used, which normalizes to a vector equal to or larger
* than the unit vector: <i>doc-len-norm(d)</i>.
* </li>
*
* <li>At indexing, users can specify that certain documents are more
* important than others, by assigning a document boost.
* For this, the score of each document is also multiplied by its boost value
* <i>doc-boost(d)</i>.
* </li>
*
* <li>Lucene is field based, hence each query term applies to a single
* field, document length normalization is by the length of the certain field,
* and in addition to document boost there are also document fields boosts.
* </li>
*
* <li>The same field can be added to a document during indexing several times,
* and so the boost of that field is the multiplication of the boosts of
* the separate additions (or parts) of that field within the document.
* </li>
*
* <li>At search time users can specify boosts to each query, sub-query, and
* each query term, hence the contribution of a query term to the score of
* a document is multiplied by the boost of that query term <i>query-boost(q)</i>.
* </li>
*
* <li>A document may match a multi term query without containing all
* the terms of that query (this is correct for some of the queries).
* </li>
* </ul>
*
* <p>Under the simplifying assumption of a single field in the index,
* we get <i>Lucene's Conceptual scoring formula</i>:
*
* <br> <br>
* <table class="padding2" style="border-spacing: 2px; border-collapse: separate; border: 0; width:auto; margin-left:auto; margin-right:auto">
* <caption>formatting only</caption>
* <tr><td>
* <table class="padding1" style="border-spacing: 0px; border-collapse: separate; border: 1px solid; margin-left:auto; margin-right:auto">
* <caption>formatting only</caption>
* <tr><td>
* <table class="padding2" style="border-spacing: 2px; border-collapse: separate; border: 0; margin-left:auto; margin-right:auto">
* <caption>formatting only</caption>
* <tr>
* <td valign="middle" style="text-align: right" rowspan="1">
* score(q,d) =
* <span style="color: #CCCC00">query-boost(q)</span> ·
* </td>
* <td valign="middle" style="text-align: center">
* <table>
* <caption>Lucene conceptual scoring formula</caption>
* <tr><td style="text-align: center"><small><span style="color: #993399">V(q) · V(d)</span></small></td></tr>
* <tr><td style="text-align: center">–––––––––</td></tr>
* <tr><td style="text-align: center"><small><span style="color: #FF33CC">|V(q)|</span></small></td></tr>
* </table>
* </td>
* <td valign="middle" style="text-align: right" rowspan="1">
* · <span style="color: #3399FF">doc-len-norm(d)</span>
* · <span style="color: #3399FF">doc-boost(d)</span>
* </td>
* </tr>
* </table>
* </td></tr>
* </table>
* </td></tr>
* <tr><td>
* <u style="text-align: center">Lucene Conceptual Scoring Formula</u>
* </td></tr>
* </table>
* <br> <br>
*
* <p>The conceptual formula is a simplification in the sense that (1) terms and documents
* are fielded and (2) boosts are usually per query term rather than per query.
*
* <p>We now describe how Lucene implements this conceptual scoring formula, and
* derive from it <i>Lucene's Practical Scoring Function</i>.
*
* <p>For efficient score computation some scoring components
* are computed and aggregated in advance:
*
* <ul>
* <li><i>Query-boost</i> for the query (actually for each query term)
* is known when search starts.
* </li>
*
* <li>Query Euclidean norm <i>|V(q)|</i> can be computed when search starts,
* as it is independent of the document being scored.
* From search optimization perspective, it is a valid question
* why bother to normalize the query at all, because all
* scored documents will be multiplied by the same <i>|V(q)|</i>,
* and hence documents ranks (their order by score) will not
* be affected by this normalization.
* There are two good reasons to keep this normalization:
* <ul>
* <li>Recall that
* <a href="http://en.wikipedia.org/wiki/Cosine_similarity">
* Cosine Similarity</a> can be used find how similar
* two documents are. One can use Lucene for e.g.
* clustering, and use a document as a query to compute
* its similarity to other documents.
* In this use case it is important that the score of document <i>d3</i>
* for query <i>d1</i> is comparable to the score of document <i>d3</i>
* for query <i>d2</i>. In other words, scores of a document for two
* distinct queries should be comparable.
* There are other applications that may require this.
* And this is exactly what normalizing the query vector <i>V(q)</i>
* provides: comparability (to a certain extent) of two or more queries.
* </li>
* </ul>
* </li>
*
* <li>Document length norm <i>doc-len-norm(d)</i> and document
* boost <i>doc-boost(d)</i> are known at indexing time.
* They are computed in advance and their multiplication
* is saved as a single value in the index: <i>norm(d)</i>.
* (In the equations below, <i>norm(t in d)</i> means <i>norm(field(t) in doc d)</i>
* where <i>field(t)</i> is the field associated with term <i>t</i>.)
* </li>
* </ul>
*
* <p><i>Lucene's Practical Scoring Function</i> is derived from the above.
* The color codes demonstrate how it relates
* to those of the <i>conceptual</i> formula:
*
* <table class="padding2" style="border-spacing: 2px; border-collapse: separate; border: 0; width:auto; margin-left:auto; margin-right:auto">
* <caption>formatting only</caption>
* <tr><td>
* <table style="border-spacing: 2px; border-collapse: separate; border: 2px solid; margin-left:auto; margin-right:auto">
* <caption>formatting only</caption>
* <tr><td>
* <table class="padding2" style="border-spacing: 2px; border-collapse: separate; border: 0; margin-left:auto; margin-right:auto">
* <caption>Lucene conceptual scoring formula</caption>
* <tr>
* <td valign="middle" style="text-align: right" rowspan="1">
* score(q,d) =
* <span style="font-size: larger">∑</span>
* </td>
* <td valign="middle" style="text-align: right" rowspan="1">
* <span style="font-size: larger">(</span>
* <A HREF="#formula_tf"><span style="color: #993399">tf(t in d)</span></A> ·
* <A HREF="#formula_idf"><span style="color: #993399">idf(t)</span></A><sup>2</sup> ·
* <A HREF="#formula_termBoost"><span style="color: #CCCC00">t.getBoost()</span></A> ·
* <A HREF="#formula_norm"><span style="color: #3399FF">norm(t,d)</span></A>
* <span style="font-size: larger">)</span>
* </td>
* </tr>
* <tr valign="top">
* <td></td>
* <td style="text-align: center"><small>t in q</small></td>
* <td></td>
* </tr>
* </table>
* </td></tr>
* </table>
* </td></tr>
* <tr><td>
* <u style="text-align: center">Lucene Practical Scoring Function</u>
* </td></tr>
* </table>
*
* <p> where
* <ol>
* <li>
* <a id="formula_tf"></A>
* <b><i>tf(t in d)</i></b>
* correlates to the term's <i>frequency</i>,
* defined as the number of times term <i>t</i> appears in the currently scored document <i>d</i>.
* Documents that have more occurrences of a given term receive a higher score.
* Note that <i>tf(t in q)</i> is assumed to be <i>1</i> and therefore it does not appear in this equation,
* However if a query contains twice the same term, there will be
* two term-queries with that same term and hence the computation would still be correct (although
* not very efficient).
* The default computation for <i>tf(t in d)</i> in
* {@link org.apache.lucene.search.similarities.ClassicSimilarity#tf(float) ClassicSimilarity} is:
*
* <br> <br>
* <table class="padding2" style="border-spacing: 2px; border-collapse: separate; border: 0; width:auto; margin-left:auto; margin-right:auto">
* <caption>term frequency computation</caption>
* <tr>
* <td valign="middle" style="text-align: right" rowspan="1">
* {@link org.apache.lucene.search.similarities.ClassicSimilarity#tf(float) tf(t in d)} =
* </td>
* <td valign="top" style="text-align: center" rowspan="1">
* frequency<sup><span style="font-size: larger">½</span></sup>
* </td>
* </tr>
* </table>
* <br> <br>
* </li>
*
* <li>
* <a id="formula_idf"></A>
* <b><i>idf(t)</i></b> stands for Inverse Document Frequency. This value
* correlates to the inverse of <i>docFreq</i>
* (the number of documents in which the term <i>t</i> appears).
* This means rarer terms give higher contribution to the total score.
* <i>idf(t)</i> appears for <i>t</i> in both the query and the document,
* hence it is squared in the equation.
* The default computation for <i>idf(t)</i> in
* {@link org.apache.lucene.search.similarities.ClassicSimilarity#idf(long, long) ClassicSimilarity} is:
*
* <br> <br>
* <table class="padding2" style="border-spacing: 2px; border-collapse: separate; border: 0; width:auto; margin-left:auto; margin-right:auto">
* <caption>inverse document frequency computation</caption>
* <tr>
* <td valign="middle" style="text-align: right">
* {@link org.apache.lucene.search.similarities.ClassicSimilarity#idf(long, long) idf(t)} =
* </td>
* <td valign="middle" style="text-align: center">
* 1 + log <span style="font-size: larger">(</span>
* </td>
* <td valign="middle" style="text-align: center">
* <table>
* <caption>inverse document frequency computation</caption>
* <tr><td style="text-align: center"><small>docCount+1</small></td></tr>
* <tr><td style="text-align: center">–––––––––</td></tr>
* <tr><td style="text-align: center"><small>docFreq+1</small></td></tr>
* </table>
* </td>
* <td valign="middle" style="text-align: center">
* <span style="font-size: larger">)</span>
* </td>
* </tr>
* </table>
* <br> <br>
* </li>
*
* <li>
* <a id="formula_termBoost"></A>
* <b><i>t.getBoost()</i></b>
* is a search time boost of term <i>t</i> in the query <i>q</i> as
* specified in the query text
* (see <A HREF="{@docRoot}/../queryparser/org/apache/lucene/queryparser/classic/package-summary.html#Boosting_a_Term">query syntax</A>),
* or as set by wrapping with
* {@link org.apache.lucene.search.BoostQuery#BoostQuery(org.apache.lucene.search.Query, float) BoostQuery}.
* Notice that there is really no direct API for accessing a boost of one term in a multi term query,
* but rather multi terms are represented in a query as multi
* {@link org.apache.lucene.search.TermQuery TermQuery} objects,
* and so the boost of a term in the query is accessible by calling the sub-query
* {@link org.apache.lucene.search.BoostQuery#getBoost() getBoost()}.
* <br> <br>
* </li>
*
* <li>
* <a id="formula_norm"></A>
* <b><i>norm(t,d)</i></b> is an index-time boost factor that solely
* depends on the number of tokens of this field in the document, so
* that shorter fields contribute more to the score.
* </li>
* </ol>
*
* @see org.apache.lucene.index.IndexWriterConfig#setSimilarity(Similarity)
* @see IndexSearcher#setSimilarity(Similarity)
*/
public abstract class TFIDFSimilarity extends Similarity {
/**
* Sole constructor. (For invocation by subclass
* constructors, typically implicit.)
*/
public TFIDFSimilarity() {}
/**
* True if overlap tokens (tokens with a position of increment of zero) are
* discounted from the document's length.
*/
protected boolean discountOverlaps = true;
/** Determines whether overlap tokens (Tokens with
* 0 position increment) are ignored when computing
* norm. By default this is true, meaning overlap
* tokens do not count when computing norms.
*
* @lucene.experimental
*
* @see #computeNorm
*/
public void setDiscountOverlaps(boolean v) {
discountOverlaps = v;
}
/**
* Returns true if overlap tokens are discounted from the document's length.
* @see #setDiscountOverlaps
*/
public boolean getDiscountOverlaps() {
return discountOverlaps;
}
/** Computes a score factor based on a term or phrase's frequency in a
* document. This value is multiplied by the {@link #idf(long, long)}
* factor for each term in the query and these products are then summed to
* form the initial score for a document.
*
* <p>Terms and phrases repeated in a document indicate the topic of the
* document, so implementations of this method usually return larger values
* when <code>freq</code> is large, and smaller values when <code>freq</code>
* is small.
*
* @param freq the frequency of a term within a document
* @return a score factor based on a term's within-document frequency
*/
public abstract float tf(float freq);
/**
* Computes a score factor for a simple term and returns an explanation
* for that score factor.
*
* <p>
* The default implementation uses:
*
* <pre class="prettyprint">
* idf(docFreq, docCount);
* </pre>
*
* Note that {@link CollectionStatistics#docCount()} is used instead of
* {@link org.apache.lucene.index.IndexReader#numDocs() IndexReader#numDocs()} because also
* {@link TermStatistics#docFreq()} is used, and when the latter
* is inaccurate, so is {@link CollectionStatistics#docCount()}, and in the same direction.
* In addition, {@link CollectionStatistics#docCount()} does not skew when fields are sparse.
*
* @param collectionStats collection-level statistics
* @param termStats term-level statistics for the term
* @return an Explain object that includes both an idf score factor
and an explanation for the term.
*/
public Explanation idfExplain(CollectionStatistics collectionStats, TermStatistics termStats) {
final long df = termStats.docFreq();
final long docCount = collectionStats.docCount();
final float idf = idf(df, docCount);
return Explanation.match(idf, "idf(docFreq, docCount)",
Explanation.match(df, "docFreq, number of documents containing term"),
Explanation.match(docCount, "docCount, total number of documents with field"));
}
/**
* Computes a score factor for a phrase.
*
* <p>
* The default implementation sums the idf factor for
* each term in the phrase.
*
* @param collectionStats collection-level statistics
* @param termStats term-level statistics for the terms in the phrase
* @return an Explain object that includes both an idf
* score factor for the phrase and an explanation
* for each term.
*/
public Explanation idfExplain(CollectionStatistics collectionStats, TermStatistics termStats[]) {
double idf = 0d; // sum into a double before casting into a float
List<Explanation> subs = new ArrayList<>();
for (final TermStatistics stat : termStats ) {
Explanation idfExplain = idfExplain(collectionStats, stat);
subs.add(idfExplain);
idf += idfExplain.getValue().floatValue();
}
return Explanation.match((float) idf, "idf(), sum of:", subs);
}
/** Computes a score factor based on a term's document frequency (the number
* of documents which contain the term). This value is multiplied by the
* {@link #tf(float)} factor for each term in the query and these products are
* then summed to form the initial score for a document.
*
* <p>Terms that occur in fewer documents are better indicators of topic, so
* implementations of this method usually return larger values for rare terms,
* and smaller values for common terms.
*
* @param docFreq the number of documents which contain the term
* @param docCount the total number of documents in the collection
* @return a score factor based on the term's document frequency
*/
public abstract float idf(long docFreq, long docCount);
/**
* Compute an index-time normalization value for this field instance.
*
* @param length the number of terms in the field, optionally {@link #setDiscountOverlaps(boolean) discounting overlaps}
* @return a length normalization value
*/
public abstract float lengthNorm(int length);
@Override
public final long computeNorm(FieldInvertState state) {
final int numTerms;
if (state.getIndexOptions() == IndexOptions.DOCS && state.getIndexCreatedVersionMajor() >= 8) {
numTerms = state.getUniqueTermCount();
} else if (discountOverlaps) {
numTerms = state.getLength() - state.getNumOverlap();
} else {
numTerms = state.getLength();
}
return SmallFloat.intToByte4(numTerms);
}
@Override
public final SimScorer scorer(float boost, CollectionStatistics collectionStats, TermStatistics... termStats) {
final Explanation idf = termStats.length == 1
? idfExplain(collectionStats, termStats[0])
: idfExplain(collectionStats, termStats);
float[] normTable = new float[256];
for (int i = 1; i < 256; ++i) {
int length = SmallFloat.byte4ToInt((byte) i);
float norm = lengthNorm(length);
normTable[i] = norm;
}
normTable[0] = 1f / normTable[255];
return new TFIDFScorer(boost, idf, normTable);
}
/** Collection statistics for the TF-IDF model. The only statistic of interest
* to this model is idf. */
class TFIDFScorer extends SimScorer {
/** The idf and its explanation */
private final Explanation idf;
private final float boost;
private final float queryWeight;
final float[] normTable;
public TFIDFScorer(float boost, Explanation idf, float[] normTable) {
// TODO: Validate?
this.idf = idf;
this.boost = boost;
this.queryWeight = boost * idf.getValue().floatValue();
this.normTable = normTable;
}
@Override
public float score(float freq, long norm) {
final float raw = tf(freq) * queryWeight; // compute tf(f)*weight
float normValue = normTable[(int) (norm & 0xFF)];
return raw * normValue; // normalize for field
}
@Override
public Explanation explain(Explanation freq, long norm) {
return explainScore(freq, norm, normTable);
}
private Explanation explainScore(Explanation freq, long encodedNorm, float[] normTable) {
List<Explanation> subs = new ArrayList<Explanation>();
if (boost != 1F) {
subs.add(Explanation.match(boost, "boost"));
}
subs.add(idf);
Explanation tf = Explanation.match(tf(freq.getValue().floatValue()), "tf(freq="+freq.getValue()+"), with freq of:", freq);
subs.add(tf);
float norm = normTable[(int) (encodedNorm & 0xFF)];
Explanation fieldNorm = Explanation.match(norm, "fieldNorm");
subs.add(fieldNorm);
return Explanation.match(
queryWeight * tf.getValue().floatValue() * norm,
"score(freq="+freq.getValue()+"), product of:",
subs);
}
}
}
