Examples of Similarity

• Database.Primitives.Similarity
  @author sarahejones, sns
• edu.ucdavis.genomics.metabolomics.util.math.Similarity
• org.apache.lucene.search.Similarity
  tanford.edu/IR-book/html/htmledition/queries-as-vectors-1.html"> Introduction To Information Retrieval, Chapter 6.

  The following describes how Lucene scoring evolves from underlying information retrieval models to (efficient) implementation. We first brief on VSM Score, then derive from it Lucene's Conceptual Scoring Formula, from which, finally, evolves Lucene's Practical Scoring Function (the latter is connected directly with Lucene classes and methods).

  Lucene combines Boolean model (BM) of Information Retrieval with Vector Space Model (VSM) of Information Retrieval - documents "approved" by BM are scored by VSM.

  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 Tf-idf values.

  VSM does not require weights to be Tf-idf values, but Tf-idf values are believed to produce search results of high quality, and so Lucene is using Tf-idf. Tf and Idf are described in more detail below, but for now, for completion, let's just say that for given term t and document (or query) x, Tf(t,x) varies with the number of occurrences of term t in x (when one increases so does the other) and idf(t) similarly varies with the inverse of the number of index documents containing term t.

  VSM score of document d for query q is the Cosine Similarity of the weighted query vectors V(q) and V(d):
   
  

  cosine-similarity(q,d)   =   V(q) · V(d) ––––––––– |V(q)| |V(d)|

  VSM Score

  
   
  Where V(q) · V(d) is the dot product of the weighted vectors, and |V(q)| and |V(d)| are their Euclidean norms.

  Note: the above equation can be viewed as the dot product of the normalized weighted vectors, in the sense that dividing V(q) by its euclidean norm is normalizing it to a unit vector.

  Lucene refines VSM score for both search quality and usability:

  • Normalizing V(d) 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 10 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: doc-len-norm(d).
  • 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 doc-boost(d).
  • 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.
  • 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.
  • 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 query-boost(q).
  • A document may match a multi term query without containing all the terms of that query (this is correct for some of the queries), and users can further reward documents matching more query terms through a coordination factor, which is usually larger when more terms are matched: coord-factor(q,d).

  Under the simplifying assumption of a single field in the index, we get Lucene's Conceptual scoring formula:
   
  

  score(q,d)   =   coord-factor(q,d) ·   query-boost(q) ·   V(q) · V(d) ––––––––– |V(q)|   ·   doc-len-norm(d)   ·   doc-boost(d)

  Lucene Conceptual Scoring Formula

  
   
  

  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.

  We now describe how Lucene implements this conceptual scoring formula, and derive from it Lucene's Practical Scoring Function.

  For efficient score computation some scoring components are computed and aggregated in advance:

  • Query-boost for the query (actually for each query term) is known when search starts.
  • Query Euclidean norm |V(q)| 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 |V(q)|, and hence documents ranks (their order by score) will not be affected by this normalization. There are two good reasons to keep this normalization:
    • Recall that Cosine Similarity 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 d3 for query d1 is comparable to the score of document d3 for query d2. 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 V(q) provides: comparability (to a certain extent) of two or more queries.
    • Applying query normalization on the scores helps to keep the scores around the unit vector, hence preventing loss of score data because of floating point precision limitations.
  • Document length norm doc-len-norm(d) and document boost doc-boost(d) are known at indexing time. They are computed in advance and their multiplication is saved as a single value in the index: norm(d). (In the equations below, norm(t in d) means norm(field(t) in doc d) where field(t) is the field associated with term t.)

  Lucene's Practical Scoring Function is derived from the above. The color codes demonstrate how it relates to those of the conceptual formula:

  score(q,d)   =   coord(q,d)  ·  queryNorm(q)  ·  ∑ ( tf(t in d)  ·  idf(t)2  ·  t.getBoost() ·  norm(t,d) ) t in q

  Lucene Practical Scoring Function

  where

  1. tf(t in d) correlates to the term's frequency, defined as the number of times term t appears in the currently scored document d. Documents that have more occurrences of a given term receive a higher score. Note that tf(t in q) is assumed to be 1 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 tf(t in d) in {@link org.apache.lucene.search.DefaultSimilarity#tf(float) DefaultSimilarity} is:
      
     

     {@link org.apache.lucene.search.DefaultSimilarity#tf(float) tf(t in d)}   =

     frequency½

     
      
     
  2. idf(t) stands for Inverse Document Frequency. This value correlates to the inverse of docFreq (the number of documents in which the term t appears). This means rarer terms give higher contribution to the total score. idf(t) appears for t in both the query and the document, hence it is squared in the equation. The default computation for idf(t) in {@link org.apache.lucene.search.DefaultSimilarity#idf(int,int) DefaultSimilarity} is:
      
     

     {@link org.apache.lucene.search.DefaultSimilarity#idf(int,int) idf(t)}  =

     1 + log (

     numDocs ––––––––– docFreq+1

     )

     
      
     
  3. coord(q,d) is a score factor based on how many of the query terms are found in the specified document. Typically, a document that contains more of the query's terms will receive a higher score than another document with fewer query terms. This is a search time factor computed in {@link #coord(int,int) coord(q,d)}by the Similarity in effect at search time.
      
     
  4. queryNorm(q) is a normalizing factor used to make scores between queries comparable. This factor does not affect document ranking (since all ranked documents are multiplied by the same factor), but rather just attempts to make scores from different queries (or even different indexes) comparable. This is a search time factor computed by the Similarity in effect at search time. The default computation in {@link org.apache.lucene.search.DefaultSimilarity#queryNorm(float) DefaultSimilarity}produces a Euclidean norm:
      
     

     queryNorm(q)   =   {@link org.apache.lucene.search.DefaultSimilarity#queryNorm(float) queryNorm(sumOfSquaredWeights)}  =

     1 –––––––––––––– sumOfSquaredWeights½

     
      
     The sum of squared weights (of the query terms) is computed by the query {@link org.apache.lucene.search.Weight} object.For example, a {@link org.apache.lucene.search.BooleanQuery boolean query}computes this value as:
      
     

     {@link org.apache.lucene.search.Weight#sumOfSquaredWeights() sumOfSquaredWeights}   =  {@link org.apache.lucene.search.Query#getBoost() q.getBoost()} 2 ·	∑	( idf(t)  ·  t.getBoost() ) 2
     	t in q

     
      
     
  5. t.getBoost() is a search time boost of term t in the query q as specified in the query text (see query syntax), or as set by application calls to {@link org.apache.lucene.search.Query#setBoost(float) setBoost()}. 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.Query#getBoost() getBoost()}.
      
     
  6. norm(t,d) encapsulates a few (indexing time) boost and length factors:
     • Document boost - set by calling {@link org.apache.lucene.document.Document#setBoost(float) doc.setBoost()}before adding the document to the index.
     • Field boost - set by calling {@link org.apache.lucene.document.Fieldable#setBoost(float) field.setBoost()}before adding the field to a document.
     • {@link #lengthNorm(String,int) lengthNorm(field)} - computedwhen the document is added to the index in accordance with the number of tokens of this field in the document, so that shorter fields contribute more to the score. LengthNorm is computed by the Similarity class in effect at indexing.

     When a document is added to the index, all the above factors are multiplied. If the document has multiple fields with the same name, all their boosts are multiplied together:
      
     

     norm(t,d)   =   {@link org.apache.lucene.document.Document#getBoost() doc.getBoost()} ·  {@link #lengthNorm(String,int) lengthNorm(field)} ·	∏	{@link org.apache.lucene.document.Fieldable#getBoost() f.getBoost}()
     	field f in d named as t

     
      
     However the resulted norm value is {@link #encodeNorm(float) encoded} as a single bytebefore being stored. At search time, the norm byte value is read from the index {@link org.apache.lucene.store.Directory directory} and{@link #decodeNorm(byte) decoded} back to a float norm value.This encoding/decoding, while reducing index size, comes with the price of precision loss - it is not guaranteed that decode(encode(x)) = x. For instance, decode(encode(0.89)) = 0.75.
      
     Compression of norm values to a single byte saves memory at search time, because once a field is referenced at search time, its norms - for all documents - are maintained in memory.
      
     The rationale supporting such lossy compression of norm values is that given the difficulty (and inaccuracy) of users to express their true information need by a query, only big differences matter.
      
     Last, note that search time is too late to modify this norm part of scoring, e.g. by using a different {@link Similarity} for search.
      
     

  @see #setDefault(Similarity) @see org.apache.lucene.index.IndexWriter#setSimilarity(Similarity) @see Searcher#setSimilarity(Similarity)
• org.apache.lucene.search.similarities.Similarity
  Similarity defines the components of Lucene scoring.

  Expert: Scoring API.

  This is a low-level API, you should only extend this API if you want to implement an information retrieval model. If you are instead looking for a convenient way to alter Lucene's scoring, consider extending a higher-level implementation such as {@link TFIDFSimilarity}, which implements the vector space model with this API, or just tweaking the default implementation: {@link DefaultSimilarity}.

  Similarity determines how Lucene weights terms, and Lucene interacts with this class at both index-time and query-time.

  At indexing time, the indexer calls {@link #computeNorm(FieldInvertState)}, allowing the Similarity implementation to set a per-document value for the field that will be later accessible via {@link AtomicReader#getNormValues(String)}. Lucene makes no assumption about what is in this norm, but it is most useful for encoding length normalization information.

  Implementations should carefully consider how the normalization is encoded: while Lucene's classical {@link TFIDFSimilarity} encodes a combination of index-time boostand length normalization information with {@link SmallFloat} into a single byte, this might not be suitable for all purposes.

  Many formulas require the use of average document length, which can be computed via a combination of {@link CollectionStatistics#sumTotalTermFreq()} and {@link CollectionStatistics#maxDoc()} or {@link CollectionStatistics#docCount()}, depending upon whether the average should reflect field sparsity.

  Additional scoring factors can be stored in named NumericDocValuesFields and accessed at query-time with {@link AtomicReader#getNumericDocValues(String)}.

  Finally, using index-time boosts (either via folding into the normalization byte or via DocValues), is an inefficient way to boost the scores of different fields if the boost will be the same for every document, instead the Similarity can simply take a constant boost parameter C, and {@link PerFieldSimilarityWrapper} can return different instances with different boosts depending upon field name.

  At query-time, Queries interact with the Similarity via these steps:

  1. The {@link #computeWeight(float,CollectionStatistics,TermStatistics)} method is called a single time,allowing the implementation to compute any statistics (such as IDF, average document length, etc) across the entire collection. The {@link TermStatistics} and {@link CollectionStatistics} passed in already contain all of the raw statistics involved, so a Similarity can freely use any combination of statistics without causing any additional I/O. Lucene makes no assumption about what is stored in the returned {@link Similarity.SimWeight} object.
  2. The query normalization process occurs a single time: {@link Similarity.SimWeight#getValueForNormalization()}is called for each query leaf node, {@link Similarity#queryNorm(float)} is called for the top-levelquery, and finally {@link Similarity.SimWeight#normalize(float,float)} passes down the normalization valueand any top-level boosts (e.g. from enclosing {@link BooleanQuery}s).
  3. For each segment in the index, the Query creates a {@link #exactSimScorer(SimWeight,AtomicReaderContext)}(for queries with exact frequencies such as TermQuerys and exact PhraseQueries) or a {@link #sloppySimScorer(SimWeight,AtomicReaderContext)} (for queries with sloppy frequencies such asSpanQuerys and sloppy PhraseQueries). The score() method is called for each matching document.

  When {@link IndexSearcher#explain(org.apache.lucene.search.Query,int)} is called, queries consult the Similarity's DocScorer for an explanation of how it computed its score. The query passes in a the document id and an explanation of how the frequency was computed. @see org.apache.lucene.index.IndexWriterConfig#setSimilarity(Similarity) @see IndexSearcher#setSimilarity(Similarity) @lucene.experimental

Examples of org.apache.lucene.search.similarities.Similarity

Examples of org.apache.lucene.search.similarities.Similarity

Examples of org.apache.lucene.search.similarities.Similarity