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{{merge from|Similarity matrix|discuss=Talk:Similarity measure#Proposed merge with Similarity matrix|date=October 2013}}
In [[computer science]], a '''similarity measure''' or '''similarity function''' is a [[real-valued function]] that quantifies the similarity between two objects. Although no single definition of a similarity measure exists, usually similarity measures are in some sense the inverse of [[Metric (mathematics)|distance metric]]s: they take on large values for similar objects and either zero or a negative value for very dissimilar objects. E.g., in the context of [[cluster analysis]], Frey and Dueck suggest defining a similarity measure


:<math>s(x_i, x_k) = -||x_i - x_k||_2^2</math>


where <math>||x_i - x_k||_2^2</math> is the [[Euclidean distance#Squared Euclidean distance|squared Euclidean distance]].<ref>{{cite journal |author1=Brendan J. Frey |author2=Delbert Dueck |title=Clustering by passing messages between data points |journal=[[Science (journal)|Science]] |volume=315 |year=2007 |pages=972–976|pmid=17218491}}</ref>
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In [[information retrieval]], [[cosine similarity]] is a commonly used similarity measure, defined on vectors arising from the [[bag of words]] model. In [[machine learning]], common [[Kernel trick|kernel functions]] such as the [[Radial basis function kernel|RBF kernel]] can be viewed as similarity functions.<ref name="primer">{{cite book|author1=Vert, Jean-Philippe|author2=Koji Tsuda|author3=Bernhard Schölkopf|authorlink3=Bernhard Schölkopf|year=2004|chapter=A primer on kernel methods|title=Kernel Methods in Computational Biology|url=http://www.eecis.udel.edu/~lliao/cis841s06/primer_on_kernel_methods_vert.pdf}}</ref>
 
==References==
{{reflist|1}}
* {{cite journal |author1=F. Gregory Ashby|author2=Daniel M. Ennis|year=2007 |title=Similarity measures |journal=Scholarpedia |volume=2 |number=12 |doi=10.4249/scholarpedia.4116}}
 
==See also==
* [[Semantic similarity]]
* [[String metric]]
* [[Affinity propagation]]
 
 
[[Category:Computer science]]
 
{{comp-sci-stub}}

Latest revision as of 00:23, 14 May 2014


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