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In [[probability theory]] and [[information theory]], the '''variation of information''' or '''shared information distance''' is a measure of the distance between two clusterings ([[Partition of a set|partitions of elements]]). It is closely related to [[mutual information]]; indeed, it is a simple linear expression involving the mutual information. Unlike the mutual information, however, the variation of information is a true [[metric (mathematics)|metric]], in that it obeys the [[triangle inequality]]. Even more, it is a [[universal metric]], in that if any other distance measure two items close-by, then the variation of information will also judge them close.<ref>Alexander Kraskov, Harald Stögbauer, Ralph G. Andrzejak, and [[Peter Grassberger]], "Hierarchical Clustering Based on Mutual Information", (2003) ''[http://arxiv.org/abs/q-bio/0311039 ArXiv q-bio/0311039]''</ref> | |||
==Background== | |||
{{Empty section|date=July 2010}} | |||
==Definition== | |||
Suppose we have two clusterings (a division of a [[Set (mathematics)|set]] into several [[subset]]s) <math>X</math> and <math>Y</math> where <math>X = \{X_{1}, X_{2}, ..,, X_{k}\}</math>, <math>p_{i} = |X_{i}| / n</math>, <math>n = \Sigma_{k} |X_{i}|</math>. Then the variation of information between two clusterings is: | |||
:<math>VI(X; Y ) = H(X) + H(Y) - 2I(X, Y)</math> | |||
where <math>H(X)</math> is [[entropy (information theory)|entropy]] of <math>X</math> and <math>I(X, Y)</math> is [[mutual information]] between <math>X</math> and <math>Y</math>. | |||
This is completely equivalent to the [[Mutual information#Metric|shared information distance]]. | |||
==References== | |||
<references/> | |||
== Further reading == | |||
* {{cite journal|last=Arabie|first=P.|coauthors=Boorman, S. A.|title=Multidimensional scaling of measures of distance between partitions|journal=Journal of Mathematical Psychology|year=1973|volume=10|pages=148–203}} | |||
* {{Cite journal|last=Meila|first=Marina | title=Comparing Clusterings by the Variation of Information |journal=Learning Theory and Kernel Machines|year=2003|pages=173–187|doi=10.1007/978-3-540-45167-9_14}} | |||
* {{cite doi|10.1016/j.jmva.2006.11.013}} | |||
* {{Cite web | |||
| last = Kingsford | |||
| first = Carl | |||
| title = Information Theory Notes | |||
| year = 2009 | |||
| url = http://www.cs.umd.edu/class/spring2009/cmsc858l/InfoTheoryHints.pdf | |||
| format = PDF | |||
| accessdate = 22 September 2009}} | |||
{{Use dmy dates|date=September 2010}} | |||
== External links == | |||
* [https://github.com/bjoern-andres/partition-comparison C++ implementation with MATLAB mex files] | |||
{{DEFAULTSORT:Variation Of Information}} | |||
[[Category:Entropy and information]] | |||
Revision as of 07:40, 3 February 2014
In probability theory and information theory, the variation of information or shared information distance is a measure of the distance between two clusterings (partitions of elements). It is closely related to mutual information; indeed, it is a simple linear expression involving the mutual information. Unlike the mutual information, however, the variation of information is a true metric, in that it obeys the triangle inequality. Even more, it is a universal metric, in that if any other distance measure two items close-by, then the variation of information will also judge them close.[1]
Background
Definition
Suppose we have two clusterings (a division of a set into several subsets) and where , , . Then the variation of information between two clusterings is:
where is entropy of and is mutual information between and .
This is completely equivalent to the shared information distance.
References
- ↑ Alexander Kraskov, Harald Stögbauer, Ralph G. Andrzejak, and Peter Grassberger, "Hierarchical Clustering Based on Mutual Information", (2003) ArXiv q-bio/0311039
Further reading
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Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
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A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - Template:Cite doi
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