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The Sørensen–Dice index, also known by other names (see Names, below), is a statistic used for comparing the similarity of two samples. It was independently developed by the botanists Thorvald Sørensen^[1] and Lee Raymond Dice,^[2] who published in 1948 and 1945 respectively.

Name

The index is known by several other names, usually Sørensen index or Dice's coefficient. Both names also see "similarity coefficient", "index", and other such variations. Common alternate spellings for Sørensen are Sorenson, Soerenson index and Sörenson index, and all three can also be seen with the –sen ending.

Formula

Sørensen's original formula was intended to be applied to presence/absence data, and is

Q S = \frac{2 C}{A + B} = \frac{2 | A \cap B |}{| A | + | B |}

where A and B are the number of species in samples A and B, respectively, and C is the number of species shared by the two samples; QS is the quotient of similarity and ranges from 0 to 1. This expression is easily extended to abundance instead of presence/absence of species. This quantitative version of the Sørensen index is also known as Czekanowski index. The Sørensen index is identical to Dice's coefficient^[3] which is always in [0, 1] range. The Sørensen index used as a distance measure, 1 − QS, is identical to Hellinger distance and Bray Curtis dissimilarity^[4] when applied to quantitative data.

It can be viewed as a similarity measure over sets:

s = \frac{2 | X \cap Y |}{| X | + | Y |}

It is not very different in form from the Jaccard index but has some different properties.

The function ranges between zero and one, like Jaccard. Unlike Jaccard, the corresponding difference function

d = 1 - \frac{2 | X \cap Y |}{| X | + | Y |}

is not a proper distance metric as it does not possess the property of triangle inequality. The simplest counterexample of this is given by the three sets {a}, {b}, and {a,b}, the distance between the first two being 1, and the difference between the third and each of the others being one-third.

Similarly to Jaccard, the set operations can be expressed in terms of vector operations over binary vectors A and B:

$s_{v} = \frac{2 | A \cdot B |}{| A |^{2} + | B |^{2}}$

which gives the same outcome over binary vectors and also gives a more general similarity metric over vectors in general terms.

For sets X and Y of keywords used in information retrieval, the coefficient may be defined as twice the shared information (intersection) over the sum of cardinalities :^[5]

When taken as a string similarity measure, the coefficient may be calculated for two strings, x and y using bigrams as follows:^[6]

s = \frac{2 n_{t}}{n_{x} + n_{y}}

where n_t is the number of character bigrams found in both strings, n_x is the number of bigrams in string x and n_y is the number of bigrams in string y. For example, to calculate the similarity between:

night

nacht

We would find the set of bigrams in each word:

{ni,ig,gh,ht}

{na,ac,ch,ht}

Each set has four elements, and the intersection of these two sets has only one element: ht.

Inserting these numbers into the formula, we calculate, s = (2 · 1) / (4 + 4) = 0.25.

Applications

The Sørensen–Dice coefficient is mainly useful for ecological community data (e.g. Looman & Campbell, 1960^[7]). Justification for its use is primarily empirical rather than theoretical (although it can be justified theoretically as the intersection of two fuzzy sets^[8]). As compared to Euclidean distance, Sørensen distance retains sensitivity in more heterogeneous data sets and gives less weight to outliers.^[9]

References

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External links

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Open Source Dice / Sorensen Scala implementation as part of the larger stringmetric project

↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

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

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

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
↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

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

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

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
↑ http://www.sekj.org/PDF/anbf40/anbf40-415.pdf
↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

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

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

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
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↑ Looman, J. and Campbell, J.B. (1960) Adaptation of Sorensen's K (1948) for estimating unit affinities in prairie vegetation. Ecology 41 (3): 409–416.
↑ Roberts, D.W. (1986) Ordination on the basis of fuzzy set theory. Vegetatio 66 (3): 123–131.
↑ McCune, Bruce & Grace, James (2002) Analysis of Ecological Communities. Mjm Software Design; ISBN 0-9721290-0-6.

[1] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

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

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

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

[2] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

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

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

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

[3] ttp://www.sekj.org/PDF/anbf40/anbf40-415.pdf

[4] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

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

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

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

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[7] Looman, J. and Campbell, J.B. (1960) Adaptation of Sorensen's K (1948) for estimating unit affinities in prairie vegetation. Ecology 41 (3): 409–416.

[8] Roberts, D.W. (1986) Ordination on the basis of fuzzy set theory. Vegetatio 66 (3): 123–131.

[9] McCune, Bruce & Grace, James (2002) Analysis of Ecological Communities. Mjm Software Design; ISBN 0-9721290-0-6.

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+The '''Sørensen–Dice index''', also known by other names (see Names, below), is a [[statistic]] used for comparing the similarity of two [[Sample (statistics)|samples]]. It was independently developed by the [[botanist]]s [[Thorvald Sørensen]]<ref>{{cite journal |last=Sørensen |first=T. |year=1948 |title=A method of establishing groups of equal amplitude in [[plant sociology]] based on similarity of species and its application to analyses of the vegetation on Danish commons |journal=[[Kongelige Danske Videnskabernes Selskab]] |volume=5 |issue=4 |pages=1–34 |doi= }}</ref> and [[Lee Raymond Dice]],<ref>{{cite journal |last=Dice |first=Lee R. |title=Measures of the Amount of Ecologic Association Between Species |jstor=1932409 |journal=Ecology |volume=26 |issue=3 |year=1945 |pages=297–302 |doi=10.2307/1932409 }}</ref> who published in 1948 and 1945 respectively.
+==Name==
+The index is known by several other names, usually '''Sørensen index''' or '''Dice's coefficient'''. Both names also see "similarity coefficient", "index", and other such variations. Common alternate spellings for Sørensen are Sorenson, Soerenson index and Sörenson index, and all three can also be seen with the –sen ending.
+==Formula==
+Sørensen's original formula was intended to be applied to presence/absence data, and is
+:<math> QS = \frac{2C}{A + B} = \frac{2 |A \cap B|}{|A| + |B|}</math>
+where ''A'' and ''B'' are the number of species in samples A and B, respectively, and ''C'' is the number of species shared by the two samples; QS is the quotient of similarity and ranges from 0 to 1. This expression is easily extended to [[Abundance (ecology)|abundance]] instead of presence/absence of species. This quantitative version of the Sørensen index is also known as ''[[Jan Czekanowski|Czekanowski]] index''. The Sørensen index is identical to [[Dice's coefficient]]<ref>http://www.sekj.org/PDF/anbf40/anbf40-415.pdf</ref> which is always in [0,&nbsp;1] range. The Sørensen index used as a distance measure, 1&nbsp;−&nbsp;''QS'', is identical to [[Hellinger distance]] and [[Bray Curtis dissimilarity]]<ref>{{cite journal |first=J. Roger |last=Bray |first2=J. T. |last2=Curtis |year=1948 |title=An Ordination of the Upland Forest Communities of Southern Wisconsin |journal=Ecological Monographs |volume=27 |issue=4 |pages=326–349 |doi=10.2307/1942268 }}</ref> when applied to quantitative data.
+It can be viewed as a similarity measure over sets:
+:<math>s = \frac{2 | X \cap Y |}{| X | + | Y |} </math>
+It is not very different in form from the [[Jaccard index]] but has some different properties.
+The function ranges between zero and one, like Jaccard. Unlike Jaccard, the corresponding difference function
+:<math>d = 1 -  \frac{2 | X \cap Y |}{| X | + | Y |} </math>
+is not a proper distance metric as it does not possess the property of triangle inequality. The simplest counterexample of this is given by the three sets {a}, {b}, and {a,b}, the distance between the first two
+being 1, and the difference between the third and each of the others being one-third.
+Similarly to Jaccard, the set operations can be expressed in terms of vector operations over binary vectors ''A'' and ''B'':
+<math>s_v = \frac{2 | A \cdot B |}{| A |^2 + | B |^2} </math>
+which gives the same outcome over binary vectors and also gives a more general similarity metric over vectors in general terms.
+For sets ''X'' and ''Y'' of keywords used in [[information retrieval]], the coefficient may be defined as twice the shared information (intersection) over the sum of cardinalities :<ref>{{cite book |last=van Rijsbergen |first=Cornelis Joost |year=1979
+|title=Information Retrieval
+|url=http://www.dcs.gla.ac.uk/Keith/Preface.html |publisher=Butterworths |location=London |isbn=3-642-12274-4 }}</ref>
+When taken as a string similarity measure, the coefficient may be calculated for two strings, ''x'' and ''y'' using [[bigram]]s as follows:<ref>{{cite conference |last=Kondrak |first=Grzegorz |coauthors=Marcu, Daniel; and Knight, Kevin |year=2003
+|title=Cognates Can Improve Statistical Translation Models
+|booktitle=Proceedings of HLT-NAACL 2003: Human Language Technology Conference of the North American Chapter of the Association for Computational Linguistics
+|pages=46–48 |url=http://aclweb.org/anthology/N/N03/N03-2016.pdf}}</ref>
+:<math>s = \frac{2 n_t}{n_x + n_y}</math>
+where ''n''<sub>''t''</sub> is the number of character bigrams found in both strings, ''n''<sub>''x''</sub> is the number of bigrams in string ''x'' and ''n''<sub>''y''</sub> is the number of bigrams in string ''y''. For example, to calculate the similarity between:
+:<code>night</code>
+:<code>nacht</code>
+We would find the set of bigrams in each word:
+:{<code>ni</code>,<code>ig</code>,<code>gh</code>,<code>ht</code>}
+:{<code>na</code>,<code>ac</code>,<code>ch</code>,<code>ht</code>}
+Each set has four elements, and the intersection of these two sets has only one element: <code>ht</code>.
+Inserting these numbers into the formula, we calculate, ''s''&nbsp;=&nbsp;(2&nbsp;·&nbsp;1)&nbsp;/&nbsp;(4&nbsp;+&nbsp;4)&nbsp;=&nbsp;0.25.
+==Applications==
+The Sørensen–Dice coefficient is mainly useful for ecological community data (e.g. Looman & Campbell, 1960<ref>[http://links.jstor.org/sici?sici=0012-9658%28196007%2941%3A3%3C409%3AAOSK%28F%3E2.0.CO%3B2-1 Looman, J. and Campbell, J.B. (1960) Adaptation of Sorensen's K (1948) for estimating unit affinities in prairie vegetation. Ecology 41 (3): 409–416.]</ref>). Justification for its use is primarily  empirical rather than theoretical (although it can be justified  theoretically as the intersection of two [[fuzzy set]]s<ref>[http://dx.doi.org/10.1007/BF00039905 Roberts, D.W. (1986) Ordination on the basis of fuzzy set theory. Vegetatio 66 (3): 123–131.]</ref>). As compared to [[Euclidean distance]], Sørensen distance retains sensitivity in more heterogeneous data sets and gives less weight to outliers.<ref>McCune, Bruce & Grace, James (2002) Analysis of Ecological Communities. Mjm Software Design; ISBN 0-9721290-0-6.</ref>
+==See also==
+* [[Correlation]]
+* [[Czekanowski similarity index]]
+* [[Jaccard index]]
+* [[Hamming distance]]
+* [[Horn’s index]]
+* [[Hurlbert’s index]]
+* [[Kulczyński similarity index]]
+* [[Pianka's index]]
+* [[MacArthur and Levin's index]]
+* [[Morisita's overlap index]]
+* [[Overlap coefficient]]
+* [[Renkonen similarity index]] (due to [[Olavi Renkonen]])
+* [[Simplified Morisita’s index]]
+* [[Tversky index]]
+* [[Universal adaptive strategy theory (UAST)]]
+==References==
+{{reflist}}
+==External links==
+{{Wikibooks|Algorithm implementation|Strings/Dice's coefficient|Dice's coefficient}}
+* Open Source [https://github.com/rockymadden/stringmetric/blob/master/core/src/main/scala/com/rockymadden/stringmetric/similarity/DiceSorensenMetric.scala Dice / Sorensen] [[Scala programming language|Scala]] implementation as part of the larger [http://rockymadden.com/stringmetric/ stringmetric project]
+{{DEFAULTSORT:Sorensen-Dice coefficient}}
+[[Category:Information retrieval]]
+[[Category:String similarity measures]]
+[[Category:Measure theory]]

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