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The Jaccard index, also known as the Jaccard similarity coefficient (originally coined coefficient de communauté by Paul Jaccard), is a statistic used for comparing the similarity and diversity of sample sets. The Jaccard coefficient measures similarity between finite sample sets, and is defined as the size of the intersection divided by the size of the union of the sample sets:

J (A, B) = \frac{| A \cap B |}{| A \cup B |} .

(If A and B are both empty, we define J(A,B)=1.) Clearly,

0 \leq J (A, B) \leq 1 .

The MinHash min-wise independent permutations locality sensitive hashing scheme may be used to efficiently compute an accurate estimate of the Jaccard similarity coefficient of pairs of sets, where each set is represented by a constant-sized signature derived from the minimum values of a hash function.

The Jaccard distance, which measures dissimilarity between sample sets, is complementary to the Jaccard coefficient and is obtained by subtracting the Jaccard coefficient from 1, or, equivalently, by dividing the difference of the sizes of the union and the intersection of two sets by the size of the union:

d_{J} (A, B) = 1 - J (A, B) = \frac{| A \cup B | - | A \cap B |}{| A \cup B |} .

An alternate interpretation of the Jaccard distance is as the ratio of the size of the symmetric difference $A △ B = (A \cup B) - (A \cap B)$ to the union.

This distance is a proper metric on sets of sets.^[1]^[2]

There is also a version of the Jaccard distance for measures, including probability measures. If $μ$ is a measure on a measurable space $X$ , then we define the Jaccard coefficient by $J_{μ} (A, B) = \frac{μ (A \cap B)}{μ (A \cup B)}$ , and the Jaccard distance by $d_{μ} (A, B) = 1 - J_{μ} (A, B) = \frac{μ (A △ B)}{μ (A \cup B)}$ . Care must be taken if $μ (A \cup B) = 0$ or $\infty$ , since these formulas are not well defined in that case.

Similarity of asymmetric binary attributes

Given two objects, A and B, each with n binary attributes, the Jaccard coefficient is a useful measure of the overlap that A and B share with their attributes. Each attribute of A and B can either be 0 or 1. The total number of each combination of attributes for both A and B are specified as follows:

M_{11}

represents the total number of attributes where A and B both have a value of 1.

M_{01}

represents the total number of attributes where the attribute of A is 0 and the attribute of B is 1.

M_{10}

represents the total number of attributes where the attribute of A is 1 and the attribute of B is 0.

M_{00}

represents the total number of attributes where A and B both have a value of 0.

Each attribute must fall into one of these four categories, meaning that

M_{11} + M_{01} + M_{10} + M_{00} = n .

The Jaccard similarity coefficient, J, is given as

J = \frac{M_{11}}{M_{01} + M_{10} + M_{11}} .

The Jaccard distance, d_J, is given as

d_{J} = \frac{M_{01} + M_{10}}{M_{01} + M_{10} + M_{11}} .

Tanimoto Similarity and Distance

Various forms of functions described as Tanimoto Similarity and Tanimoto Distance occur in the literature and on the Internet. Most of these are synonyms for Jaccard Similarity and Jaccard Distance, but some are mathematically different. Many sources^[3] cite an unavailable IBM Technical Report^[4] as the seminal reference.

In "A Computer Program for Classifying Plants", published in October 1960,^[5] a method of classification based on a similarity ratio, and a derived distance function, is given. It seems that this is the most authoritative source for the meaning of the terms "Tanimoto Similarity" and "Tanimoto Distance". The similarity ratio is equivalent to Jaccard similarity, but the distance function is not the same as Jaccard Distance.

Tanimoto's Definitions of Similarity and Distance

In that paper, a "similarity ratio" is given over bitmaps, where each bit of a fixed-size array represents the presence or absence of a characteristic in the plant being modelled. The definition of the ratio is the number of common bits, divided by the number of bits set in either sample.

Presented in mathematical terms, if samples X and Y are bitmaps, $X_{i}$ is the ith bit of X, and $\land, \lor$ are bitwise and, or operators respectively, then the similarity ratio $T_{s}$ is

$T_{s} (X, Y) = \frac{\sum_{i} (X_{i} \land Y_{i})}{\sum_{i} (X_{i} \lor Y_{i})}$

If each sample is modelled instead as a set of attributes, this value is equal to the Jaccard Coefficient of the two sets. Jaccard is not cited in the paper, and it seems likely that the authors were not aware of it.

Tanimoto goes on to define a distance coefficient based on this ratio, defined over values with non-zero similarity:

$T_{d} (X, Y) = - \log_{2} (T_{s} (X, Y))$

This coefficient is, deliberately, not a distance metric. It is chosen to allow the possibility of two specimens, which are quite different to each other, to both be similar to a third. It is easy to construct an example which disproves the property of triangle inequality.

Other Definitions of Tanimoto Distance

Tanimoto Distance is often referred to, erroneously, as a synonym for Jaccard Distance ( $1 - T_{s}$ ). This function is a proper distance metric. "Tanimoto Distance" is often stated as being a proper distance metric, probably because of its confusion with Jaccard Distance.

If Jaccard or Tanimoto Similarity is expressed over a bit vector, then it can be written as

$f (A, B) = \frac{A \cdot B}{{| A |}^{2} + {| B |}^{2} - A \cdot B}$

where the same calculation is expressed in terms of vector scalar product and magnitude. This representation relies on the fact that, for a bit vector (where the value of each dimension is either 0 or 1) then $A \cdot B = \sum_{i} A_{i} B_{i} = \sum_{i} (A_{i} \land B_{i})$ and ${| A |}^{2} = \sum_{i} A_{i}^{2} = \sum_{i} A_{i}$ .

This is a potentially confusing representation, because the function as expressed over vectors is more general, unless its domain is explicitly restricted. Properties of $T_{s}$ do not necessarily extend to $f$ . In particular, the difference function $(1 - f)$ does not preserve triangle inequality, and is not therefore a proper distance metric, whereas $(1 - T_{s})$ is.

There is a real danger that the combination of "Tanimoto Distance" being defined using this formula, along with the statement "Tanimoto Distance is a proper distance metric" will lead to the false conclusion that the function $(1 - f)$ is in fact a distance metric over vectors or multisets in general, whereas its use in similarity search or clustering algorithms may fail to produce correct results.

Lipkus^[1] uses a definition of Tanimoto similarity which is equivalent to $f$ , and refers to Tanimoto distance as the function $(1 - f)$ . It is however made clear within the paper that the context is restricted by the use of a (positive) weighting vector $W$ such that, for any vector A being considered, $A_{i} \in {0, W_{i}}$ . Under these circumstances, the function is a proper distance metric, and so a set of vectors governed by such a weighting vector forms a metric space under this function.

Notes

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

Template:More footnotes

References

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Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

External links

Introduction to Data Mining lecture notes from Tan, Steinbach, Kumar
SimMetrics a sourceforge implementation of Jaccard index and many other similarity metrics
Web based tool for comparing texts using Jaccard coefficient
Tutorial on how to calculate different similarities
Open Source Jaccard Scala implementation as part of the larger stringmetric project

↑ ^1.0 ^1.1 Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
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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

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

[lipkus-1] 1.0 ^1.1 Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

[2] Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

[3] For example 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

[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

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

[5] 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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-Of course plants include a variety of leafy greens, nuts, seeds, fruits, roots, and other wild vegetables. At this stage of the progression, we are deteriorating on all levels. Nuts help to lower cholesterol, reduce the risk of heart disease and are also credited with reducing the risk of some cancers like breast cancer. As such, this has over two additional cookbook recipes that consist of over 120 recipes each. Benefits of Paleo Diet - Contrary to what many critics say, the Paleo diet has many benefits that are too good to ignore. <br><br>A good rule of thumb when going to the supermarket is to shop around the edges of the building where all the fresh food is kept. Anyone that has been to the store lately can tell you that these items are not always cheap. The ingredients all put together are all very good for the body for keeping your body in line and healthy. Not only are there high nutritional values but they keep your cholesterol level at a healthy level. Fitness expert Ben Greenfield trained for the 2013 Ironman Triathlon World Championships in Kona, Hawaii by following a high-fat, low-carb ketogenic diet and completed the epic endurance race in an impressive 9:59:26. <br><br>The human body needs many things for energy, growth and longevity, and also to build an immune system that can fight off unwanted invasion. - Wash arugula, spinach and blackberries set aside to dry. Those that follow this program can expect a lot of red meat as well as fatty food. What is known: Since the end of the NBA Finals, James has lost more than 10 pounds. For example, changes in your activity level and sleep are highly encouraged in addition to dietary changes. <br><br>Still, he said that's better than his previously sedentary lifestyle of couch-surfing and boozing. Special Paleo packages will supply the necessary vitamins and minerals with no need to worry about cooking or getting the Paleo ingredients. If you're going to get one thing out of your diet, it should be dairy. "We can use this information to help manage and prevent obesity, through ensuring that the diets we eat have a sufficient level of protein to satisfy our appetite," said Raubenheimer, who led the study. Results from most diets take a great deal of time, but not with this plan. <br><br>Anything which does not fall into these four categories should be viewed with great skepticism and avoided entirely. Another good thing is that few people really eat a good variety of fresh fruit. FOS are extremely good at enhancing the performance of pro biotics in general. The occurrence of diabetes, for example, is almost unknown to aboriginal people even now who naturally follow this sort of diet. No wonder that anti obesity solutions form a billion dollar business worldwide. <br><br>At the distance of a click, we can find recipes from all over the world. Some important vitamins are A, B1 or thiamine, B3 or niacin, B6 or pyridoxine, B9 or folic acid, B12, vitamin C and D and finally vitamin K. Even though most of us are not going to be able to afford to switch to a diet that is loaded with the amount of fish we need, there are solutions available and the best on the market today is Omega Daily which provides all we need in a single capsule designed to be put to immediate use by our bodies. Exercising does more than just burn calories or build muscle. Some even documented which they were capable of do away with chronic health conditions.<br><br>In case you loved this article and you wish to receive much more information concerning [http://gritsandgroceries.info/ paleo dinner ideas] kindly visit the website.
+The '''Jaccard index''', also known as the '''Jaccard similarity coefficient''' (originally coined ''coefficient de communauté'' by [[Paul Jaccard]]), is a [[statistic]] used for comparing the [[Similarity measure|similarity]] and [[diversity index|diversity]] of [[Sample (statistics)|sample]] sets. The Jaccard coefficient measures similarity between finite sample sets, and is defined as the size of the [[intersection (set theory)|intersection]] divided by the size of the [[Union (set theory)|union]] of the sample sets:
+:<math> J(A,B) = {{|A \cap B|}\over{|A \cup B|}}.</math>
+(If ''A'' and ''B'' are both empty, we define ''J''(''A'',''B'')=1.) Clearly,
+:<math> 0\le J(A,B)\le 1.</math>
+The [[MinHash]] min-wise independent permutations [[locality sensitive hashing]] scheme may be used to efficiently compute an accurate estimate of the Jaccard similarity coefficient of pairs of sets, where each set is represented by a constant-sized signature derived from the minimum values of a [[hash function]].
+The '''Jaccard distance''', which measures ''dis''similarity between sample sets, is complementary to the Jaccard coefficient and is obtained by subtracting the Jaccard coefficient from 1, or, equivalently, by dividing the difference of the sizes of the union and the intersection of two sets by the size of the union:
+:<math> d_J(A,B) = 1 - J(A,B) = { { |A \cup B| - |A \cap B| } \over |A \cup B| }.</math>
+An alternate interpretation of the Jaccard distance is as the ratio of the size of the [[symmetric difference]] <math>A \triangle B = (A \cup B) - (A \cap B)</math> to the union.
+This distance is a proper [[Distance function|metric]] on sets of sets.<ref name="lipkus">{{citation |last=Lipkus |first=Alan H
+|title=A proof of the triangle inequality for the Tanimoto distance
+|journal=J Math Chem |volume=26 |number=1-3 |year=1999 |pages=263–265 }}</ref><ref>{{citation |last1=Levandowsky |first1=Michael |last2=Winter |first2=David |title=Distance between sets|journal=Nature |volume=234 |number=5 |year=1971 |pages=34–35 }}</ref>
+There is also a version of the Jaccard distance for [[measures]], including [[probability measure]]s. If <math>\mu</math> is a measure on a [[measurable space]] <math>X</math>, then we define the Jaccard coefficient by <math>J_\mu(A,B) = {{\mu(A \cap B)} \over {\mu(A \cup B)}}</math>, and the Jaccard distance by <math>d_\mu(A,B) = 1 - J_\mu(A,B) = {{\mu(A \triangle B)} \over {\mu(A \cup B)}}</math>. Care must be taken if <math>\mu(A \cup B) = 0</math> or <math>\infty</math>, since these formulas are not well defined in that case.
+== Similarity of asymmetric binary attributes ==
+Given two objects, ''A'' and ''B'', each with ''n'' [[binary numeral system|binary]] attributes, the Jaccard coefficient is a useful measure of the overlap that ''A'' and ''B'' share with their attributes.  Each attribute of ''A'' and ''B'' can either be 0 or 1.  The total number of each combination of attributes for both ''A'' and ''B'' are specified as follows:
+:<math>M_{11}</math> represents the total number of attributes where ''A'' and ''B'' both have a value of 1.
+:<math>M_{01}</math> represents the total number of attributes where the attribute of ''A'' is 0 and the attribute of ''B'' is 1.
+:<math>M_{10}</math> represents the total number of attributes where the attribute of ''A'' is 1 and the attribute of ''B'' is 0.
+:<math>M_{00}</math> represents the total number of attributes where ''A'' and ''B'' both have a value of 0.
+Each attribute must fall into one of these four categories, meaning that
+:<math>M_{11} + M_{01} + M_{10} + M_{00} = n.</math>
+The Jaccard similarity coefficient, ''J'', is given as
+:<math>J = {M_{11} \over M_{01} + M_{10} + M_{11}}.</math>
+The Jaccard distance, ''d''<sub>''J''</sub>, is given as
+:<math>d_J = {M_{01} + M_{10} \over M_{01} + M_{10} + M_{11}}.</math>
+== Tanimoto Similarity and Distance ==
+<!-- [[Tanimoto score]] redirects here, please change that redirect if you change this section title -->
+Various forms of functions described as  Tanimoto Similarity  and Tanimoto Distance occur  in the literature and on the Internet. Most of these are synonyms for Jaccard Similarity and Jaccard Distance, but some are mathematically different. Many sources<ref>For example {{cite book |first=Huihuan |last=Qian |first2=Xinyu |last2=Wu |first3=Yangsheng |last3=Xu |title=Intelligent Surveillance Systems |publisher=Springer |year=2011 |page=161 |isbn=978-94-007-1137-2 }}</ref> cite an  unavailable IBM Technical Report<ref>{{cite journal |last=Tanimoto |first=T. |title=An Elementary Mathematical theory of Classification and Prediction |journal=Internal IBM Technical Report |date=17 Nov 1957 |issue=8? |volume=1957 }}</ref> as the seminal reference.
+In "A Computer Program for Classifying Plants", published in October 1960,<ref>{{cite journal |first=David J. |last=Rogers |first2=Taffee T. |last2=Tanimoto |title=A Computer Program for Classifying Plants |journal=[[Science (journal)|Science]] |volume=132 |issue=3434 |pages=1115–1118 |year=1960 |doi=10.1126/science.132.3434.1115 }}</ref> a method of classification based on a similarity ratio, and a derived distance function, is given. It seems that this is  the most authoritative  source for the meaning of the terms "Tanimoto Similarity" and "Tanimoto Distance". The similarity ratio is equivalent to Jaccard similarity, but the distance function is ''not'' the same as Jaccard Distance.
+=== Tanimoto's Definitions of Similarity and Distance ===
+In that paper, a "similarity ratio" is  given over [[Bit array|bitmaps]], where each bit of a fixed-size array represents the presence or absence of a characteristic in the plant being modelled. The definition of the ratio is the number of common bits, divided by the number of bits set in either sample.
+Presented in mathematical terms, if samples ''X'' and ''Y'' are bitmaps, <math>X_i</math> is the ''i''th bit of ''X'', and <math> \land , \lor </math> are [[bitwise operation|bitwise]] ''[[logical conjunction|and]]'', ''[[logical disjunction|or]]'' operators respectively, then the similarity ratio <math>T_s</math> is
+<math> T_s(X,Y) =  \frac{\sum_i ( X_i \land Y_i)}{\sum_i ( X_i \lor Y_i)}</math>
+If each sample is modelled instead as a set of attributes, this value is  equal to the Jaccard Coefficient of the two sets. Jaccard is not cited in the paper, and it seems likely that the authors were not aware of it.
+Tanimoto goes on to define a distance coefficient based on this ratio, defined over values with non-zero similarity:
+<math>T_d(X,Y) = -{\log} _2 ( T_s(X,Y) ) </math>
+This coefficient is, deliberately, not a distance metric. It is chosen to allow the possibility of two specimens, which are quite different to each other, to both be similar to a third. It is  easy to construct an example which disproves the property of [[Triangle inequality#Metric space|triangle inequality]].
+=== Other Definitions of Tanimoto Distance ===
+Tanimoto Distance is often referred to, erroneously, as a synonym for Jaccard Distance (<math> 1 - T_s</math>). This function is a proper distance metric. "Tanimoto Distance" is often stated as being a proper distance metric, probably because of its confusion with Jaccard Distance.
+If Jaccard or Tanimoto Similarity is expressed over a bit vector, then it can be written as
+<math>
+f(A,B) =\frac{ A \cdot B}{{\vert A\vert}^2 +{ \vert B\vert}^2 -  A \cdot B }
+</math>
+where the same calculation is expressed in terms of vector scalar product and magnitude. This representation relies on the fact that, for a bit vector (where the value of each dimension is either 0 or 1) then <math>A \cdot B = \sum_i A_iB_i = \sum_i ( A_i \land B_i)</math> and <math>{\vert A\vert}^2 = \sum_i A_i^2 = \sum_i A_i </math>.
+This is a potentially confusing representation, because the function as expressed over vectors is more general, unless its domain is explicitly restricted. Properties of <math> T_s </math> do not necessarily extend to <math>f</math>. In particular, the difference function <math>( 1 - f)</math> does not preserve [[triangle inequality]], and is not therefore a proper distance metric, whereas <math>( 1 - T_s) </math> is.
+There is a real danger that the combination of "Tanimoto Distance" being defined using this formula, along with the statement "Tanimoto Distance is a proper distance metric" will lead to the false conclusion that the function <math>(1 - f)</math> is in fact a distance metric over vectors or multisets in general, whereas its use in similarity search or clustering algorithms may fail to produce correct results.
+Lipkus<ref name="lipkus" /> uses a definition of Tanimoto similarity which is equivalent to <math>f</math>, and refers to Tanimoto distance as the function <math> (1 - f) </math>. It is however made clear within the paper that the context is restricted by the use of a (positive) weighting vector <math>W</math> such that, for any vector ''A'' being considered, <math> A_i \in \{0,W_i\} </math>. Under these circumstances, the  function  is a proper distance metric, and so a set of vectors governed by such a weighting vector forms a metric space under this function.
+== See also ==
+* [[Sørensen similarity index]]
+* [[simple matching coefficient]]
+* [[Mountford's index of similarity]]
+* [[Hamming distance]]
+* [[Dice's coefficient]], which is equivalent: <math>J=D/(2-D)</math> and <math>D=2J/(1+J)</math>
+* [[Tversky index]]
+* [[Correlation]]
+* [[Mutual information]], a normalized [[Mutual information#Metric|metricated]] variant of which is an entropic Jaccard distance.
+==Notes==
+{{reflist}}
+{{More footnotes|date=March 2011}}
+== References ==
+*{{citation|first1=Pang-Ning|last1=Tan|first2=Michael|last2=Steinbach|first3=Vipin|last3=Kumar|title=Introduction to Data Mining|year=2005|isbn=0-321-32136-7}}.
+*{{citation|first=Paul|last=Jaccard|authorlink=Paul Jaccard|year=1901|title=Étude comparative de la distribution florale dans une portion des Alpes et des Jura|journal=Bulletin de la Société Vaudoise des Sciences Naturelles|volume=37|pages=547–579}}.
+*{{citation|first=Paul|last=Jaccard|authorlink=Paul Jaccard|year=1912|title=The distribution of the flora in the alpine zone|journal=New Phytologist|volume=11|pages=37–50}}.
+*{{citation|last=Tanimoto|first=Taffee T.|series=IBM Internal Report|date=November 17, 1957}}.
+== External links ==
+* [http://www-users.cs.umn.edu/~kumar/dmbook/dmslides/chap2_data.pdf Introduction to Data Mining lecture notes from Tan, Steinbach, Kumar]
+* [http://sourceforge.net/projects/simmetrics/ SimMetrics a sourceforge implementation of Jaccard index and many other similarity metrics]
+* [http://www.idea-miner.de/cgi-bin/INT_Tools/ver_vergleich_0_1/cmp_menu2.cgi Web based tool for comparing texts using Jaccard coefficient]
+* [http://www.gettingcirrius.com/2011/01/calculating-similarity-part-2-jaccard.html Tutorial on how to calculate different similarities]
+* Open Source [https://github.com/rockymadden/stringmetric/blob/master/core/src/main/scala/com/rockymadden/stringmetric/similarity/JaccardMetric.scala Jaccard] [[Scala programming language|Scala]] implementation as part of the larger [http://rockymadden.com/stringmetric/ stringmetric project]
+{{DEFAULTSORT:Jaccard Index}}
+[[Category:Index numbers]]
+[[Category:Measure theory]]
+[[Category:Clustering criteria]]
+[[Category:String similarity measures]]

Bulk density: Difference between revisions

Revision as of 23:24, 20 December 2013

Contents

Similarity of asymmetric binary attributes

Tanimoto Similarity and Distance

Tanimoto's Definitions of Similarity and Distance

Other Definitions of Tanimoto Distance

See also

Notes

References

External links

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Revision as of 23:24, 20 December 2013

Similarity of asymmetric binary attributes

Tanimoto Similarity and Distance

Tanimoto's Definitions of Similarity and Distance

Other Definitions of Tanimoto Distance

See also

Notes

References

External links

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