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In [[data mining]], '''cluster-weighted modeling (CWM)''' is an algorithm-based approach to non-linear prediction of outputs ([[Dependent and independent variables|dependent variables]]) from inputs ([[Dependent and independent variables|independent variables]]) based on [[density estimation]] using a set of models (clusters) that are each notionally appropriate in a sub-region of the input space. The overall approach works in jointly input-output space and an initial version was proposed by [[Neil Gershenfeld]].<ref>Gershenfeld, N. (1997) "Nonlinear Inference and Cluster-Weighted Modeling", ''Annals of the New York Academy of Sciences'', 808, 18–24. {{DOI|10.1111/j.1749-6632.1997.tb51651.x}}</ref><ref name=nature>Gershenfeld, N., Schoner, B.* & Metois, E. (1999) [http://www.nature.com/nature/journal/v397/n6717/pdf/397329a0.pdf Cluster-weighted modelling for time-series analysis], Nature, 397 (28 Jan. 1999), 329–332 </ref> | |||
==Basic form of model== | |||
The procedure for cluster-weighted modeling of an input-output problem can be outlined as follows.<ref name=nature/> In order to construct predicted values for an output variable ''y'' from an input variable ''x'', the modeling and calibration procedure arrives at a [[joint probability distribution|joint probability density function]], ''p''(''y'',''x''). Here the "variables" might be uni-variate, multivariate or time-series. For convenience, any model parameters are not indicated in the notation here and several different treatments of these are possible, including setting them to fixed values as a step in the calibration or treating them using a [[Bayesian analysis]]. The required predicted values are obtained by constructing the [[conditional probability distribution|conditional probability density]] ''p''(''y''|''x'') from which the prediction using the [[conditional expected value]] can be obtained, with the [[conditional variance]] providing an indication of uncertainty. | |||
The important step of the modeling is that ''p''(''y''|''x'') is assumed to take the following form, as a [[mixture model]]: | |||
:<math>p(y,x)=\sum_1^n w_jp_j(y,x), </math> | |||
where ''n'' is the number of clusters and {''w<sub>j</sub>''} are weights that sum to one. The functions ''p<sub>j</sub>''(''y'',''x'') are joint probability density functions that relate to each of the ''n'' clusters. These functions are modeled using a decomposition into a conditional and a [[marginal distribution|marginal density]]: | |||
:<math>p_j(y,x)=p_j(y|x)p_j(x), </math> | |||
where: | |||
:*''p<sub>j</sub>''(''y''|''x'') is a model for predicting ''y'' given ''x'', and given that the input-output pair should be associated with cluster ''j'' on the basis of the value of ''x''. This model might be a [[regression analysis|regression model]] in the simplest cases. | |||
:*''p<sub>j</sub>''(''x'') is formally a density for values of ''x'', given that the input-output pair should be associated with cluster ''j''. The relative sizes of these functions between the clusters determines whether a particular value of ''x'' is associated with any given cluster-center. This density might be a [[Gaussian function]] centered at a parameter representing the cluster-center. | |||
In the same way as for [[regression analysis]], it will be important to consider preliminary [[data transformation]]s as part of the overall modeling strategy if the core components of the model are to be simple regression models for the cluster-wise condition densities, and [[normal distribution]]s for the cluster-weighting densities ''p<sub>j</sub>''(''x''). | |||
==General versions== | |||
The basic CWM algorithm gives a single output cluster for each input cluster. However, CWM can be extended to multiple clusters which are still associated with the same input cluster.<ref name="feldkamp">{{cite journal|last=Feldkamp|first=L.A.|coauthors=Prokhorov, D.V.; Feldkamp, T.M.|date=2001|title=Cluster-weighted modeling with multiclusters|journal=International Joint Conference on Neural Networks|volume=3|issue=1|pages=1710–1714|url=http://ieeexplore.ieee.org/Xplore/login.jsp?url=/iel5/7474/20319/00938419.pdf?temp=x}}</ref> Each cluster in CWM is localized to a Gaussian input region, and this contains its own trainable local model.<ref name="mit">{{cite journal|last=Boyden|first=Edward S.|title=Tree-based Cluster Weighted Modeling: Towards A Massively Parallel Real-Time Digital Stradivarius|publisher=MIT Media Lab|location=Cambridge, MA|url=http://edboyden.org/violin.pdf}}</ref> It is recognized as a versatile inference algorithm which provides simplicity, generality, and flexibility; even when a feedforward layered network might be preferred, it is sometimes used as a "second opinion" on the nature of the training problem.<ref name="dearborn"/> | |||
The original form proposed by Gershenfeld describes two innovations: | |||
* Enabling CWM to work with continuous streams of data | |||
* Addressing the problem of local minima encountered by the CWM parameter adjustment process<ref name="dearborn">{{cite journal|last=Prokhorov|first=A New Approach to Cluster-Weighted Modeling Danil V.|coauthors=Lee A. Feldkamp, and Timothy M. Feldkamp|title=A New Approach to Cluster-Weighted Modeling|publisher=Ford Research Laboratory|location=Dearborn, MI|url=http://home.comcast.net/~dvp/cwm.pdf}}</ref> | |||
CWM can be used to classify media in printer applications, using at least two parameters to generate an output that has a joint dependency on the input parameters.<ref name="media">{{cite journal|last=Gao|first=Jun|coauthors=Ross R. Allen|date=2003-07-24|title=CLUSTER-WEIGHTED MODELING FOR MEDIA CLASSIFICATION|publisher=World Intellectual Property Organization|location=Palo Alto, CA |url=http://www.wipo.int/pctdb/en/wo.jsp?wo=2003059630}}</ref> | |||
==References== | |||
{{Reflist}} | |||
[[Category:Multivariate statistics]] | |||
[[Category:Data clustering algorithms]] | |||
[[Category:Estimation of densities]] | |||
Revision as of 00:54, 12 November 2013
In data mining, cluster-weighted modeling (CWM) is an algorithm-based approach to non-linear prediction of outputs (dependent variables) from inputs (independent variables) based on density estimation using a set of models (clusters) that are each notionally appropriate in a sub-region of the input space. The overall approach works in jointly input-output space and an initial version was proposed by Neil Gershenfeld.[1][2]
Basic form of model
The procedure for cluster-weighted modeling of an input-output problem can be outlined as follows.[2] In order to construct predicted values for an output variable y from an input variable x, the modeling and calibration procedure arrives at a joint probability density function, p(y,x). Here the "variables" might be uni-variate, multivariate or time-series. For convenience, any model parameters are not indicated in the notation here and several different treatments of these are possible, including setting them to fixed values as a step in the calibration or treating them using a Bayesian analysis. The required predicted values are obtained by constructing the conditional probability density p(y|x) from which the prediction using the conditional expected value can be obtained, with the conditional variance providing an indication of uncertainty.
The important step of the modeling is that p(y|x) is assumed to take the following form, as a mixture model:
where n is the number of clusters and {wj} are weights that sum to one. The functions pj(y,x) are joint probability density functions that relate to each of the n clusters. These functions are modeled using a decomposition into a conditional and a marginal density:
where:
- pj(y|x) is a model for predicting y given x, and given that the input-output pair should be associated with cluster j on the basis of the value of x. This model might be a regression model in the simplest cases.
- pj(x) is formally a density for values of x, given that the input-output pair should be associated with cluster j. The relative sizes of these functions between the clusters determines whether a particular value of x is associated with any given cluster-center. This density might be a Gaussian function centered at a parameter representing the cluster-center.
In the same way as for regression analysis, it will be important to consider preliminary data transformations as part of the overall modeling strategy if the core components of the model are to be simple regression models for the cluster-wise condition densities, and normal distributions for the cluster-weighting densities pj(x).
General versions
The basic CWM algorithm gives a single output cluster for each input cluster. However, CWM can be extended to multiple clusters which are still associated with the same input cluster.[3] Each cluster in CWM is localized to a Gaussian input region, and this contains its own trainable local model.[4] It is recognized as a versatile inference algorithm which provides simplicity, generality, and flexibility; even when a feedforward layered network might be preferred, it is sometimes used as a "second opinion" on the nature of the training problem.[5]
The original form proposed by Gershenfeld describes two innovations:
- Enabling CWM to work with continuous streams of data
- Addressing the problem of local minima encountered by the CWM parameter adjustment process[5]
CWM can be used to classify media in printer applications, using at least two parameters to generate an output that has a joint dependency on the input parameters.[6]
References
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.
- ↑ Gershenfeld, N. (1997) "Nonlinear Inference and Cluster-Weighted Modeling", Annals of the New York Academy of Sciences, 808, 18–24. Electronic Instrument Positions Staff (Standard ) Cameron from Clarence Creek, usually spends time with hobbies and interests which include knotting, property developers in singapore apartment For sale and boomerangs. Has enrolled in a world contiki journey. Is extremely thrilled specifically about visiting .
- ↑ 2.0 2.1 Gershenfeld, N., Schoner, B.* & Metois, E. (1999) Cluster-weighted modelling for time-series analysis, Nature, 397 (28 Jan. 1999), 329–332
- ↑ 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 - ↑ 5.0 5.1 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 - ↑ 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