Halting problem: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
→Representation as a set: adjusted definition of set to be more succinct, definition taken from University of Oxford lecture notes: https://www.cs.ox.ac.uk/files/5999/MOC8.pdf
en>Yobot
m WP:CHECKWIKI error fixes using AWB (10616)
 
(One intermediate revision by one other user not shown)
Line 1: Line 1:
Clustering is the problem of partioning data points into groups based on their similarity.  '''Correlation clustering''' provides a method for clustering a set of objects into the optimum number of clusters without specifying that number in advance.<ref>[http://www.cs.columbia.edu/~hila/clustering.pdf Becker, Hila, "A Survey of Correlation Clustering", 5 May 2005]</ref>
It depends on the quality of the Wordpress theme but even if it's not a professional one you will be able to average 50-60$ EACH link. What I advise you do next is save the backup data file to a remote place like a CD-ROM, external disk drive if you have one or a provider such as Dropbox. The effect is to promote older posts by moving them back onto the front page and into the rss feed. s and intelligently including a substantial amount of key words in the title tags, image links, etc. If you are happy with your new look then click "Activate 'New Theme'" in the top right corner. <br><br>Most Word - Press web developers can provide quality CMS website solutions and they price their services at reasonable rates. WPTouch is among the more well known Word - Press smartphone plugins which is currently in use by thousands of users. This plugin allows a blogger get more Facebook fans on the related fan page. Apart from these, you are also required to give some backlinks on other sites as well. But in case you want some theme or plugin in sync with your business needs, it is advisable that you must seek some professional help. <br><br>This gives a clearer picture that online shoppers are familiar with the WP ecommerce system. By using Word - Press MLM websites or blogs, you and your companies presence on the internet can be created swiftly and simply. For a much deeper understanding of simple wordpress themes", check out Upon browsing such, you'll be able to know valuable facts. Every single Theme might be unique, providing several alternatives for webpage owners to reap the benefits of in an effort to instantaneously adjust their web page appear. " Thus working with a Word - Press powered web application, making any changes in the website design or website content is really easy and self explanatory. <br><br>If you have any kind of concerns regarding where and how you can make use of [http://roaaad.com/link//wordpress_backup_2592602 backup plugin], you can call us at the internet site. Additionally Word - Press add a default theme named Twenty Fourteen. In case you need to hire PHP developers or hire Offshore Code - Igniter development services or you are looking for Word - Press development experts then Mindfire Solutions would be the right choice for a Software Development partner. The templates are designed to be stand alone pages that have a different look and feel from the rest of your website. The company gains commission from the customers' payment. This includes enriching the content with proper key words, tactfully defining the tags and URL. <br><br>This advice is critical because you don't want to waste too expensive time establishing your Word - Press blog the exact method. Here's a list of some exciting Word - Press features that have created waves in the web development industry:. It can be concluded that white label SEO comprise of a third party who resells a contract involving IT expert or consultant, SEO professional and end user. Word - Press is the most popular personal publishing platform which was launched in 2003. However, if you're just starting out your blog site or business site, you can still search for an ideal theme for it without breaking your bank account.
 
==Description of the problem==
In [[machine learning]], '''correlation clustering''' or '''cluster editing''' operates in a scenario where the relationship between the objects are known instead of the actual representation of the objects. For example, given a [[signed graph]] <math>G=(V,E)</math> where the edge label indicates whether two nodes are similar (+) or different (&minus;), the task is to cluster the vertices so that similar objects are grouped together. Unlike other clustering algorithms this does not require [[Determining the number of clusters in a data set|choosing the number of clusters]] <math>k</math> in advance because the objective, to minimize the disagreements, is independent of the number of clusters.
 
It may not be possible to find a perfect clustering, where all similar items are in a cluster while all dissimilar ones are in different clusters. If the graph indeed admits a perfect clustering, then simply deleting all the negative edges and finding the connected components in the remaining graph will return the required clusters.
 
But, in general a graph may not have a perfect clustering. For example, given nodes ''a,b,c'' such that ''a,b'' and ''a,c'' are similar while ''b,c'' are dissimilar, a perfect clustering is not possible. In such cases, the task is to find a clustering that maximizes the number of agreements (number of + edges inside clusters plus the number of - edges between clusters) or minimizes the number of disagreements (the number of - edges inside clusters plus the number of + edges between clusters). This problem of maximizing the agreements is NP-complete (multiway cut problem reduces to maximizing weighted agreements and the problem of partitioning into triangles<ref>{{Cite conference
| author=Garey, M. and Johnson, D (W.H. Freeman and Company).
| title=Computers and Intractability: A Guide to the Theory of NP-Completeness
| year=2000
}}</ref> can be reduced to the unweighted version)
 
==Algorithms==
Bansal et al.<ref>{{Cite conference
| title=Correlation Clustering
| author=Bansal, N., Blum, A. and Chawla, S.
  | booktitle=Machine Learning Journal (Special Issue on Theoretical Advances in Data Clustering)
| pages=86–113,
| year=2004
| doi=10.1023/B:MACH.0000033116.57574.95
}}</ref> discuss the NP-completeness proof and also present both a constant factor approximation algorithm and [[polynomial-time approximation scheme]] to find the clusters in this setting. Ailon et al.<ref>{{Cite conference
| title=Aggregating inconsistent information: ranking and clustering
| author=Ailon, Nir  and Charikar, Moses  and Newman, Alantha
| booktitle=STOC '05: Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
| pages=684–693,
| year=2005
| doi=10.1145/1060590.1060692
}}</ref> propose a randomized 3-[[approximation algorithm]] for the same problem.
 
<code>
CC-Pivot(G=(V,E<sup>+</sup>,E<sup>-</sup>))
    Pick random pivot i &isin; V
    Set <math>C=\{i\}</math>, V'=&Oslash;
    For all j &isin; V, j &ne; i;
        If (i,j) &isin; E<sup>+</sup> then
            Add j to C
        Else (If (i,j) &isin; E<sup>-</sup>)
            Add j to V'
    Let G' be the subgraph induced by V'
    Return clustering C,CC-Pivot(G')
</code>
 
The authors show that the above algorithm is a 3-[[approximation algorithm]] for correlation clustering.
 
==Optimal number of clusters==
In 2011, it was shown by Bagon and Galun<ref>Bagon, S.; Galun, M. (2011) [http://arxiv.org/pdf/1112.2903v1.pdf "Large Scale Correlation Clustering Optimization"  {{arXiv|1112.2903v1}}]</ref>
that the optimization of the correlation clustering functional is closely related to well known discrete optimization methods.
In their work they proposed a probabilistic analysis of the underlying implicit model that allows the correlation clustering functional to estimate the underlying number of clusters.
This analysis suggests the functional assumes a uniform prior over all possible partitions regardless of their number of clusters.
Thus, a non-uniform prior over the number of clusters emerges.
 
Several discrete optimization algorithms are proposed in this work that scales gracefully with the number of elements (experiments show results with more than 100,000 variables).
The work of Bagon and Galun also evaluated the effectiveness of the recovery of the underlying number of clusters in several applications.
 
==Correlation clustering (data mining)==
 
'''Correlation clustering''' also relates to a different task, where [[correlation]]s among attributes of [[feature vector]]s in a [[high-dimensional space]] are assumed to exist guiding the [[cluster analysis|clustering process]]. These correlations may be different in different clusters, thus a global [[decorrelation]] cannot reduce this to traditional (uncorrelated) clustering.
 
Correlations among subsets of attributes result in different spatial shapes of clusters. Hence, the similarity between cluster objects is defined by taking into account the local correlation patterns. With this notion, the term has been introduced in <ref>{{Cite conference
| title=Computing Clusters of Correlation Connected Objects
| author=Böhm, C., Kailing, K., Kröger, P., Zimek, A.
| booktitle=Proc. ACM SIGMOD International Conference on Management of Data (SIGMOD'04), Paris, France
| pages=455–467
| year=2004
| url=http://doi.acm.org/10.1145/1007568.1007620
| doi=10.1145/1007568.1007620
}}
</ref> simultaneously with the notion discussed above.
Different methods for correlation clustering of this type are discussed in,<ref>{{Cite journal
| title=Correlation Clustering
| author=Zimek, A.
| year=2008
| url=http://edoc.ub.uni-muenchen.de/8736/
}}</ref> the relationship to different types of clustering is discussed in,<ref>{{cite journal
  | last = Kriegel
  | first = H.-P.
  | coauthors = Kröger, P., Zimek, A.
  | title = Clustering High Dimensional Data: A Survey on Subspace Clustering, Pattern-based Clustering, and Correlation Clustering
  | journal = ACM Transactions on Knowledge Discovery from Data (TKDD)
  | volume = 3
  | issue = 1
  | pages = 1–58
  | date = March 2009
  | url = http://doi.acm.org/10.1145/1497577.1497578
  | doi = 10.1145/1497577.1497578}}
</ref> see also [[Clustering high-dimensional data]].
 
Correlation clustering (according to this definition) can be shown to be closely related to [[biclustering]]. As in biclustering, the goal is to identify groups of objects that share a correlation in some of their attributes; where the correlation is usually typical for the individual clusters.
 
==References==
{{Reflist}}
 
[[Category:Cluster analysis]]
[[Category:Computational problems in graph theory]]

Latest revision as of 10:48, 1 January 2015

It depends on the quality of the Wordpress theme but even if it's not a professional one you will be able to average 50-60$ EACH link. What I advise you do next is save the backup data file to a remote place like a CD-ROM, external disk drive if you have one or a provider such as Dropbox. The effect is to promote older posts by moving them back onto the front page and into the rss feed. s and intelligently including a substantial amount of key words in the title tags, image links, etc. If you are happy with your new look then click "Activate 'New Theme'" in the top right corner.

Most Word - Press web developers can provide quality CMS website solutions and they price their services at reasonable rates. WPTouch is among the more well known Word - Press smartphone plugins which is currently in use by thousands of users. This plugin allows a blogger get more Facebook fans on the related fan page. Apart from these, you are also required to give some backlinks on other sites as well. But in case you want some theme or plugin in sync with your business needs, it is advisable that you must seek some professional help.

This gives a clearer picture that online shoppers are familiar with the WP ecommerce system. By using Word - Press MLM websites or blogs, you and your companies presence on the internet can be created swiftly and simply. For a much deeper understanding of simple wordpress themes", check out Upon browsing such, you'll be able to know valuable facts. Every single Theme might be unique, providing several alternatives for webpage owners to reap the benefits of in an effort to instantaneously adjust their web page appear. " Thus working with a Word - Press powered web application, making any changes in the website design or website content is really easy and self explanatory.

If you have any kind of concerns regarding where and how you can make use of backup plugin, you can call us at the internet site. Additionally Word - Press add a default theme named Twenty Fourteen. In case you need to hire PHP developers or hire Offshore Code - Igniter development services or you are looking for Word - Press development experts then Mindfire Solutions would be the right choice for a Software Development partner. The templates are designed to be stand alone pages that have a different look and feel from the rest of your website. The company gains commission from the customers' payment. This includes enriching the content with proper key words, tactfully defining the tags and URL.

This advice is critical because you don't want to waste too expensive time establishing your Word - Press blog the exact method. Here's a list of some exciting Word - Press features that have created waves in the web development industry:. It can be concluded that white label SEO comprise of a third party who resells a contract involving IT expert or consultant, SEO professional and end user. Word - Press is the most popular personal publishing platform which was launched in 2003. However, if you're just starting out your blog site or business site, you can still search for an ideal theme for it without breaking your bank account.

Retrieved from "https://en.formulasearchengine.com/index.php?title=Halting_problem&oldid=263385"