Biclustering

2012-10-19T12:01:38Z

Wikikoff: /* Algorithms */ typo fixed

{{Underlinked|date=June 2010}}

'''Biclustering''', '''co-clustering''', or '''two-[[mode (statistics)|mode]] clustering'''<ref>
{{cite journal
| author = Van Mechelen I, Bock HH, De Boeck P
| year = 2004
| title = Two-mode clustering methods:a structured overview
| journal = Statistical Methods in Medical Research
| volume = 13
| issue = 5
| pages = 363–94
| doi = 10.1191/0962280204sm373ra
| pmid = 15516031
}}
</ref> is a [[data mining]] technique which allows simultaneous [[cluster analysis|clustering]] of the rows and columns of a [[matrix (mathematics)|matrix]].
The term was first introduced by Mirkin<ref name="mirkin">
{{cite book
| last = Mirkin
| first = Boris
| title = Mathematical Classification and Clustering
| publisher = Kluwer Academic Publishers
| year = 1996
| isbn = 0-7923-4159-7 }}
</ref> (recently by Cheng and Church<ref>
{{cite journal
| author = Cheng Y, Church GM
| year = 2000
| title = Biclustering of expression data
| journal = Proceedings of the 8th International Conference on Intelligent Systems for Molecular Biology
| pages = 93–103
}}
</ref> in [[gene expression]] analysis), although the technique was originally introduced much earlier<ref name="mirkin"/> (i.e., by J.A. Hartigan<ref>
{{cite journal
| author = Hartigan JA
| year = 1972
| month =
| title = Direct clustering of a data matrix
| journal = Journal of the American Statistical Association
| volume = 67
| issue = 337
| pages = 123–9
| doi = 10.2307/2284710
| publisher = American Statistical Association
| jstor = 2284710
}}
</ref>).

Given a set of <math>m</math> rows in <math>n</math> columns (i.e., an <math>m \times n</math> matrix), the biclustering algorithm generates biclusters - a subset of rows which exhibit similar behavior across a subset of columns, or vice versa.

== Complexity ==

The complexity of the biclustering problem depends on the exact problem formulation, and particularly on the merit function used to evaluate the quality of a given bicluster. However most interesting variants of this problem are [[NP-complete]] requiring either large computational effort or the use of lossy heuristics to short-circuit the calculation.<ref name=madeira-oliveira />

== Type of Bicluster ==

Different biclustering algorithms have different definitions of bicluster.<ref name="madeira-oliveira">
{{cite journal
| author = Madeira SC, Oliveira AL
| year = 2004
| title = Biclustering Algorithms for Biological Data Analysis: A Survey
| journal = IEEE Transactions on Computational Biology and Bioinformatics
| volume = 1
| issue = 1
| pages = 24–45
| doi = 10.1109/TCBB.2004.2
| pmid = 17048406
}}
</ref>

They are:

#Bicluster with constant values (a),
#Bicluster with constant values on rows (b) or columns (c),
#Bicluster with coherent values (d, e).

{| border="0" cellspacing="20"
|
{| | border="1px solid black" cellpadding="5" cellspacing="0"
|+a) Bicluster with constant values
|-
| 2.0 || 2.0 || 2.0 || 2.0 || 2.0
|-
| 2.0 || 2.0 || 2.0 || 2.0 || 2.0
|-
| 2.0 || 2.0 || 2.0 || 2.0 || 2.0
|-
| 2.0 || 2.0 || 2.0 || 2.0 || 2.0
|-
| 2.0 || 2.0 || 2.0 || 2.0 || 2.0
|}
|
{| | border="1px solid black" cellpadding="5" cellspacing="0"
|+b) Bicluster with constant values on rows
|-
| 1.0 || 1.0 || 1.0 || 1.0 || 1.0
|-
| 2.0 || 2.0 || 2.0 || 2.0 || 2.0
|-
| 3.0 || 3.0 || 3.0 || 3.0 || 3.0
|-
| 4.0 || 4.0 || 4.0 || 4.0 || 4.0
|-
| 4.0 || 4.0 || 4.0 || 4.0 || 4.0
|}
|
{| | border="1px solid black" cellpadding="5" cellspacing="0"
|+c) Bicluster with constant values on columns
|-
| 1.0 || 2.0 || 3.0 || 4.0 || 5.0
|-
| 1.0 || 2.0 || 3.0 || 4.0 || 5.0
|-
| 1.0 || 2.0 || 3.0 || 4.0 || 5.0
|-
| 1.0 || 2.0 || 3.0 || 4.0 || 5.0
|-
| 1.0 || 2.0 || 3.0 || 4.0 || 5.0
|}
|}

{| border="0" cellspacing="20"
|
{| | border="1px solid black" cellpadding="5" cellspacing="0"
|+d) Bicluster with coherent values (additive)
|-
| 1.0 || 4.0 || 5.0 || 0.0 || 1.5
|-
| 4.0 || 7.0 || 8.0 || 3.0 || 4.5
|-
| 3.0 || 6.0 || 7.0 || 2.0 || 3.5
|-
| 5.0 || 8.0 || 9.0 || 4.0 || 5.5
|-
| 2.0 || 5.0 || 6.0 || 1.0 || 2.5
|}
|
{| | border="1px solid black" cellpadding="5" cellspacing="0"
|+e) Bicluster with coherent values (multiplicative)
|-
| 1.0 || 0.5 || 2.0 || 0.2 || 0.8
|-
| 2.0 || 1.0 || 4.0 || 0.4 || 1.6
|-
| 3.0 || 1.5 || 6.0 || 0.6 || 2.4
|-
| 4.0 || 2.0 || 8.0 || 0.8 || 3.2
|-
| 5.0 || 2.5 || 10.0 || 1.0 || 4.0
|}
|}



The relationship between these cluster models and other types of clustering such as [[correlation 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>

== Algorithms ==

There are many biclustering algorithms developed for [[bioinformatics]], including: block clustering, CTWC (Coupled Two-Way Clustering), ITWC (Interrelated Two-Way Clustering), δ-bicluster, δ-pCluster, δ-pattern, FLOC, OPC, Plaid Model, OPSMs (Order-preserving submatrixes), Gibbs, SAMBA (Statistical-Algorithmic Method for Bicluster Analysis),<ref>
{{cite journal
| author = Tanay A, Sharan R, Kupiec M and Shamir R
| year = 2004
| title = Revealing modularity and organization in the yeast molecular network by integrated analysis of highly heterogeneous genomewide data
| journal = Proc Natl Acad Sci USA
| volume = 101
| issue = 9
| pages = 2981–2986
| doi = 10.1073/pnas.0308661100
| pmid = 14973197
| pmc = 365731
}}</ref> Robust Biclustering Algorithm (RoBA), Crossing Minimization,<ref name=ahsan/> cMonkey,<ref>
{{cite journal
| author = Reiss DJ, Baliga NS, Bonneau R
| year = 2006
| title = Integrated biclustering of heterogeneous genome-wide datasets for the inference of global regulatory networks
| journal = BMC Bioinformatics
| volume = 2
| pages = 280–302
| doi = 10.1186/1471-2105-7-280
| pmid = 16749936
| pmc = 1502140
}}</ref> PRMs, DCC, LEB (Localize and Extract Biclusters), QUBIC (QUalitative BIClustering), BCCA (Bi-Correlation Clustering Algorithm) and FABIA (Factor Analysis for Bicluster Acquisition).<ref>
{{cite journal
| author = [[Sepp Hochreiter|Hochreiter S]], Bodenhofer U, Heusel M, Mayr A, Mitterecker A, Kasim A, Khamiakova T, Van Sanden S, Lin D, Talloen W, Bijnens L, Gohlmann HWH, Shkedy Z, Clevert DA
| year = 2010
| title = FABIA: factor analysis for bicluster acquisition
| journal = Bioinformatics
| pmid = 20418340
| volume = 26
| issue = 12
| pmc = 2881408
| pages = 1520–1527
| doi = 10.1093/bioinformatics/btq227
}}</ref> Biclustering algorithms have also been proposed and used in other application fields under the names coclustering, bidimensional clustering, and subspace clustering.<ref name=madeira-oliveira />

Given the known importance of discovering local patterns in time series data, recent proposals have addressed the biclustering problem in the specific case of time series gene expression data. In this case, the interesting biclusters can be restricted to those with contiguous columns. This restriction leads to a tractable problem and enables the development of efficient exhaustive enumeration algorithms such as CCC-Biclustering <ref name="ccc-biclustering">
{{cite journal
| author = Madeira SC, Teixeira MC, Sá-Correia I, Oliveira AL
| year = 2010
| title = Identification of Regulatory Modules in Time Series Gene Expression Data using a Linear Time Biclustering Algorithm
| journal = IEEE Transactions on Computational Biology and Bioinformatics
| volume = 1
| issue = 7
| pages = 153–165
| doi = 10.1109/TCBB.2008.34
}}
</ref> and ''e''-CCC-Biclustering.<ref name="e-ccc-biclustering">
{{cite journal
| author = Madeira SC, Oliveira AL
| year = 2009
| title = A polynomial time biclustering algorithm for finding approximate expression patterns in gene expression time series
| journal = Algorithms for Molecular Biology
| volume = 4
| issue = 8
}}
</ref> These algorithms ﬁnd and report all maximal biclusters with coherent and contiguous columns with perfect/approximate expression patterns, in time linear/polynomial in the size of the time series gene expression matrix using eﬃcient string
processing techniques based on suffix trees.

Some recent algorithms have attempted to include additional support for biclustering rectangular matrices in the form of other datatypes, including cMonkey.

There is an ongoing debate about how to judge the results of these methods, as biclustering allows overlap between clusters and some algorithms allow the exclusion of hard-to-reconcile columns/conditions. Not all of the available algorithms are deterministic and the analyst must pay attention to the degree to which results represent stable minima. Because this is an unsupervised-classification problem, the lack of a gold standard makes it difficult to spot errors in the results. One approach is to utilize multiple biclustering algorithms, with majority or super-majority voting amongst them deciding the best result. Another way is to analyse the quality of shifting and scaling patterns in biclusters.<ref>
{{cite journal
| author = Aguilar-Ruiz JS
| year = 2005
| title = Shifting and scaling patterns from gene expression data
| journal = Bioinformatics
| volume = 21
| issue = 10
| pages = 3840–3845
| doi = 10.1093/bioinformatics/bti641
| pmid = 16144809
}}
</ref> Biclustering has been used in the domain of text mining (or classification) where it is popularly known as co-clustering
.<ref name="chi-sim">{{cite journal
| author = Bission G. and Hussain F.
| year = 2008
| title = Chi-Sim: A new similarity measure for the co-clustering task
| journal = ICMLA
| pages = 211–217
| doi = 10.1109/ICMLA.2008.103

}}
</ref> Text corpora are represented in a vectorial form as a matrix D whose rows denote the documents and whose columns denote the words in the dictionary. Matrix elements Dij denote occurrence of word j in document i. Co-clustering algorithms are then applied to discover blocks in D that correspond to a group of documents (rows) characterized by a group of words(columns).

Several approaches have been proposed based on the information contents of the resulting blocks: matrix-based approaches such as SVD and BVD, and graph-based approaches. Information-theoretic algorithms iteratively assign each row to a cluster of documents and each column to a cluster of words such that the mutual information is maximized. Matrix-based methods focus on the decomposition of matrices into blocks such that the error between the original matrix and the regenerated matrices from the decomposition is minimized. Graph-based methods tend to minimize the cuts between the clusters. Given two groups of documents d1 and d2, the number of cuts can be measured as the number of words that occur in documents of groups d1 and d2.

More recently (Bisson and Hussain)<ref name="chi-sim"/> have proposed a new approach of using the similarity between words and the similarity between documents to co-cluster the matrix. Their method (known as '''χ-Sim''', for cross similarity) is based on finding document-document similarity and word-word similarity, and then using classical clustering methods such as hierarchical clustering. Instead of explicitly clustering rows and columns alternately, they consider higher-order occurrences of words, inherently taking into account the documents in which they occur. Thus, the similarity between two words is calculated based on the documents in which they occur and also the documents in which "similar" words occur. The idea here is that two documents about the same topic do not necessarily use the same set of words to describe it but a subset of the words and other similar words that are characteristic of that topic. This approach of taking higher-order similarities takes the latent semantic structure of the whole corpus into consideration with the result of generating a better clustering of the documents and words.

In contrast to other approaches, FABIA is a multiplicative model that assumes realistic non-Gaussian signal distributions with [[heavy tails]]. FABIA utilizes well understood model selection techniques like variational approaches and applies the Bayesian framework. The generative framework allows FABIA to determine the [[information content]] of each bicluster to separate spurious biclusters from true biclusters.

== See also ==
* [[Formal concept analysis]]
* [[Biclique]]
* [[Galois connection]]

== References ==
{{Reflist|refs=
<ref name=ahsan>
{{cite journal
|last1=Abdullah
|first1=Ahsan
|last2=Hussain
|first2=Amir
|title=A new biclustering technique based on crossing minimization
|journal=Neurocomputing, vol. 69 issue 16-18
|year=2006
|pages=1882–1896
|url= http://linkinghub.elsevier.com/retrieve/pii/S0925231206001615
|doi=10.1016/j.neucom.2006.02.018
|volume=69
|issue=16–18
}}
</ref>
}}

=== Others ===
<div class="references-small">
* A. Tanay. R. Sharan, and R. Shamir, "Biclustering Algorithms: A Survey", In ''Handbook of Computational Molecular Biology'', Edited by Srinivas Aluru, Chapman (2004)
* {{cite journal | author = Kluger Y, Basri R, Chang JT, Gerstein MB | year = 2003 | title = Spectral Biclustering of Microarray Data: Coclustering Genes and Conditions | url = | journal = Genome Research | volume = 13 | issue = 4| pages = 703–716 | doi = 10.1101/gr.648603 | pmid = 12671006 | pmc = 430175 }}

=== External links ===
* [http://www.bioinf.jku.at/software/fabia/fabia.html FABIA: Factor Analysis for Bicluster Acquisition, an R package] —software

[[Category:Cluster analysis]]
[[Category:Bioinformatics]]

[[fr:Classification double]]

Irene Brickner

2011-09-12T12:23:39Z

Wikikoff:

'''Irene Brickner''' (* [[25. Juni]] [[1960]]) ist eine österreichische [[Journalist]]in und Autorin.

Irene Brickner arbeitete unter anderen bei der Tageszeitung [[Neue AZ]], bei den [[Niederösterreichische Nachrichten|NÖN]] und beim [[ORF]]. Für [[Profil (Zeitschrift)|profil]] und [[Falter (Zeitung)|Falter]] war sie als freie Mitarbeiterin tätig. Seit 2000 arbeitet die Politikwissenschaftlerin beim [[Der Standard|Standard]] im Chronik-Ressort.

Bekannt ist Brickner wegen ihrer Berichterstattung über Menschenrechtsthemen und ihre Reportagen über Asyl- und Fremdenrechtsfragen, über Gleichstellungspolitik, aber auch über Umweltthemen.

Brickner wurde im Jahr 2004 mit dem [[Concordia-Preis]], Kategorie Menschenrechte, 2005 mit dem Klimaschutzpreis in der Kategorie Journalismus, 2006 mit dem Journalistinnenpreis "Spitze Feder", 2007 mit dem [[Leopold Ungar|Prälat-Leopold-Ungar]]-JournalistInnenpreis und 2010 mit dem Sonderpreis JournalistInnen des MiA-Awards (Auszeichnung für besondere Leistungen von in Österreich lebenden Frauen mit Migrationshintergrund) für ihre kritische Berichterstattung über die Härten des Fremdenrechts ausgezeichnet. 2010 bekam sie für ihren Blog auf derStandard.at (Brickners Blog) vom Österreichischen Journalisten Club [[ÖJC]] den [[Dr.-Karl-Renner-Publizistikpreis]] in der Kategorie Online verliehen. Ihre Meinung gilt nicht zuletzt bei ihren Lesern als sehr umstritten. Eine noch laufende online-Umfrage ergab, dass sich über 80% der Blog Leser einen Blog mit anderer Autorin wünschen.<ref>Meinungsumfrage auf derstandard.at zur Beliebtheit Brickner's Blog. Stand 11.9. 2011: von 72 Teilnehmenden, 63 für eine neue Autorin[http://derstandard.at/plink/1304553659657?sap=2&_pid=21502841#pid21502841]</ref>

Im Jahr 2007 veröffentlichte sie gemeinsam mit der Standard-Redakteurin Johanna Ruzicka im österreichischen Residenz-Verlag das Buch "Heiße Zeiten - 50 Antworten auf brennende Fragen zum Klimawandel".

== Einzelnachweise ==

<references />

== Weblinks ==

* {{DNB-Portal|133438309}}

{{Normdaten|PND=133438309|VIAF=8575578}}

{{SORTIERUNG:Brickner, Irene}}
[[Kategorie:Österreichischer Journalist]]
[[Kategorie:Geboren 1960]]
[[Kategorie:Frau]]

{{Personendaten
|NAME=Brickner, Irene
|ALTERNATIVNAMEN=
|KURZBESCHREIBUNG=österreichische Journalistin
|GEBURTSDATUM=25. Juni 1960
|GEBURTSORT=
|STERBEDATUM=
|STERBEORT=
}}

Wikipedia - Benutzerbeiträge [de]

Biclustering

Irene Brickner