928:
feature words in the text, will eventually cluster the feature words. This is called co-clustering. There are two advantages of co-clustering: one is clustering the test based on words clusters can extremely decrease the dimension of clustering, it can also appropriate to measure the distance between the tests. Second is mining more useful information and can get the corresponding information in test clusters and words clusters. This corresponding information can be used to describe the type of texts and words, at the same time, the result of words clustering can be also used to text mining and information retrieval.
975:. 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
816:, 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), Robust Biclustering Algorithm (RoBA), Crossing Minimization, cMonkey, PRMs, DCC, LEB (Localize and Extract Biclusters), QUBIC (QUalitative BIClustering), BCCA (Bi-Correlation Clustering Algorithm) BIMAX, ISA and FABIA (
851:-CCC-Biclustering. The approximate patterns in CCC-Biclustering algorithms allow a given number of errors, per gene, relatively to an expression profile representing the expression pattern in the Bicluster. The e-CCC-Biclustering algorithm uses approximate expressions to find and report all maximal CCC-Bicluster's by a discretized matrix A and efficient string processing techniques.
183:(KL-distance) between P and Q. P represents the distribution of files and feature words before Biclustering, while Q is the distribution after Biclustering. KL-distance is for measuring the difference between two random distributions. KL = 0 when the two distributions are the same and KL increases as the difference increases. Thus, the aim of the algorithm was to find the minimum
943:
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
306:
For
Biclusters with coherent values on rows and columns, an overall improvement over the algorithms for Biclusters with constant values on rows or on columns should be considered. This algorithm may contain analysis of variance between groups, using co-variance between both rows and columns. In Cheng
982:
In text databases, for a document collection defined by a document by term D matrix (of size m by n, m: number of documents, n: number of terms) the cover-coefficient based clustering methodology yields the same number of clusters both for documents and terms (words) using a double-stage probability
927:
Text clustering can solve the high-dimensional sparse problem, which means clustering text and words at the same time. When clustering text, we need to think about not only the words information, but also the information of words clusters that was composed by words. Then, according to similarity of
820:
for
Bicluster Acquisition), runibic, and recently proposed hybrid method EBIC (evolutionary-based Biclustering), which was shown to detect multiple patterns with very high accuracy. More recently, IMMD-CC is proposed that is developed based on the iterative complexity reduction concept. IMMD-CC is
297:
Unlike the constant-value
Biclusters, these types of Biclusters cannot be evaluated solely based on the variance of their values. To finish the identification, the columns and the rows should be normalized first. There are, however, other algorithms, without the normalization step, that can find
280:
is used to compute constant
Biclusters. Hence, a perfect Bicluster may be equivalently defined as a matrix with a variance of zero. In order to prevent the partitioning of the data matrix into Biclusters with the only one row and one column; Hartigan assumes that there are, for example,
247:
When a
Biclustering algorithm tries to find a constant-value Bicluster, it reorders the rows and columns of the matrix to group together similar rows and columns, eventually grouping Biclusters with similar values. This method is sufficient when the data is normalized. A
226:. The maximum size Bicluster is equivalent to the maximum edge biclique in the bipartite graph. In the complex case, the element in matrix A is used to compute the quality of a given Bicluster and solve the more restricted version of the problem. It requires either large
202:
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, the most interesting variants of this problem are
174:
In 2001 and 2003, I. S. Dhillon published two algorithms applying biclustering to files and words. One version was based on bipartite spectral graph partitioning. The other was based on information theory. Dhillon assumed the loss of
2218:
N.K. Verma, S. Bajpai, A. Singh, A. Nagrare, S. Meena, Yan Cui, "A Comparison of
Biclustering Algorithms" in International conference on Systems in Medicine and Biology (ICSMB 2010)in IIT Kharagpur India, pp. 90–97, Dec.
2222:
J. Gupta, S. Singh and N.K. Verma "MTBA: MATLAB Toolbox for
Biclustering Analysis", IEEE Workshop on Computational Intelligence: Theories, Applications and Future Directions", IIT Kanpur India, pp. 148–152, Jul.
888:
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
2280:
Adetayo Kasim, Ziv Shkedy, Sebastian Kaiser, Sepp
Hochreiter, Willem Talloen (2016), Applied Biclustering Methods for Big and High-Dimensional Data Using R, Chapman & Hall/CRC Press
307:
and Church's theorem, a
Bicluster is defined as a subset of rows and columns with almost the same score. The similarity score is used to measure the coherence of rows and columns.
1984:
Madeira SC, Teixeira MC, Sá-Correia I, Oliveira AL (2010). "Identification of Regulatory Modules in Time Series Gene Expression Data using a Linear Time Biclustering Algorithm".
904:
voting amongst them to decide the best result. Another way is to analyze the quality of shifting and scaling patterns in Biclusters. Biclustering has been used in the domain of
1599:
Kriegel, H.-P.; Kröger, P.; Zimek, A. (March 2009). "Clustering High Dimensional Data: A Survey on Subspace Clustering, Pattern-based Clustering, and Correlation Clustering".
1021:
1513:
824:
Biclustering algorithms have also been proposed and used in other application fields under the names co-clustering, bi-dimensional clustering, and subspace clustering.
153:
155:
matrix). The Biclustering algorithm generates Biclusters. A Bicluster is a subset of rows which exhibit similar behavior across a subset of columns, or vice versa.
127:
107:
87:
67:
1774:, Bodenhofer U, Heusel M, Mayr A, Mitterecker A, Kasim A, Khamiakova T, Van Sanden S, Lin D, Talloen W, Bijnens L, Gohlmann HW, Shkedy Z, Clevert DA (2010).
194:
To cluster more than two types of objects, in 2005, Bekkerman expanded the mutual information in Dhillon's theorem from a single pair into multiple pairs.
971:, for cross similarity) is based on finding document-document similarity and word-word similarity, and then using classical clustering methods such as
2283:
Orzechowski, P., Sipper, M., Huang, X., & Moore, J. H. (2018). EBIC: an evolutionary-based parallel biclustering algorithm for pattern discovery.
167:
in 1972. The term "Biclustering" was then later used and refined by Boris G. Mirkin. This algorithm was not generalized until 2000, when Y. Cheng and
924:
algorithms are then applied to discover blocks in D that correspond to a group of documents (rows) characterized by a group of words(columns).
963:
More recently (Bisson and Hussain) have proposed a new approach of using the similarity between words and the similarity between documents to
2139:
1960:
1266:
1158:
1174:
R. Balamurugan; A.M. Natarajan; K. Premalatha (2016). "A Modified Harmony Search Method for Biclustering Microarray Gene Expression Data".
1319:
858:
find and report all maximal Biclusters with coherent and contiguous columns with perfect/approximate expression patterns, in time linear/
191:
instead of KL-distance to design a Biclustering algorithm that was suitable for any kind of matrix, unlike the KL-distance algorithm.
1636:"Revealing modularity and organization in the yeast molecular network by integrated analysis of highly heterogeneous genomewide data"
884:
There is an ongoing debate about how to judge the results of these methods, as Biclustering allows overlap between clusters and some
862:
which is obtained by manipulating a discretized version of original expression matrix in the size of the time-series gene expression
1023:
where t is the number of non-zero entries in D. Note that in D each row and each column must contain at least one non-zero element.
900:
makes it difficult to spot errors in the results. One approach is to utilize multiple Biclustering algorithms, with the majority or
171:
proposed a biclustering algorithm based on the mean squared residue score (MSR) and applied it to biological gene expression data.
983:
experiment. According to the cover coefficient concept number of clusters can also be roughly estimated by the following formula
931:
Several approaches have been proposed based on the information contents of the resulting blocks: matrix-based approaches such as
909:
180:
979:
structure of the whole corpus into consideration with the result of generating a better clustering of the documents and words.
877:
Some recent algorithms have attempted to include additional support for Biclustering rectangular matrices in the form of other
1488:
1443:
1398:
1353:
2323:
821:
able to identify co-cluster centroids from highly sparse transformation obtained by iterative multi-mode discretization.
932:
893:
2029:"A polynomial time biclustering algorithm for finding approximate expression patterns in gene expression time series"
1081:
G. Govaert; M. Nadif (2008). "Block clustering with bernoulli mixture models: Comparison of different approaches".
2313:
1031:
1722:"Integrated biclustering of heterogeneous genome-wide datasets for the inference of global regulatory networks"
976:
944:
minimized. Graph-based methods tend to minimize the cuts between the clusters. Given two groups of documents d
42:. The term was first introduced by Boris Mirkin to name a technique introduced many years earlier, in 1972, by
273:
2318:
1051:
972:
874:. These algorithms are also applied to solve problems and sketch the analysis of computational complexity.
1210:
797:
916:
D whose rows denote the documents and whose columns denote the words in the dictionary. Matrix elements D
1034:. FABIA utilizes well understood model selection techniques like variational approaches and applies the
936:
1320:
https://www.cs.princeton.edu/courses/archive/fall03/cs597F/Articles/biclustering_of_expression_data.pdf
1931:
Fanaee-T H, Thoresen, M (2020). "Iterative Multi-mode Discretization: Applications to Co-clustering".
1693:
Abdullah, Ahsan; Hussain, Amir (2006). "A new biclustering technique based on crossing minimization".
2165:"Concepts and effectiveness of the cover coefficient based clustering methodology for text databases"
1647:
1338:
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
1035:
913:
897:
863:
39:
1422:
Banerjee, Arindam; Dhillon, Inderjit; Ghosh, Joydeep; Merugu, Srujana; Modha, Dharmendra S. (2004).
1215:
1428:
Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining
1383:
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
1039:
986:
2164:
1556:
Madeira SC, Oliveira AL (2004). "Biclustering Algorithms for Biological Data Analysis: A Survey".
2197:
2145:
2009:
1966:
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1616:
1581:
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1494:
1449:
1404:
1359:
1302:
1236:
1201:
Van Mechelen I, Bock HH, De Boeck P (2004). "Two-mode clustering methods:a structured overview".
1131:
908:(or classification) which is popularly known as co-clustering. Text corpora are represented in a
176:
952:, the number of cuts can be measured as the number of words that occur in documents of groups d
831:. Recent proposals have addressed the Biclustering problem in the specific case of time-series
132:
2269:
2135:
2122:
Bisson G.; Hussain F. (2008). "Chi-Sim: A New Similarity Measure for the Co-clustering Task".
2101:
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2001:
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either 0 or 1 in the binary matrix A, a Bicluster is equal to a biclique in the corresponding
1825:"runibic: a Bioconductor package for parallel row-based biclustering of gene expression data"
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35:
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1424:"A generalized maximum entropy approach to bregman co-clustering and matrix approximation"
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832:
817:
269:
223:
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1026:
In contrast to other approaches, FABIA is a multiplicative model that assumes realistic
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2055:
2028:
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1110:"Stellar-Mass Black Hole Optimization for Biclustering Microarray Gene Expression Data"
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Data mining technique for simultaneous clustering of the rows and columns of a matrix
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The relationship between these cluster models and other types of clustering such as
2013:
1874:"EBIC: an evolutionary-based parallel biclustering algorithm for pattern discovery"
1539:
1453:
207:. NP-complete has two conditions. In the simple case that there is an only element
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1109:
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1942:
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871:
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204:
184:
31:
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Proceedings of the 22nd international conference on Machine learning - ICML '05
1334:"Co-clustering documents and words using bipartite spectral graph partitioning"
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data. In this case, the interesting Biclusters can be restricted to those with
1224:
1187:
885:
859:
809:
231:
2240:"Spectral Biclustering of Microarray Data: Coclustering Genes and Conditions"
2226:
A. Tanay. R. Sharan, and R. Shamir, "Biclustering Algorithms: A Survey", In
1738:
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1612:
1480:
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1423:
1322:
Cheng Y, Church G M. Biclustering of expression data//Ismb. 2000, 8: 93–103.
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Biclusters within the data matrix. When the data matrix is partitioned into
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2005:
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2008 Seventh International Conference on Machine Learning and Applications
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1997:
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Dhillon, Inderjit S.; Mallela, Subramanyam; Modha, Dharmendra S. (2003).
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316:
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227:
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of each Bicluster to separate spurious Biclusters from true Biclusters.
1951:
1937:. Lecture Notes in Computer Science. Vol. 12323. pp. 94–105.
1306:
2255:
89:-dimensional feature vector, the entire dataset can be represented as
889:
1932:
1298:
1890:
1038:
framework. The generative framework allows FABIA to determine the
298:
Biclusters which have rows and columns with different approaches.
276:, by splitting the original data matrix into a set of Biclusters,
1986:
IEEE/ACM Transactions on Computational Biology and Bioinformatics
1558:
IEEE/ACM Transactions on Computational Biology and Bioinformatics
256:
are equal to a given constant μ. In tangible data, these entries
1469:"Multi-way distributional clustering via pairwise interactions"
2298:
FABIA: Factor Analysis for Bicluster Acquisition, an R package
827:
Given the known importance of discovering local patterns in
187:
between P and Q. In 2004, Arindam Banerjee used a weighted-
1285:
Hartigan JA (1972). "Direct clustering of a data matrix".
2080:"Shifting and scaling patterns from gene expression data"
293:
Bicluster with constant values on rows (b) or columns (c)
1467:
Bekkerman, Ron; El-Yaniv, Ran; McCallum, Andrew (2005).
1176:
International Journal of Data Mining and Bioinformatics
1823:
Orzechowski P, Pańszczyk A, Huang X, Moore JH (2018).
1108:
R. Balamurugan; A.M. Natarajan; K. Premalatha (2015).
989:
135:
115:
95:
75:
55:
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and enables the development of efficient exhaustive
1872:Orzechowski P, Sipper M, Huang X, Moore JH (2018).
1551:
1549:
700:e) Bicluster with coherent values (multiplicative)
1776:"FABIA: factor analysis for bicluster acquisition"
1514:"The maximum edge biclique problem is NP-complete"
1151:Co-clustering: models, algorithms and applications
1015:
147:
121:
101:
81:
61:
2238:Kluger Y, Basri R, Chang JT, Gerstein MB (2003).
1601:ACM Transactions on Knowledge Discovery from Data
1640:Proceedings of the National Academy of Sciences
1287:Journal of the American Statistical Association
1634:Tanay A, Sharan R, Kupiec M, Shamir R (2004).
606:d) Bicluster with coherent values (additive)
506:c) Bicluster with constant values on columns
8:
600:
312:
2228:Handbook of Computational Molecular Biology
920:denote occurrence of word j in document i.
2117:
2115:
1280:
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1259:Mathematical Classification and Clustering
1083:Computational Statistics and Data Analysis
412:b) Bicluster with constant values on rows
163:Biclustering was originally introduced by
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847:algorithms such as CCC-Biclustering and
1720:Reiss DJ, Baliga NS, Bonneau R (2006).
1203:Statistical Methods in Medical Research
1073:
1379:"Information-theoretic co-clustering"
935:and BVD, and graph-based approaches.
839:columns. This restriction leads to a
302:Bicluster with coherent values (d, e)
252:is a matrix(I,J) in which all values
179:during biclustering was equal to the
7:
2172:ACM Transactions on Database Systems
34:technique which allows simultaneous
28:Co-clustering or two-mode clustering
967:the matrix. Their method (known as
2163:Can, F.; Ozkarahan, E. A. (1990).
318:a) Bicluster with constant values
243:Bicluster with constant values (a)
234:to short-circuit the calculation.
14:
260:may be represented with the form
2033:Algorithms for Molecular Biology
2027:Madeira SC, Oliveira AL (2009).
289:Biclusters, the algorithm ends.
1114:Applied Artificial Intelligence
1261:. Kluwer Academic Publishers.
1002:
990:
1:
2097:10.1093/bioinformatics/bti641
1900:10.1093/bioinformatics/bty401
1841:10.1093/bioinformatics/bty512
1792:10.1093/bioinformatics/btq227
1531:10.1016/S0166-218X(03)00333-0
1332:Dhillon, Inderjit S. (2001).
1149:G. Govaert; M. Nadif (2013).
1127:10.1080/08839514.2015.1016391
1016:{\displaystyle (m\times n)/t}
38:of the rows and columns of a
1707:10.1016/j.neucom.2006.02.018
1518:Discrete Applied Mathematics
808:There are many Biclustering
1943:10.1007/978-3-030-61527-7_7
894:unsupervised classification
230:effort or the use of lossy
2340:
1095:10.1016/j.csda.2007.09.007
1030:signal distributions with
250:perfect constant Bicluster
69:samples represented by an
1225:10.1191/0962280204sm373ra
1188:10.1504/IJDMB.2016.082205
181:Kullback–Leibler-distance
148:{\displaystyle m\times n}
2078:Aguilar-Ruiz JS (2005).
1739:10.1186/1471-2105-7-280
1661:10.1073/pnas.0308661100
1613:10.1145/1497577.1497578
1481:10.1145/1102351.1102357
1436:10.1145/1014052.1014111
1052:Formal concept analysis
973:hierarchical clustering
896:problem, the lack of a
2132:10.1109/ICMLA.2008.103
1257:Mirkin, Boris (1996).
1017:
798:correlation clustering
149:
123:
103:
83:
63:
2046:10.1186/1748-7188-4-8
1391:10.1145/956750.956764
1346:10.1145/502512.502550
1018:
937:Information-theoretic
892:. Because this is an
881:, including cMonkey.
150:
124:
104:
84:
64:
2324:NP-complete problems
2126:. pp. 211–217.
1998:10.1109/TCBB.2008.34
1701:(16–18): 1882–1896.
1430:. pp. 509–514.
1340:. pp. 269–274.
987:
870:techniques based on
274:Hartigan's algorithm
133:
113:
93:
73:
53:
2184:10.1145/99935.99938
1652:2004PNAS..101.2981T
1570:10.1109/TCBB.2004.2
1040:information content
701:
607:
507:
413:
319:
238:Types of Biclusters
1726:BMC Bioinformatics
1512:Peeters R (2003).
1475:. pp. 41–48.
1385:. pp. 89–98.
1013:
699:
605:
505:
411:
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177:mutual information
145:
129:columns (i.e., an
119:
99:
79:
59:
2256:10.1101/gr.648603
2141:978-0-7695-3495-4
2090:(10): 3840–3845.
1962:978-3-030-61526-0
1934:Discovery Science
1884:(21): 3719–3726.
1835:(24): 4302–4304.
1786:(12): 1520–1527.
1268:978-0-7923-4159-8
1160:978-1-84821-473-6
1062:Galois connection
868:string processing
841:tractable problem
800:is discussed in.
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122:{\displaystyle n}
102:{\displaystyle m}
82:{\displaystyle n}
62:{\displaystyle m}
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2314:Cluster analysis
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2234:, Chapman (2004)
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1646:(9): 2981–2986.
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1089:(6): 3233–3245.
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866:using efficient
829:time-series data
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189:Bregman distance
169:George M. Church
165:John A. Hartigan
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24:block clustering
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2300:—software
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1687:
1633:
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1628:
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1597:
1593:
1555:
1554:
1547:
1511:
1510:
1506:
1491:
1466:
1465:
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1446:
1421:
1420:
1416:
1401:
1376:
1375:
1371:
1356:
1331:
1330:
1326:
1318:
1314:
1299:10.2307/2284710
1284:
1283:
1276:
1269:
1256:
1255:
1248:
1216:10.1.1.706.4201
1200:
1199:
1195:
1173:
1172:
1168:
1161:
1153:. ISTE, Wiley.
1148:
1147:
1143:
1107:
1106:
1102:
1080:
1079:
1075:
1070:
1048:
985:
984:
977:latent semantic
959:
955:
951:
947:
919:
833:gene expression
818:Factor analysis
806:
795:
310:
272:. According to
240:
224:bipartite graph
221:
200:
161:
131:
130:
111:
110:
91:
90:
71:
70:
51:
50:
49:Given a set of
17:
12:
11:
5:
2337:
2335:
2327:
2326:
2321:
2319:Bioinformatics
2316:
2306:
2305:
2302:
2301:
2293:
2292:External links
2290:
2289:
2288:
2285:Bioinformatics
2281:
2278:
2250:(4): 703–716.
2235:
2232:Srinivas Aluru
2224:
2220:
2214:
2211:
2208:
2207:
2178:(4): 483–517.
2155:
2140:
2111:
2084:Bioinformatics
2070:
2019:
1992:(7): 153–165.
1976:
1961:
1923:
1878:Bioinformatics
1864:
1829:Bioinformatics
1815:
1780:Bioinformatics
1763:
1712:
1695:Neurocomputing
1685:
1626:
1591:
1545:
1524:(3): 651–654.
1504:
1489:
1459:
1444:
1414:
1399:
1369:
1354:
1324:
1312:
1293:(337): 123–9.
1274:
1267:
1246:
1193:
1182:(4): 269–289.
1166:
1159:
1141:
1120:(4): 353–381.
1100:
1072:
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1064:
1059:
1054:
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1012:
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949:
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902:super-majority
814:bioinformatics
812:developed for
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2166:
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2137:
2133:
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2116:
2112:
2107:
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2098:
2093:
2089:
2085:
2081:
2074:
2071:
2066:
2062:
2057:
2052:
2047:
2042:
2038:
2034:
2030:
2023:
2020:
2015:
2011:
2007:
2003:
1999:
1995:
1991:
1987:
1980:
1977:
1972:
1968:
1964:
1958:
1953:
1948:
1944:
1940:
1936:
1935:
1927:
1924:
1919:
1915:
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1901:
1897:
1892:
1887:
1883:
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1253:
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1234:
1230:
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1217:
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1209:(5): 363–94.
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966:
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942:
938:
934:
929:
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923:
922:Co-clustering
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911:
907:
903:
899:
898:gold standard
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228:computational
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45:
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37:
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2243:
2230:, Edited by
2227:
2193:2374.MIA/246
2175:
2171:
2158:
2123:
2087:
2083:
2073:
2036:
2032:
2022:
1989:
1985:
1979:
1933:
1926:
1881:
1877:
1867:
1832:
1828:
1818:
1783:
1779:
1772:Hochreiter S
1766:
1729:
1725:
1715:
1698:
1694:
1688:
1643:
1639:
1629:
1604:
1600:
1594:
1564:(1): 24–45.
1561:
1557:
1521:
1517:
1507:
1472:
1462:
1427:
1417:
1382:
1372:
1337:
1327:
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1290:
1286:
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1202:
1196:
1179:
1175:
1169:
1150:
1144:
1117:
1113:
1103:
1086:
1082:
1076:
1028:non-Gaussian
1025:
981:
968:
962:
930:
926:
883:
876:
872:suffix trees
853:
848:
826:
823:
807:
794:
309:
305:
301:
300:
296:
292:
291:
286:
282:
268:denotes the
265:
261:
257:
253:
249:
246:
242:
241:
217:
213:
208:
201:
193:
173:
162:
48:
27:
23:
20:Biclustering
19:
18:
1952:10852/82994
1732:: 280–302.
1607:(1): 1–58.
1032:heavy tails
941:iteratively
939:algorithms
906:text mining
845:enumeration
205:NP-complete
185:KL-distance
159:Development
32:data mining
2308:Categories
1891:1801.03039
1490:1595931805
1445:1581138881
1400:1581137370
1355:158113391X
1068:References
965:co-cluster
912:form as a
886:algorithms
860:polynomial
856:algorithms
837:contiguous
810:algorithms
804:Algorithms
262:n(i,j) + μ
232:heuristics
198:Complexity
36:clustering
1971:222832035
1586:206628783
1211:CiteSeerX
997:×
879:datatypes
140:×
2274:12671006
2202:14309214
2150:15506600
2106:16144809
2065:19497096
2039:(8): 8.
2006:20150677
1918:29790909
1859:29939213
1810:20418340
1758:16749936
1680:14973197
1621:17363900
1578:17048406
1409:12286784
1364:11847258
1241:19058237
1233:15516031
1136:44624424
1057:Biclique
1046:See also
1036:Bayesian
910:vectoral
278:variance
109:rows in
2056:2709627
2014:7369531
1909:6198864
1850:6289127
1801:2881408
1749:1502140
1648:Bibcode
1540:3102766
1454:2719002
1307:2284710
2272:
2265:430175
2262:
2219:16–18.
2213:Others
2200:
2148:
2138:
2104:
2063:
2053:
2012:
2004:
1969:
1959:
1916:
1906:
1857:
1847:
1808:
1798:
1756:
1746:
1678:
1671:365731
1668:
1619:
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1576:
1538:
1499:858524
1497:
1487:
1452:
1442:
1407:
1397:
1362:
1352:
1305:
1265:
1239:
1231:
1213:
1157:
1134:
914:matrix
890:minima
864:matrix
854:These
266:n(i,j)
264:where
258:a(i,j)
254:a(i,j)
40:matrix
2223:2013.
2198:S2CID
2168:(PDF)
2146:S2CID
2010:S2CID
1967:S2CID
1886:arXiv
1617:S2CID
1582:S2CID
1536:S2CID
1495:S2CID
1450:S2CID
1405:S2CID
1360:S2CID
1303:JSTOR
1237:S2CID
1132:S2CID
969:χ-Sim
956:and d
948:and d
270:noise
30:is a
2270:PMID
2136:ISBN
2102:PMID
2061:PMID
2002:PMID
1957:ISBN
1914:PMID
1855:PMID
1806:PMID
1754:PMID
1676:PMID
1574:PMID
1485:ISBN
1440:ISBN
1395:ISBN
1350:ISBN
1263:ISBN
1229:PMID
1155:ISBN
785:4.0
779:10.0
768:3.2
751:2.4
734:1.6
717:0.8
691:2.5
674:5.5
657:3.5
640:4.5
623:1.5
591:5.0
574:5.0
557:5.0
540:5.0
523:5.0
497:5.0
480:4.0
463:3.0
446:2.0
429:1.0
403:2.0
386:2.0
369:2.0
352:2.0
335:2.0
2260:PMC
2252:doi
2188:hdl
2180:doi
2128:doi
2092:doi
2051:PMC
2041:doi
1994:doi
1947:hdl
1939:doi
1904:PMC
1896:doi
1845:PMC
1837:doi
1796:PMC
1788:doi
1744:PMC
1734:doi
1703:doi
1666:PMC
1656:doi
1644:101
1609:doi
1566:doi
1526:doi
1522:131
1477:doi
1432:doi
1387:doi
1342:doi
1295:doi
1221:doi
1184:doi
1122:doi
1091:doi
933:SVD
782:1.0
776:2.5
773:5.0
765:0.8
762:8.0
759:2.0
756:4.0
748:0.6
745:6.0
742:1.5
739:3.0
731:0.4
728:4.0
725:1.0
722:2.0
714:0.2
711:2.0
708:0.5
705:1.0
688:1.0
685:6.0
682:5.0
679:2.0
671:4.0
668:9.0
665:8.0
662:5.0
654:2.0
651:7.0
648:6.0
645:3.0
637:3.0
634:8.0
631:7.0
628:4.0
620:0.0
617:5.0
614:4.0
611:1.0
588:4.0
585:3.0
582:2.0
579:1.0
571:4.0
568:3.0
565:2.0
562:1.0
554:4.0
551:3.0
548:2.0
545:1.0
537:4.0
534:3.0
531:2.0
528:1.0
520:4.0
517:3.0
514:2.0
511:1.0
494:5.0
491:5.0
488:5.0
485:5.0
477:4.0
474:4.0
471:4.0
468:4.0
460:3.0
457:3.0
454:3.0
451:3.0
443:2.0
440:2.0
437:2.0
434:2.0
426:1.0
423:1.0
420:1.0
417:1.0
400:2.0
397:2.0
394:2.0
391:2.0
383:2.0
380:2.0
377:2.0
374:2.0
366:2.0
363:2.0
360:2.0
357:2.0
349:2.0
346:2.0
343:2.0
340:2.0
332:2.0
329:2.0
326:2.0
323:2.0
2310::
2268:.
2258:.
2248:13
2246:.
2242:.
2196:.
2186:.
2176:15
2174:.
2170:.
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2134:.
2114:^
2100:.
2088:21
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2082:.
2059:.
2049:.
2035:.
2031:.
2008:.
2000:.
1988:.
1965:.
1955:.
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1603:.
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1560:.
1548:^
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1471:.
1448:.
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1381:.
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1336:.
1301:.
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1249:^
1235:.
1227:.
1219:.
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1180:16
1178:.
1130:.
1118:29
1116:.
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1087:52
1085:.
960:.
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2204:.
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2182::
2152:.
2130::
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2067:.
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1996::
1990:1
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1949::
1941::
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77:n
57:m
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