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Can triconcepts become triclusters?

Dmitry I. Ignatov, Sergei O. Kuznetsov, Jonas Poelmans, Leonid E. Zhukov
2013 International Journal of General Systems  
This definition is a scalable relaxation of the notion of triconcept in Triadic Concept Analysis, whereas each triconcept of the initial dataset is contained in a certain tricluster.  ...  Two novel approaches to triclustering of three-way binary data are proposed.  ...  As in case of triconcepts, we still call the three components of a tricluster by extent, intent and modus, respectively. Let us explain the structure of the proposed triclusters.  ... 
doi:10.1080/03081079.2013.798899 fatcat:uy7wlrefarbingfqx25yzch3qu

Triadic Formal Concept Analysis and triclustering: searching for optimal patterns

Dmitry I. Ignatov, Dmitry V. Gnatyshak, Sergei O. Kuznetsov, Boris G. Mirkin
2015 Machine Learning  
An ideal triadic pattern is a totally dense maximal cuboid (formal triconcept).  ...  Relaxations of this notion under consideration are: OAC-triclusters; triclusters optimal with respect to the leastsquare criterion; and graph partitions obtained by using spectral clustering.  ...  Then the model can be rewritten by putting r * gmb = r gmb − λ 0 on the left, so that λ 0 becomes a similarity shift value rather than an intercept.  ... 
doi:10.1007/s10994-015-5487-y fatcat:qpedyeugvzgmbaidv3izlhcvja

Multimodal Clustering for Community Detection [article]

Dmitry I. Ignatov and Alexander Semenov and Daria Komissarova and Dmitry V. Gnatyshak
2017 arXiv   pre-print
Among different types of such generalized patterns one can find biclusters and formal concepts (maximal bicliques) for 2-mode case, triclusters and triconcepts for 3-mode case, closed n-sets for n-mode  ...  Introduction Online social networking services generate massive amounts of data, which can become a valuable source for guiding Internet advertisement efforts or provide sociological insights.  ...  (see Proposition 1): for every triconcept in a given tricontext there exists a tricluster of the same tricontext in which the triconcept is contained w.r.t. component-wise inclusion.  ... 
arXiv:1702.08557v1 fatcat:o3nqgd7csba33f3nya7se4ffwa

Towards a Unified Taxonomy of Biclustering Methods [article]

Dmitry I. Ignatov, Bruce W. Watson
2017 arXiv   pre-print
Being an unsupervised machine learning and data mining technique, biclustering and its multimodal extensions are becoming popular tools for analysing object-attribute data in different domains.  ...  In particular we hope that FCART can become our tool of choice in the near future [40] .  ...  There exist relaxations of triconcept and poliadic concept notions, triclusters and n-clusters, which allow for certain entries inside such n-dic concept to be zeros [20, 31, 32] ; the theoretical and  ... 
arXiv:1702.05376v1 fatcat:lzso53vqgvbphkjnmuk7uk6yb4

Introduction to Formal Concept Analysis and Its Applications in Information Retrieval and Related Fields [chapter]

Dmitry I. Ignatov
2015 Communications in Computer and Information Science  
Can it become open in addition to its extendability? Can it finally handle big volumes of heterogeneous data in a suitable way for an FCART analyst?  ...  Guided by the idea of finding scalable and noise-tolerant triconcepts, we had a look at triclustering paradigm in general for a triadic binary data, i.e. for tricontexts as input datasets.  ... 
doi:10.1007/978-3-319-25485-2_3 fatcat:m2zad3btkjhkja2mdwmjfbkahi

CLA 2014 CLA Conference Series CLA 2014 Volume editors Steering Committee Program Chairs Program Committee Additional Reviewers Organization Committee

Karell Bertet, Sebastian Rudolph, Karell Bertet, Sebastian Rudolph, Sebastian Rudolph, Radim Bělohlávek, Ben Sadok, Yahia, Jean Diatta, Sergei Kuznetsov, Engelbert Nguifo, Manuel Ojeda (+54 others)
Proceedings P. J. ˇ Safárik University   unpublished
worst case the maximal number of triclusters usually is exponential (e.g. in case of formal triconcepts), showing that these methods are hardly scalable.  ...  In our context, a word becomes a pattern, a document becomes a set of sessions S ui of a given user and the corpus becomes the whole set S of all sessions. Denition 3 (tf ×idf ).  ...  In this way, the concept lattice can be considered as a materialized view of the data resulting from a SPARQL query.  ... 

Contributions to Biclustering of Microarray Data Using Formal Concept Analysis [article]

Amina Houari
2018 arXiv   pre-print
and triconcepts [Ignatov et al., 2015] .  ...  Passing to the binary matrix, column C 1 becomes {0,0,0,0,1,1}.  ... 
arXiv:1811.09562v1 fatcat:koql6oifrvgsnk6j56bpne6jvm