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Attribute Selection using Contranominal Scales [article]

Dominik Dürrschnabel, Maren Koyda, Gerd Stumme
2021 arXiv   pre-print
Leveraging this algorithm, we introduce delta-adjusting, a novel approach in order to decrease the number of contranominal scales in a formal context by the selection of an appropriate attribute subset  ...  In this work, we propose the algorithm ContraFinder that enables the computation of all contranominal scales of a given formal context.  ...  Using this, we defined the contranominal-influence of an attribute. This measure allows us to select a subset of attributes in order to reduce a formal context to itsδ-adjusted subcontext.  ... 
arXiv:2106.10978v2 fatcat:gakbvn2lsrblnlgztwqznbe3o4

Null Models for Formal Contexts

Maximilian Felde, Tom Hanika, Gerd Stumme
2020 Information  
These random models are in particular useful for, but not limited to, comparing the performance of algorithms.  ...  Thus we suggest a novel approach using Dirichlet distributions. We recollect and analyze the classical coin-toss model, recapitulate some of its shortcomings and examine its stochastic properties.  ...  The number of concepts for a contranominal scale with n attributes is 2 n , thus having 2 n intents and therefore zero pseudo-intents.  ... 
doi:10.3390/info11030135 fatcat:5u4nmmiaszdqrotyjpzgtaaue4

WebGeneKFCA: an On-line Conceptual Analysis Tool for Genomic Expression Data

José María Fernández-Calabozo, Carmen Peláez-Moreno, Francisco J. Valverde-Albacete
2012 International Conference on Concept Lattices and their Applications  
As a second contribution, we present a mechanism to visualise a sequence of concept lattices by fixing the intents against the concept lattice of the contranominal scale of attributes B(M, M, =) .  ...  , viz. the contranominal scale of attributes.  ...  To ensure this property, the CL corresponding to a particular φ (ϕ) is drawn over the silhouette of the CL of a (virtual) contranominal scale involving all possible attributes, N c M = B(M, M, =) .  ... 
dblp:conf/cla/Fernandez-CalabozoPV12 fatcat:rlw3omfbfzeaxmz3vxh3wtw7fi

Relevant Attributes in Formal Contexts [article]

Tom Hanika and Maren Koyda and Gerd Stumme
2018 arXiv   pre-print
Building up on this we introduce a method for attribute selection in formal contexts.  ...  ., random sampling, parallelization, or attribute extraction. A so far not investigated method in the realm of formal concept analysis is attribute selection, as done in machine learning.  ...  The relative relevance of an objects in the case of the contranominal scale is r(m) all m ∈ M .  ... 
arXiv:1812.08868v1 fatcat:zzmgs3sbqnftlino5nb5nlrxra

Dualization in Lattices Given by Ordered Sets of Irreducibles [article]

Mikhail A. Babin, Sergei O. Kuznetsov
2015 arXiv   pre-print
The contranominal scale has the following property, which we will use later: for any H ⊆ M one has H ′′ = H and H ′ = {g i | m i / ∈ H, 1 ≤ i ≤ n}.  ...  scale.  ... 
arXiv:1504.01145v2 fatcat:n5zsomhlpnbdviuo4urk4ewve4

Boolean Substructures in Formal Concept Analysis [article]

Maren Koyda, Gerd Stumme
2021 arXiv   pre-print
It is known that a (concept) lattice contains an n-dimensional Boolean suborder if and only if the context contains an n-dimensional contra-nominal scale as subcontext.  ...  To study particular parts of a formal context the selection of a subcontext is useful.  ...  Considering many-valued contexts, Ganter and Kuznetzov [6] select features based on their scaling.  ... 
arXiv:2104.07159v1 fatcat:v3p6bojvajcdffnfbyoqz6okqu

Discovery data topology with the closure structure. Theoretical and practical aspects [article]

Tatiana Makhalova, Aleksey Buzmakov, Sergei O. Kuznetsov, Amedeo Napoli
2021 arXiv   pre-print
We present and demonstrate theoretical results, and as well, practical results using the GDPM algorithm.  ...  Finally, a series of experiments shows how GDPM can be practically used and what can be expected from the output.  ...  consider the number of combinations of attributes that make a contranominal-scale subcontext of size n.  ... 
arXiv:2010.02628v3 fatcat:norn5mopb5fpxpdkhrczjpe2yi

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  
FCA is an applied branch of Lattice Theory, a mathematical discipline which enables formalisation of concepts as basic units of human thinking and analysing data in the object-attribute form.  ...  There is a special type of scale, contranominal scale, which is rare case in real data, but has important theoretical meaning.  ...  The objects of a scale are called scale values, the attributes are called scale attributes. attributes like color.  ... 
doi:10.1007/978-3-319-25485-2_3 fatcat:m2zad3btkjhkja2mdwmjfbkahi

Shapley and Banzhaf Vectors of a Formal Concept

Dmitry I. Ignatov, Léonard Kwuida
The introduced indices are related to extensional concept stability and based on counting generators, especially those that contain a selected attribute.  ...  (in the form of JSM-hypotheses or other patterns) along with individual importance of their single attributes (or more complex constituent elements).  ...  with and without a selected attribute.  ... 
doi:10.24451/arbor.12975 fatcat:ddncjafi7fepfhw6q33ysx4agi

Fast algorithms for implication bases and attribute exploration using proper premises

Uwe Ryssel, Felix Distel, Daniel Borchmann
2013 Annals of Mathematics and Artificial Intelligence  
It holds that for some n ≥ 2, consisting of two contranominal scales of dimension n × n and one attribute a with empty extent.  ...  Selected features will have the Boolean value true and not selected features will have the value false.  ... 
doi:10.1007/s10472-013-9355-9 fatcat:nik4rwzxevgorpgudiri6f57gm

Intrinsic Dimension of Geometric Data Sets [article]

Tom Hanika and Friedrich Martin Schneider and Gerd Stumme
2020 arXiv   pre-print
There is a large body of literature investigating its origin and impact, using methods from mathematics as well as from computer science.  ...  For every concept (A, B) ∈ B(K), 6.2. 2 . 2 Intrinsic Dimension of Scales. There are particular formal contexts used for scaling non-binary attributes into binary ones.  ...  The most common scales are the nominal scale, K nom n := ([n], [n], =), and the contranominal scale, K con n := ([n], [n], =), where [n] := {1, . . . , n} for a natural number n ≥ 1.  ... 
arXiv:1801.07985v3 fatcat:m7s3yj2y7veu3hpb7qie5ncdmi