47,414 research outputs found
Visualizing and Interacting with Concept Hierarchies
Concept Hierarchies and Formal Concept Analysis are theoretically well
grounded and largely experimented methods. They rely on line diagrams called
Galois lattices for visualizing and analysing object-attribute sets. Galois
lattices are visually seducing and conceptually rich for experts. However they
present important drawbacks due to their concept oriented overall structure:
analysing what they show is difficult for non experts, navigation is
cumbersome, interaction is poor, and scalability is a deep bottleneck for
visual interpretation even for experts. In this paper we introduce semantic
probes as a means to overcome many of these problems and extend usability and
application possibilities of traditional FCA visualization methods. Semantic
probes are visual user centred objects which extract and organize reduced
Galois sub-hierarchies. They are simpler, clearer, and they provide a better
navigation support through a rich set of interaction possibilities. Since probe
driven sub-hierarchies are limited to users focus, scalability is under control
and interpretation is facilitated. After some successful experiments, several
applications are being developed with the remaining problem of finding a
compromise between simplicity and conceptual expressivity
Computing iceberg concept lattices with Titanic
International audienceWe introduce the notion of iceberg concept lattices and show their use in knowledge discovery in databases. Iceberg lattices are a conceptual clustering method, which is well suited for analyzing very large databases. They also serve as a condensed representation of frequent itemsets, as starting point for computing bases of association rules, and as a visualization method for association rules. Iceberg concept lattices are based on the theory of Formal Concept Analysis, a mathematical theory with applications in data analysis, information retrieval, and knowledge discovery. We present a new algorithm called TITANIC for computing (iceberg) concept lattices. It is based on data mining techniques with a level-wise approach. In fact, TITANIC can be used for a more general problem: Computing arbitrary closure systems when the closure operator comes along with a so-called weight function. The use of weight functions for computing closure systems has not been discussed in the literature up to now. Applications providing such a weight function include association rule mining, functional dependencies in databases, conceptual clustering, and ontology engineering. The algorithm is experimentally evaluated and compared with Ganter's Next-Closure algorithm. The evaluation shows an important gain in efficiency, especially for weakly correlated data
Real-space observation of short-period cubic lattice of skyrmions in MnGe
Emergent phenomena and functions arising from topological electron-spin
textures in real space or momentum space are attracting growing interest for
new concept of states of matter as well as for possible applications to
spintronics. One such example is a magnetic skyrmion, a topologically stable
nanoscale spin vortex structure characterized by a topological index.
Real-space regular arrays of skyrmions are described by combination of
multi-directional spin helixes. Nanoscale configurations and characteristics of
the two-dimensional skyrmion hexagonal-lattice have been revealed extensively
by real-space observations. Other three-dimensional forms of skyrmion lattices,
such as a cubic-lattice of skyrmions, are also anticipated to exist, yet their
direct observations remain elusive. Here we report real-space observations of
spin configurations of the skyrmion cubic-lattice in MnGe with a very short
period (~3 nm) and hence endowed with the largest skyrmion number density. The
skyrmion lattices parallel to the {100} atomic lattices are directly observed
using Lorentz transmission electron microscopes (Lorentz TEMs). It enables the
first simultaneous observation of magnetic skyrmions and underlying
atomic-lattice fringes. These results indicate the emergence of
skyrmion-antiskyrmion lattice in MnGe, which is a source of emergent
electromagnetic responses and will open a possibility of controlling
few-nanometer scale skyrmion lattices through atomic lattice modulations
Mining Biclusters of Similar Values with Triadic Concept Analysis
Biclustering numerical data became a popular data-mining task in the
beginning of 2000's, especially for analysing gene expression data. A bicluster
reflects a strong association between a subset of objects and a subset of
attributes in a numerical object/attribute data-table. So called biclusters of
similar values can be thought as maximal sub-tables with close values. Only few
methods address a complete, correct and non redundant enumeration of such
patterns, which is a well-known intractable problem, while no formal framework
exists. In this paper, we introduce important links between biclustering and
formal concept analysis. More specifically, we originally show that Triadic
Concept Analysis (TCA), provides a nice mathematical framework for
biclustering. Interestingly, existing algorithms of TCA, that usually apply on
binary data, can be used (directly or with slight modifications) after a
preprocessing step for extracting maximal biclusters of similar values.Comment: Concept Lattices and their Applications (CLA) (2011
Towards an Automatic Extraction of Smartphone Users' Contextual Behaviors
International audienceThis paper presents a new method for automatically extracting smartphone users' contextual behaviors from the digital traces collected during their interactions with their devices. Our goal is in particular to understand the impact of users' context (e.g., location, time, environment, etc.) on the applications they run on their smartphones. We propose a methodology to analyze digital traces and to automatically identify the significant information that characterizes users' behaviors. In earlier work, we have used Formal Concept Analysis and Galois lattices to extract relevant knowledge from heterogeneous and complex contextual data; however, the interpretation of the obtained Galois lattices was performed manually. In this article, we aim at automating this interpretation process, through the provision of original metrics. Therefore our methodology returns relevant information without requiring any expertise in data analysis. We illustrate our contribution on real data collected from volunteer users
Spectral Lattices of reducible matrices over completed idempotent semifields
Proceedings of: 10th International Conference on Concept Lattices and Their Applications. (CLA 2013). La Rochelle, France, October 15-18, 2013.Previous work has shown a relation between L-valued extensions of FCA and the spectra of some matrices related to L-valued contexts. We investigate the spectra of reducible matrices over completed idempotent semifields in the framework of dioids, naturally-ordered semirings, that encompass several of those extensions. Considering special sets of eigenvectors also brings out complete lattices in the picture and we argue that such structure may be more important than standard eigenspace structure for matrices over completed idempotent semifields.FJVA is supported by EU FP7 project LiMoSINe (contract 288024). CPM has been partially supported by the Spanish Government-Comisión Interministerial de Ciencia y Tecnología project TEC2011-26807 for this paper.Publicad
A Categorical View on Algebraic Lattices in Formal Concept Analysis
Formal concept analysis has grown from a new branch of the mathematical field
of lattice theory to a widely recognized tool in Computer Science and
elsewhere. In order to fully benefit from this theory, we believe that it can
be enriched with notions such as approximation by computation or
representability. The latter are commonly studied in denotational semantics and
domain theory and captured most prominently by the notion of algebraicity, e.g.
of lattices. In this paper, we explore the notion of algebraicity in formal
concept analysis from a category-theoretical perspective. To this end, we build
on the the notion of approximable concept with a suitable category and show
that the latter is equivalent to the category of algebraic lattices. At the
same time, the paper provides a relatively comprehensive account of the
representation theory of algebraic lattices in the framework of Stone duality,
relating well-known structures such as Scott information systems with further
formalisms from logic, topology, domains and lattice theory.Comment: 36 page
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