25 research outputs found
Using the Chu construction for generalizing formal concept analysis
Abstract. The goal of this paper is to show a connection between FCA generalisations and the Chu construction on the category ChuCors, the category of formal contexts and Chu correspondences. All needed categorical properties like categorical product, tensor product and its bifunctor properties are presented and proved. Finally, the second order generalisation of FCA is represented by a category built up in terms of the Chu construction
Structure of the icosahedral Ti-Zr-Ni quasicrystal
The atomic structure of the icosahedral Ti-Zr-Ni quasicrystal is determined
by invoking similarities to periodic crystalline phases, diffraction data and
the results from ab initio calculations. The structure is modeled by
decorations of the canonical cell tiling geometry. The initial decoration model
is based on the structure of the Frank-Kasper phase W-TiZrNi, the 1/1
approximant structure of the quasicrystal. The decoration model is optimized
using a new method of structural analysis combining a least-squares refinement
of diffraction data with results from ab initio calculations. The resulting
structural model of icosahedral Ti-Zr-Ni is interpreted as a simple decoration
rule and structural details are discussed.Comment: 12 pages, 8 figure
Quantitative Concept Analysis
Formal Concept Analysis (FCA) begins from a context, given as a binary
relation between some objects and some attributes, and derives a lattice of
concepts, where each concept is given as a set of objects and a set of
attributes, such that the first set consists of all objects that satisfy all
attributes in the second, and vice versa. Many applications, though, provide
contexts with quantitative information, telling not just whether an object
satisfies an attribute, but also quantifying this satisfaction. Contexts in
this form arise as rating matrices in recommender systems, as occurrence
matrices in text analysis, as pixel intensity matrices in digital image
processing, etc. Such applications have attracted a lot of attention, and
several numeric extensions of FCA have been proposed. We propose the framework
of proximity sets (proxets), which subsume partially ordered sets (posets) as
well as metric spaces. One feature of this approach is that it extracts from
quantified contexts quantified concepts, and thus allows full use of the
available information. Another feature is that the categorical approach allows
analyzing any universal properties that the classical FCA and the new versions
may have, and thus provides structural guidance for aligning and combining the
approaches.Comment: 16 pages, 3 figures, ICFCA 201