237,423 research outputs found
On mining complex sequential data by means of FCA and pattern structures
Nowadays data sets are available in very complex and heterogeneous ways.
Mining of such data collections is essential to support many real-world
applications ranging from healthcare to marketing. In this work, we focus on
the analysis of "complex" sequential data by means of interesting sequential
patterns. We approach the problem using the elegant mathematical framework of
Formal Concept Analysis (FCA) and its extension based on "pattern structures".
Pattern structures are used for mining complex data (such as sequences or
graphs) and are based on a subsumption operation, which in our case is defined
with respect to the partial order on sequences. We show how pattern structures
along with projections (i.e., a data reduction of sequential structures), are
able to enumerate more meaningful patterns and increase the computing
efficiency of the approach. Finally, we show the applicability of the presented
method for discovering and analyzing interesting patient patterns from a French
healthcare data set on cancer. The quantitative and qualitative results (with
annotations and analysis from a physician) are reported in this use case which
is the main motivation for this work.
Keywords: data mining; formal concept analysis; pattern structures;
projections; sequences; sequential data.Comment: An accepted publication in International Journal of General Systems.
The paper is created in the wake of the conference on Concept Lattice and
their Applications (CLA'2013). 27 pages, 9 figures, 3 table
The Foundation of Pattern Structures and their Applications
This thesis is divided into a theoretical part, aimed at developing statements around the newly introduced concept of pattern morphisms, and a practical part, where we present use cases of pattern structures.
A first insight of our work clarifies the facts on projections of pattern structures. We discovered that a projection of a pattern structure does not always lead again to a pattern structure.
A solution to this problem, and one of the most important points of this thesis, is the introduction of pattern morphisms in Chapter4. Pattern morphisms make it possible to describe relationships between pattern structures, and thus enable a deeper understanding of pattern structures in general. They also provide the means to describe projections of pattern structures that lead to pattern structures again. In Chapter5 and Chapter6, we looked at the impact of morphisms between pattern structures on concept lattices and on their representations and thus clarified the theoretical background of existing research in this field.
The application part reveals that random forests can be described through pattern structures, which constitutes another central achievement of our work.
In order to demonstrate the practical relevance of our findings, we included a use case where this finding is used to build an algorithm that solves a real world classification problem of red wines. The prediction accuracy of the random forest is better, but the high interpretability makes our algorithm valuable.
Another approach to the red wine classification problem is presented in Chapter 8, where, starting from an elementary pattern structure, we built a classification model that yielded good results
Some results on designs of resolution IV with (weak) minimum aberration
It is known that all resolution IV regular designs of run size
where must be projections of the maximal even design
with factors and, therefore, are even designs. This paper derives a
general and explicit relationship between the wordlength pattern of any even
design and that of its complement in the maximal even design. Using
these identities, we identify some (weak) minimum aberration designs
of resolution IV and the structures of their complementary designs. Based on
these results, several families of minimum aberration designs of
resolution IV are constructed.Comment: Published in at http://dx.doi.org/10.1214/08-AOS670 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Optical M0bius Strips in Three Dimensional Ellipse Fields: Lines of Linear Polarization
The minor axes of, and the normals to, the polarization ellipses that
surround singular lines of linear polarization in three dimensional optical
ellipse fields are shown to be organized into Mobius strips and into structures
we call rippled rings (r-rings). The Mobius strips have two full twists, and
can be either right- or left-handed. The major axes of the surrounding ellipses
generate cone-like structures. Three orthogonal projections that give rise to
15 indices are used to characterize the different structures. These indices, if
independent, could generate 839,808 geometrically and topologically distinct
lines; selection rules are presented that reduce the number of lines to 8,248,
some 5,562 of which have been observed in a computer simulation. Statistical
probabilities are presented for the most important index combinations in random
fields. It is argued that it is presently feasible to perform experimental
measurements of the Mobius strips, r-rings, and cones described here
theoretically
Families of superhard crystalline carbon allotropes induced via cold-compressed graphite and nanotubes
We report a general scheme to systematically construct two classes of
structural families of superhard sp3 carbon allotropes of cold compressed
graphite through the topological analysis of odd 5+7 or even 4+8 membered
carbon rings stemmed from the stacking of zigzag and armchair chains. Our
results show that the previously proposed M, bct-C4, W and Z allotropes belong
to our currently proposed families and that depending on the topological
arrangement of the native carbon rings numerous other members are found that
can help us understand the structural phase transformation of cold-compressed
graphite and carbon nanotubes (CNTs). In particular, we predict the existence
of two simple allotropes, R- and P-carbon, which match well the experimental
X-ray diffraction patterns of cold-compressed graphite and CNTs, respectively,
display a transparent wide-gap insulator ground state and possess a large
Vickers hardness comparable to diamond.Comment: 5 pages, 4 figures, accepted by Phys. Rev. Let
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