7,913 research outputs found
Empirical comparison of the performance of location estimates of fuzzy number-valued data
© Springer Nature Switzerland AG 2019. Several location measures have already been proposed in the literature in order to summarize the central tendency of a random fuzzy number in a robust way. Among them, fuzzy trimmed means and fuzzy M-estimators of location extend two successful approaches from the real-valued settings. The aim of this work is to present an empirical comparison of different location estimators, including both fuzzy trimmed means and fuzzy M-estimators, to study their differences in finite sample behaviour.status: publishe
Possibilistic and fuzzy clustering methods for robust analysis of non-precise data
This work focuses on robust clustering of data affected by imprecision. The imprecision is managed in terms of fuzzy sets. The clustering process is based on the fuzzy and possibilistic approaches. In both approaches the observations are assigned to the clusters by means of membership degrees. In fuzzy clustering the membership degrees express the degrees of sharing of the observations to the clusters. In contrast, in possibilistic clustering the membership degrees are degrees of typicality. These two sources of information are complementary because the former helps to discover the best fuzzy partition of the observations while the latter reflects how well the observations are described by the centroids and, therefore, is helpful to identify outliers. First, a fully possibilistic k-means clustering procedure is suggested. Then, in order to exploit the benefits of both the approaches, a joint possibilistic and fuzzy clustering method for fuzzy data is proposed. A selection procedure for choosing the parameters of the new clustering method is introduced. The effectiveness of the proposal is investigated by means of simulated and
real-life data
Optimizing an Organized Modularity Measure for Topographic Graph Clustering: a Deterministic Annealing Approach
This paper proposes an organized generalization of Newman and Girvan's
modularity measure for graph clustering. Optimized via a deterministic
annealing scheme, this measure produces topologically ordered graph clusterings
that lead to faithful and readable graph representations based on clustering
induced graphs. Topographic graph clustering provides an alternative to more
classical solutions in which a standard graph clustering method is applied to
build a simpler graph that is then represented with a graph layout algorithm. A
comparative study on four real world graphs ranging from 34 to 1 133 vertices
shows the interest of the proposed approach with respect to classical solutions
and to self-organizing maps for graphs
Lectures on Holographic Space Time
Summary of three talks on the Holographic Space Time models of early universe
cosmology, particle physics, and the asymptotically de Sitter final state of
our universe.Comment: LaTex2e. 32 page
Making inferences with small numbers of training sets
A potential methodological problem with empirical studies that assess project effort prediction system is discussed. Frequently, a hold-out strategy is deployed so that the data set is split into a training and a validation set. Inferences are then made concerning the relative accuracy of the different prediction techniques under examination. This is typically done on very small numbers of sampled training sets. It is shown that such studies can lead to almost random results (particularly where relatively small effects are being studied). To illustrate this problem, two data sets are analysed using a configuration problem for case-based prediction and results generated from 100 training sets. This enables results to be produced with quantified confidence limits. From this it is concluded that in both cases using less than five training sets leads to untrustworthy results, and ideally more than 20 sets should be deployed. Unfortunately, this raises a question over a number of empirical validations of prediction techniques, and so it is suggested that further research is needed as a matter of urgency
A copula-based approach to aggregation functions
This paper presents the role of copula functions in the theory of aggregation operators and an axiomatic characterization of Archimedean aggregation functions. In this context we are focusing our attention about several properties of aggregation functions, like supermodularity and Schur-concavity.Aggregation functions, supermodularity, Schur-concavity, copula, Archimedean copulae
Properties of Dark Matter Haloes in Clusters, Filaments, Sheets and Voids
Using a series of high-resolution N-body simulations of the concordance
cosmology we investigate how the formation histories, shapes and angular
momenta of dark-matter haloes depend on environment. We first present a
classification scheme that allows to distinguish between haloes in clusters,
filaments, sheets and voids in the large-scale distribution of matter. This
method is based on a local-stability criterion for the orbits of test particles
and closely relates to the Zel'dovich approximation. Applying this scheme to
our simulations we then find that: i) Mass assembly histories and formation
redshifts strongly depend on environment for haloes of mass M<M* (haloes of a
given mass tend to be older in clusters and younger in voids) and are
independent of it for larger masses; ii) Low-mass haloes in clusters are
generally less spherical and more oblate than in other regions; iii) Low-mass
haloes in clusters have a higher median spin than in filaments and present a
more prominent fraction of rapidly spinning objects; we identify recent major
mergers as a likely source of this effect. For all these relations, we provide
accurate functional fits as a function of halo mass and environment. We also
look for correlations between halo-spin directions and the large-scale
structures: the strongest effect is seen in sheets where halo spins tend to lie
within the plane of symmetry of the mass distribution. Finally, we measure the
spatial auto-correlation of spin directions and the cross-correlation between
the directions of intrinsic and orbital angular momenta of neighbouring haloes.
While the first quantity is always very small, we find that spin-orbit
correlations are rather strong especially for low-mass haloes in clusters and
high-mass haloes in filaments.Comment: 13 pages, 13 figures. Version accepted for publication in MNRAS
(references added). Version with high-resolution figures available at
http://www.exp-astro.phys.ethz.ch/hahn/pub/HPCD06.pd
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