16,331 research outputs found
A Quantitative Clustering Approach to Ultrametricity in Spin Glasses
We discuss the problem of ultrametricity in mean field spin glasses by means
of a hierarchical clustering algorithm. We complement the clustering approach
with quantitative testing: we discuss both in some detail. We show that the
elimination of the (in this context accidental) spin flip symmetry plays a
crucial role in the analysis, since the symmetry hides the real nature of the
data. We are able to use in the analysis disorder averaged quantities. We are
able to exhibit a number of features of the low phase of the mean field
theory, and to claim that the full hierarchical structure can be observed
without ambiguities only on very large lattice volumes, not currently
accessible by numerical simulations.Comment: 15 pages with color figure
The Haar Wavelet Transform of a Dendrogram: Additional Notes
We consider the wavelet transform of a finite, rooted, node-ranked, -way
tree, focusing on the case of binary () trees. We study a Haar wavelet
transform on this tree. Wavelet transforms allow for multiresolution analysis
through translation and dilation of a wavelet function. We explore how this
works in our tree context.Comment: 37 pp, 1 fig. Supplementary material to "The Haar Wavelet Transform
of a Dendrogram", http://arxiv.org/abs/cs.IR/060810
A spatial analysis of multivariate output from regional climate models
Climate models have become an important tool in the study of climate and
climate change, and ensemble experiments consisting of multiple climate-model
runs are used in studying and quantifying the uncertainty in climate-model
output. However, there are often only a limited number of model runs available
for a particular experiment, and one of the statistical challenges is to
characterize the distribution of the model output. To that end, we have
developed a multivariate hierarchical approach, at the heart of which is a new
representation of a multivariate Markov random field. This approach allows for
flexible modeling of the multivariate spatial dependencies, including the
cross-dependencies between variables. We demonstrate this statistical model on
an ensemble arising from a regional-climate-model experiment over the western
United States, and we focus on the projected change in seasonal temperature and
precipitation over the next 50 years.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS369 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Resolving structural variability in network models and the brain
Large-scale white matter pathways crisscrossing the cortex create a complex
pattern of connectivity that underlies human cognitive function. Generative
mechanisms for this architecture have been difficult to identify in part
because little is known about mechanistic drivers of structured networks. Here
we contrast network properties derived from diffusion spectrum imaging data of
the human brain with 13 synthetic network models chosen to probe the roles of
physical network embedding and temporal network growth. We characterize both
the empirical and synthetic networks using familiar diagnostics presented in
statistical form, as scatter plots and distributions, to reveal the full range
of variability of each measure across scales in the network. We focus on the
degree distribution, degree assortativity, hierarchy, topological Rentian
scaling, and topological fractal scaling---in addition to several summary
statistics, including the mean clustering coefficient, shortest path length,
and network diameter. The models are investigated in a progressive, branching
sequence, aimed at capturing different elements thought to be important in the
brain, and range from simple random and regular networks, to models that
incorporate specific growth rules and constraints. We find that synthetic
models that constrain the network nodes to be embedded in anatomical brain
regions tend to produce distributions that are similar to those extracted from
the brain. We also find that network models hardcoded to display one network
property do not in general also display a second, suggesting that multiple
neurobiological mechanisms might be at play in the development of human brain
network architecture. Together, the network models that we develop and employ
provide a potentially useful starting point for the statistical inference of
brain network structure from neuroimaging data.Comment: 24 pages, 11 figures, 1 table, supplementary material
Combining Clustering techniques and Formal Concept Analysis to characterize Interestingness Measures
Formal Concept Analysis "FCA" is a data analysis method which enables to
discover hidden knowledge existing in data. A kind of hidden knowledge
extracted from data is association rules. Different quality measures were
reported in the literature to extract only relevant association rules. Given a
dataset, the choice of a good quality measure remains a challenging task for a
user. Given a quality measures evaluation matrix according to semantic
properties, this paper describes how FCA can highlight quality measures with
similar behavior in order to help the user during his choice. The aim of this
article is the discovery of Interestingness Measures "IM" clusters, able to
validate those found due to the hierarchical and partitioning clustering
methods "AHC" and "k-means". Then, based on the theoretical study of sixty one
interestingness measures according to nineteen properties, proposed in a recent
study, "FCA" describes several groups of measures.Comment: 13 pages, 2 figure
Hierarchical growing cell structures: TreeGCS
We propose a hierarchical clustering algorithm (TreeGCS) based upon the Growing Cell Structure (GCS) neural network of Fritzke. Our algorithm refines and builds upon the GCS base, overcoming an inconsistency in the original GCS algorithm, where the network topology is susceptible to the ordering of the input vectors. Our algorithm is unsupervised, flexible, and dynamic and we have imposed no additional parameters on the underlying GCS algorithm. Our ultimate aim is a hierarchical clustering neural network that is both consistent and stable and identifies the innate hierarchical structure present in vector-based data. We demonstrate improved stability of the GCS foundation and evaluate our algorithm against the hierarchy generated by an ascendant hierarchical clustering dendogram. Our approach emulates the hierarchical clustering of the dendogram. It demonstrates the importance of the parameter settings for GCS and how they affect the stability of the clustering
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