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Variable grouping in multivariate time series via correlation
The decomposition of high-dimensional multivariate time series (MTS) into a number of low-dimensional MTS is a useful but challenging task because the number of possible dependencies between variables is likely to be huge. This paper is about a systematic study of the âvariable groupingsâ problem in MTS. In particular, we investigate different methods of utilizing the information regarding correlations among MTS variables. This type of method does not appear to have been studied before. In all, 15 methods are suggested and applied to six datasets where there are identifiable mixed groupings of MTS variables. This paper describes the general methodology, reports extensive experimental results, and concludes with useful insights on the strength and weakness of this type of grouping metho
Community detection for correlation matrices
A challenging problem in the study of complex systems is that of resolving,
without prior information, the emergent, mesoscopic organization determined by
groups of units whose dynamical activity is more strongly correlated internally
than with the rest of the system. The existing techniques to filter
correlations are not explicitly oriented towards identifying such modules and
can suffer from an unavoidable information loss. A promising alternative is
that of employing community detection techniques developed in network theory.
Unfortunately, this approach has focused predominantly on replacing network
data with correlation matrices, a procedure that tends to be intrinsically
biased due to its inconsistency with the null hypotheses underlying the
existing algorithms. Here we introduce, via a consistent redefinition of null
models based on random matrix theory, the appropriate correlation-based
counterparts of the most popular community detection techniques. Our methods
can filter out both unit-specific noise and system-wide dependencies, and the
resulting communities are internally correlated and mutually anti-correlated.
We also implement multiresolution and multifrequency approaches revealing
hierarchically nested sub-communities with `hard' cores and `soft' peripheries.
We apply our techniques to several financial time series and identify
mesoscopic groups of stocks which are irreducible to a standard, sectorial
taxonomy, detect `soft stocks' that alternate between communities, and discuss
implications for portfolio optimization and risk management.Comment: Final version, accepted for publication on PR
Coupled Two-Way Clustering Analysis of Gene Microarray Data
We present a novel coupled two-way clustering approach to gene microarray
data analysis. The main idea is to identify subsets of the genes and samples,
such that when one of these is used to cluster the other, stable and
significant partitions emerge. The search for such subsets is a computationally
complex task: we present an algorithm, based on iterative clustering, which
performs such a search. This analysis is especially suitable for gene
microarray data, where the contributions of a variety of biological mechanisms
to the gene expression levels are entangled in a large body of experimental
data. The method was applied to two gene microarray data sets, on colon cancer
and leukemia. By identifying relevant subsets of the data and focusing on them
we were able to discover partitions and correlations that were masked and
hidden when the full dataset was used in the analysis. Some of these partitions
have clear biological interpretation; others can serve to identify possible
directions for future research
Dynamic fluctuations coincide with periods of high and low modularity in resting-state functional brain networks
We investigate the relationship of resting-state fMRI functional connectivity
estimated over long periods of time with time-varying functional connectivity
estimated over shorter time intervals. We show that using Pearson's correlation
to estimate functional connectivity implies that the range of fluctuations of
functional connections over short time scales is subject to statistical
constraints imposed by their connectivity strength over longer scales. We
present a method for estimating time-varying functional connectivity that is
designed to mitigate this issue and allows us to identify episodes where
functional connections are unexpectedly strong or weak. We apply this method to
data recorded from participants, and show that the number of
unexpectedly strong/weak connections fluctuates over time, and that these
variations coincide with intermittent periods of high and low modularity in
time-varying functional connectivity. We also find that during periods of
relative quiescence regions associated with default mode network tend to join
communities with attentional, control, and primary sensory systems. In
contrast, during periods where many connections are unexpectedly strong/weak,
default mode regions dissociate and form distinct modules. Finally, we go on to
show that, while all functional connections can at times manifest stronger
(more positively correlated) or weaker (more negatively correlated) than
expected, a small number of connections, mostly within the visual and
somatomotor networks, do so a disproportional number of times. Our statistical
approach allows the detection of functional connections that fluctuate more or
less than expected based on their long-time averages and may be of use in
future studies characterizing the spatio-temporal patterns of time-varying
functional connectivityComment: 47 Pages, 8 Figures, 4 Supplementary Figure
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