29,493 research outputs found
Multiscale Granger causality analysis by \`a trous wavelet transform
Since interactions in neural systems occur across multiple temporal scales,
it is likely that information flow will exhibit a multiscale structure, thus
requiring a multiscale generalization of classical temporal precedence
causality analysis like Granger's approach. However, the computation of
multiscale measures of information dynamics is complicated by theoretical and
practical issues such as filtering and undersampling: to overcome these
problems, we propose a wavelet-based approach for multiscale Granger causality
(GC) analysis, which is characterized by the following properties: (i) only the
candidate driver variable is wavelet transformed (ii) the decomposition is
performed using the \`a trous wavelet transform with cubic B-spline filter. We
measure GC, at a given scale, by including the wavelet coefficients of the
driver times series, at that scale, in the regression model of the target. To
validate our method, we apply it to publicly available scalp EEG signals, and
we find that the condition of closed eyes, at rest, is characterized by an
enhanced GC among channels at slow scales w.r.t. eye open condition, whilst the
standard Granger causality is not significantly different in the two
conditions.Comment: 4 pages, 3 figure
Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System
Peer reviewedPublisher PD
Deep Dictionary Learning: A PARametric NETwork Approach
Deep dictionary learning seeks multiple dictionaries at different image
scales to capture complementary coherent characteristics. We propose a method
for learning a hierarchy of synthesis dictionaries with an image classification
goal. The dictionaries and classification parameters are trained by a
classification objective, and the sparse features are extracted by reducing a
reconstruction loss in each layer. The reconstruction objectives in some sense
regularize the classification problem and inject source signal information in
the extracted features. The performance of the proposed hierarchical method
increases by adding more layers, which consequently makes this model easier to
tune and adapt. The proposed algorithm furthermore, shows remarkably lower
fooling rate in presence of adversarial perturbation. The validation of the
proposed approach is based on its classification performance using four
benchmark datasets and is compared to a CNN of similar size
Inference of hidden structures in complex physical systems by multi-scale clustering
We survey the application of a relatively new branch of statistical
physics--"community detection"-- to data mining. In particular, we focus on the
diagnosis of materials and automated image segmentation. Community detection
describes the quest of partitioning a complex system involving many elements
into optimally decoupled subsets or communities of such elements. We review a
multiresolution variant which is used to ascertain structures at different
spatial and temporal scales. Significant patterns are obtained by examining the
correlations between different independent solvers. Similar to other
combinatorial optimization problems in the NP complexity class, community
detection exhibits several phases. Typically, illuminating orders are revealed
by choosing parameters that lead to extremal information theory correlations.Comment: 25 pages, 16 Figures; a review of earlier work
Post-processing partitions to identify domains of modularity optimization
We introduce the Convex Hull of Admissible Modularity Partitions (CHAMP)
algorithm to prune and prioritize different network community structures
identified across multiple runs of possibly various computational heuristics.
Given a set of partitions, CHAMP identifies the domain of modularity
optimization for each partition ---i.e., the parameter-space domain where it
has the largest modularity relative to the input set---discarding partitions
with empty domains to obtain the subset of partitions that are "admissible"
candidate community structures that remain potentially optimal over indicated
parameter domains. Importantly, CHAMP can be used for multi-dimensional
parameter spaces, such as those for multilayer networks where one includes a
resolution parameter and interlayer coupling. Using the results from CHAMP, a
user can more appropriately select robust community structures by observing the
sizes of domains of optimization and the pairwise comparisons between
partitions in the admissible subset. We demonstrate the utility of CHAMP with
several example networks. In these examples, CHAMP focuses attention onto
pruned subsets of admissible partitions that are 20-to-1785 times smaller than
the sets of unique partitions obtained by community detection heuristics that
were input into CHAMP.Comment: http://www.mdpi.com/1999-4893/10/3/9
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