1,283 research outputs found
Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs
Laplacian mixture models identify overlapping regions of influence in
unlabeled graph and network data in a scalable and computationally efficient
way, yielding useful low-dimensional representations. By combining Laplacian
eigenspace and finite mixture modeling methods, they provide probabilistic or
fuzzy dimensionality reductions or domain decompositions for a variety of input
data types, including mixture distributions, feature vectors, and graphs or
networks. Provable optimal recovery using the algorithm is analytically shown
for a nontrivial class of cluster graphs. Heuristic approximations for scalable
high-performance implementations are described and empirically tested.
Connections to PageRank and community detection in network analysis demonstrate
the wide applicability of this approach. The origins of fuzzy spectral methods,
beginning with generalized heat or diffusion equations in physics, are reviewed
and summarized. Comparisons to other dimensionality reduction and clustering
methods for challenging unsupervised machine learning problems are also
discussed.Comment: 13 figures, 35 reference
Sparse Predictive Structure of Deconvolved Functional Brain Networks
The functional and structural representation of the brain as a complex
network is marked by the fact that the comparison of noisy and intrinsically
correlated high-dimensional structures between experimental conditions or
groups shuns typical mass univariate methods. Furthermore most network
estimation methods cannot distinguish between real and spurious correlation
arising from the convolution due to nodes' interaction, which thus introduces
additional noise in the data. We propose a machine learning pipeline aimed at
identifying multivariate differences between brain networks associated to
different experimental conditions. The pipeline (1) leverages the deconvolved
individual contribution of each edge and (2) maps the task into a sparse
classification problem in order to construct the associated "sparse deconvolved
predictive network", i.e., a graph with the same nodes of those compared but
whose edge weights are defined by their relevance for out of sample predictions
in classification. We present an application of the proposed method by decoding
the covert attention direction (left or right) based on the single-trial
functional connectivity matrix extracted from high-frequency
magnetoencephalography (MEG) data. Our results demonstrate how network
deconvolution matched with sparse classification methods outperforms typical
approaches for MEG decoding
Complex Networks from Classical to Quantum
Recent progress in applying complex network theory to problems in quantum
information has resulted in a beneficial crossover. Complex network methods
have successfully been applied to transport and entanglement models while
information physics is setting the stage for a theory of complex systems with
quantum information-inspired methods. Novel quantum induced effects have been
predicted in random graphs---where edges represent entangled links---and
quantum computer algorithms have been proposed to offer enhancement for several
network problems. Here we review the results at the cutting edge, pinpointing
the similarities and the differences found at the intersection of these two
fields.Comment: 12 pages, 4 figures, REVTeX 4-1, accepted versio
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