2,144 research outputs found
A Regularized Graph Layout Framework for Dynamic Network Visualization
Many real-world networks, including social and information networks, are
dynamic structures that evolve over time. Such dynamic networks are typically
visualized using a sequence of static graph layouts. In addition to providing a
visual representation of the network structure at each time step, the sequence
should preserve the mental map between layouts of consecutive time steps to
allow a human to interpret the temporal evolution of the network. In this
paper, we propose a framework for dynamic network visualization in the on-line
setting where only present and past graph snapshots are available to create the
present layout. The proposed framework creates regularized graph layouts by
augmenting the cost function of a static graph layout algorithm with a grouping
penalty, which discourages nodes from deviating too far from other nodes
belonging to the same group, and a temporal penalty, which discourages large
node movements between consecutive time steps. The penalties increase the
stability of the layout sequence, thus preserving the mental map. We introduce
two dynamic layout algorithms within the proposed framework, namely dynamic
multidimensional scaling (DMDS) and dynamic graph Laplacian layout (DGLL). We
apply these algorithms on several data sets to illustrate the importance of
both grouping and temporal regularization for producing interpretable
visualizations of dynamic networks.Comment: To appear in Data Mining and Knowledge Discovery, supporting material
(animations and MATLAB toolbox) available at
http://tbayes.eecs.umich.edu/xukevin/visualization_dmkd_201
A deep matrix factorization method for learning attribute representations
Semi-Non-negative Matrix Factorization is a technique that learns a
low-dimensional representation of a dataset that lends itself to a clustering
interpretation. It is possible that the mapping between this new representation
and our original data matrix contains rather complex hierarchical information
with implicit lower-level hidden attributes, that classical one level
clustering methodologies can not interpret. In this work we propose a novel
model, Deep Semi-NMF, that is able to learn such hidden representations that
allow themselves to an interpretation of clustering according to different,
unknown attributes of a given dataset. We also present a semi-supervised
version of the algorithm, named Deep WSF, that allows the use of (partial)
prior information for each of the known attributes of a dataset, that allows
the model to be used on datasets with mixed attribute knowledge. Finally, we
show that our models are able to learn low-dimensional representations that are
better suited for clustering, but also classification, outperforming
Semi-Non-negative Matrix Factorization, but also other state-of-the-art
methodologies variants.Comment: Submitted to TPAMI (16-Mar-2015
Optimization with Sparsity-Inducing Penalties
Sparse estimation methods are aimed at using or obtaining parsimonious
representations of data or models. They were first dedicated to linear variable
selection but numerous extensions have now emerged such as structured sparsity
or kernel selection. It turns out that many of the related estimation problems
can be cast as convex optimization problems by regularizing the empirical risk
with appropriate non-smooth norms. The goal of this paper is to present from a
general perspective optimization tools and techniques dedicated to such
sparsity-inducing penalties. We cover proximal methods, block-coordinate
descent, reweighted -penalized techniques, working-set and homotopy
methods, as well as non-convex formulations and extensions, and provide an
extensive set of experiments to compare various algorithms from a computational
point of view
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