1,257 research outputs found
Matrix completion and extrapolation via kernel regression
Matrix completion and extrapolation (MCEX) are dealt with here over
reproducing kernel Hilbert spaces (RKHSs) in order to account for prior
information present in the available data. Aiming at a faster and
low-complexity solver, the task is formulated as a kernel ridge regression. The
resultant MCEX algorithm can also afford online implementation, while the class
of kernel functions also encompasses several existing approaches to MC with
prior information. Numerical tests on synthetic and real datasets show that the
novel approach performs faster than widespread methods such as alternating
least squares (ALS) or stochastic gradient descent (SGD), and that the recovery
error is reduced, especially when dealing with noisy data
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
Group-Lasso on Splines for Spectrum Cartography
The unceasing demand for continuous situational awareness calls for
innovative and large-scale signal processing algorithms, complemented by
collaborative and adaptive sensing platforms to accomplish the objectives of
layered sensing and control. Towards this goal, the present paper develops a
spline-based approach to field estimation, which relies on a basis expansion
model of the field of interest. The model entails known bases, weighted by
generic functions estimated from the field's noisy samples. A novel field
estimator is developed based on a regularized variational least-squares (LS)
criterion that yields finitely-parameterized (function) estimates spanned by
thin-plate splines. Robustness considerations motivate well the adoption of an
overcomplete set of (possibly overlapping) basis functions, while a sparsifying
regularizer augmenting the LS cost endows the estimator with the ability to
select a few of these bases that ``better'' explain the data. This parsimonious
field representation becomes possible, because the sparsity-aware spline-based
method of this paper induces a group-Lasso estimator for the coefficients of
the thin-plate spline expansions per basis. A distributed algorithm is also
developed to obtain the group-Lasso estimator using a network of wireless
sensors, or, using multiple processors to balance the load of a single
computational unit. The novel spline-based approach is motivated by a spectrum
cartography application, in which a set of sensing cognitive radios collaborate
to estimate the distribution of RF power in space and frequency. Simulated
tests corroborate that the estimated power spectrum density atlas yields the
desired RF state awareness, since the maps reveal spatial locations where idle
frequency bands can be reused for transmission, even when fading and shadowing
effects are pronounced.Comment: Submitted to IEEE Transactions on Signal Processin
Non-convex regularization in remote sensing
In this paper, we study the effect of different regularizers and their
implications in high dimensional image classification and sparse linear
unmixing. Although kernelization or sparse methods are globally accepted
solutions for processing data in high dimensions, we present here a study on
the impact of the form of regularization used and its parametrization. We
consider regularization via traditional squared (2) and sparsity-promoting (1)
norms, as well as more unconventional nonconvex regularizers (p and Log Sum
Penalty). We compare their properties and advantages on several classification
and linear unmixing tasks and provide advices on the choice of the best
regularizer for the problem at hand. Finally, we also provide a fully
functional toolbox for the community.Comment: 11 pages, 11 figure
A Survey on Graph Kernels
Graph kernels have become an established and widely-used technique for
solving classification tasks on graphs. This survey gives a comprehensive
overview of techniques for kernel-based graph classification developed in the
past 15 years. We describe and categorize graph kernels based on properties
inherent to their design, such as the nature of their extracted graph features,
their method of computation and their applicability to problems in practice. In
an extensive experimental evaluation, we study the classification accuracy of a
large suite of graph kernels on established benchmarks as well as new datasets.
We compare the performance of popular kernels with several baseline methods and
study the effect of applying a Gaussian RBF kernel to the metric induced by a
graph kernel. In doing so, we find that simple baselines become competitive
after this transformation on some datasets. Moreover, we study the extent to
which existing graph kernels agree in their predictions (and prediction errors)
and obtain a data-driven categorization of kernels as result. Finally, based on
our experimental results, we derive a practitioner's guide to kernel-based
graph classification
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