5,899 research outputs found
Graph learning under sparsity priors
Graph signals offer a very generic and natural representation for data that
lives on networks or irregular structures. The actual data structure is however
often unknown a priori but can sometimes be estimated from the knowledge of the
application domain. If this is not possible, the data structure has to be
inferred from the mere signal observations. This is exactly the problem that we
address in this paper, under the assumption that the graph signals can be
represented as a sparse linear combination of a few atoms of a structured graph
dictionary. The dictionary is constructed on polynomials of the graph
Laplacian, which can sparsely represent a general class of graph signals
composed of localized patterns on the graph. We formulate a graph learning
problem, whose solution provides an ideal fit between the signal observations
and the sparse graph signal model. As the problem is non-convex, we propose to
solve it by alternating between a signal sparse coding and a graph update step.
We provide experimental results that outline the good graph recovery
performance of our method, which generally compares favourably to other recent
network inference algorithms
A Primer on Reproducing Kernel Hilbert Spaces
Reproducing kernel Hilbert spaces are elucidated without assuming prior
familiarity with Hilbert spaces. Compared with extant pedagogic material,
greater care is placed on motivating the definition of reproducing kernel
Hilbert spaces and explaining when and why these spaces are efficacious. The
novel viewpoint is that reproducing kernel Hilbert space theory studies
extrinsic geometry, associating with each geometric configuration a canonical
overdetermined coordinate system. This coordinate system varies continuously
with changing geometric configurations, making it well-suited for studying
problems whose solutions also vary continuously with changing geometry. This
primer can also serve as an introduction to infinite-dimensional linear algebra
because reproducing kernel Hilbert spaces have more properties in common with
Euclidean spaces than do more general Hilbert spaces.Comment: Revised version submitted to Foundations and Trends in Signal
Processin
Distributed Dictionary Learning
The paper studies distributed Dictionary Learning (DL) problems where the
learning task is distributed over a multi-agent network with time-varying
(nonsymmetric) connectivity. This formulation is relevant, for instance, in
big-data scenarios where massive amounts of data are collected/stored in
different spatial locations and it is unfeasible to aggregate and/or process
all the data in a fusion center, due to resource limitations, communication
overhead or privacy considerations. We develop a general distributed
algorithmic framework for the (nonconvex) DL problem and establish its
asymptotic convergence. The new method hinges on Successive Convex
Approximation (SCA) techniques coupled with i) a gradient tracking mechanism
instrumental to locally estimate the missing global information; and ii) a
consensus step, as a mechanism to distribute the computations among the agents.
To the best of our knowledge, this is the first distributed algorithm with
provable convergence for the DL problem and, more in general, bi-convex
optimization problems over (time-varying) directed graphs
An agent-driven semantical identifier using radial basis neural networks and reinforcement learning
Due to the huge availability of documents in digital form, and the deception
possibility raise bound to the essence of digital documents and the way they
are spread, the authorship attribution problem has constantly increased its
relevance. Nowadays, authorship attribution,for both information retrieval and
analysis, has gained great importance in the context of security, trust and
copyright preservation. This work proposes an innovative multi-agent driven
machine learning technique that has been developed for authorship attribution.
By means of a preprocessing for word-grouping and time-period related analysis
of the common lexicon, we determine a bias reference level for the recurrence
frequency of the words within analysed texts, and then train a Radial Basis
Neural Networks (RBPNN)-based classifier to identify the correct author. The
main advantage of the proposed approach lies in the generality of the semantic
analysis, which can be applied to different contexts and lexical domains,
without requiring any modification. Moreover, the proposed system is able to
incorporate an external input, meant to tune the classifier, and then
self-adjust by means of continuous learning reinforcement.Comment: Published on: Proceedings of the XV Workshop "Dagli Oggetti agli
Agenti" (WOA 2014), Catania, Italy, Sepember. 25-26, 201
Learning parametric dictionaries for graph signals
In sparse signal representation, the choice of a dictionary often involves a
tradeoff between two desirable properties -- the ability to adapt to specific
signal data and a fast implementation of the dictionary. To sparsely represent
signals residing on weighted graphs, an additional design challenge is to
incorporate the intrinsic geometric structure of the irregular data domain into
the atoms of the dictionary. In this work, we propose a parametric dictionary
learning algorithm to design data-adapted, structured dictionaries that
sparsely represent graph signals. In particular, we model graph signals as
combinations of overlapping local patterns. We impose the constraint that each
dictionary is a concatenation of subdictionaries, with each subdictionary being
a polynomial of the graph Laplacian matrix, representing a single pattern
translated to different areas of the graph. The learning algorithm adapts the
patterns to a training set of graph signals. Experimental results on both
synthetic and real datasets demonstrate that the dictionaries learned by the
proposed algorithm are competitive with and often better than unstructured
dictionaries learned by state-of-the-art numerical learning algorithms in terms
of sparse approximation of graph signals. In contrast to the unstructured
dictionaries, however, the dictionaries learned by the proposed algorithm
feature localized atoms and can be implemented in a computationally efficient
manner in signal processing tasks such as compression, denoising, and
classification
Graph Signal Processing: Overview, Challenges and Applications
Research in Graph Signal Processing (GSP) aims to develop tools for
processing data defined on irregular graph domains. In this paper we first
provide an overview of core ideas in GSP and their connection to conventional
digital signal processing. We then summarize recent developments in developing
basic GSP tools, including methods for sampling, filtering or graph learning.
Next, we review progress in several application areas using GSP, including
processing and analysis of sensor network data, biological data, and
applications to image processing and machine learning. We finish by providing a
brief historical perspective to highlight how concepts recently developed in
GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE
- …