9,630 research outputs found
A Multiscale Pyramid Transform for Graph Signals
Multiscale transforms designed to process analog and discrete-time signals
and images cannot be directly applied to analyze high-dimensional data residing
on the vertices of a weighted graph, as they do not capture the intrinsic
geometric structure of the underlying graph data domain. In this paper, we
adapt the Laplacian pyramid transform for signals on Euclidean domains so that
it can be used to analyze high-dimensional data residing on the vertices of a
weighted graph. Our approach is to study existing methods and develop new
methods for the four fundamental operations of graph downsampling, graph
reduction, and filtering and interpolation of signals on graphs. Equipped with
appropriate notions of these operations, we leverage the basic multiscale
constructs and intuitions from classical signal processing to generate a
transform that yields both a multiresolution of graphs and an associated
multiresolution of a graph signal on the underlying sequence of graphs.Comment: 16 pages, 13 figure
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
Multi-view Metric Learning in Vector-valued Kernel Spaces
We consider the problem of metric learning for multi-view data and present a
novel method for learning within-view as well as between-view metrics in
vector-valued kernel spaces, as a way to capture multi-modal structure of the
data. We formulate two convex optimization problems to jointly learn the metric
and the classifier or regressor in kernel feature spaces. An iterative
three-step multi-view metric learning algorithm is derived from the
optimization problems. In order to scale the computation to large training
sets, a block-wise Nystr{\"o}m approximation of the multi-view kernel matrix is
introduced. We justify our approach theoretically and experimentally, and show
its performance on real-world datasets against relevant state-of-the-art
methods
Data-Driven Shape Analysis and Processing
Data-driven methods play an increasingly important role in discovering
geometric, structural, and semantic relationships between 3D shapes in
collections, and applying this analysis to support intelligent modeling,
editing, and visualization of geometric data. In contrast to traditional
approaches, a key feature of data-driven approaches is that they aggregate
information from a collection of shapes to improve the analysis and processing
of individual shapes. In addition, they are able to learn models that reason
about properties and relationships of shapes without relying on hard-coded
rules or explicitly programmed instructions. We provide an overview of the main
concepts and components of these techniques, and discuss their application to
shape classification, segmentation, matching, reconstruction, modeling and
exploration, as well as scene analysis and synthesis, through reviewing the
literature and relating the existing works with both qualitative and numerical
comparisons. We conclude our report with ideas that can inspire future research
in data-driven shape analysis and processing.Comment: 10 pages, 19 figure
Advances in Hyperspectral Image Classification: Earth monitoring with statistical learning methods
Hyperspectral images show similar statistical properties to natural grayscale
or color photographic images. However, the classification of hyperspectral
images is more challenging because of the very high dimensionality of the
pixels and the small number of labeled examples typically available for
learning. These peculiarities lead to particular signal processing problems,
mainly characterized by indetermination and complex manifolds. The framework of
statistical learning has gained popularity in the last decade. New methods have
been presented to account for the spatial homogeneity of images, to include
user's interaction via active learning, to take advantage of the manifold
structure with semisupervised learning, to extract and encode invariances, or
to adapt classifiers and image representations to unseen yet similar scenes.
This tutuorial reviews the main advances for hyperspectral remote sensing image
classification through illustrative examples.Comment: IEEE Signal Processing Magazine, 201
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