10,523 research outputs found
A comparison of two techniques for bibliometric mapping: Multidimensional scaling and VOS
VOS is a new mapping technique that can serve as an alternative to the
well-known technique of multidimensional scaling. We present an extensive
comparison between the use of multidimensional scaling and the use of VOS for
constructing bibliometric maps. In our theoretical analysis, we show the
mathematical relation between the two techniques. In our experimental analysis,
we use the techniques for constructing maps of authors, journals, and keywords.
Two commonly used approaches to bibliometric mapping, both based on
multidimensional scaling, turn out to produce maps that suffer from artifacts.
Maps constructed using VOS turn out not to have this problem. We conclude that
in general maps constructed using VOS provide a more satisfactory
representation of a data set than maps constructed using well-known
multidimensional scaling approaches
Structured sampling and fast reconstruction of smooth graph signals
This work concerns sampling of smooth signals on arbitrary graphs. We first
study a structured sampling strategy for such smooth graph signals that
consists of a random selection of few pre-defined groups of nodes. The number
of groups to sample to stably embed the set of -bandlimited signals is
driven by a quantity called the \emph{group} graph cumulative coherence. For
some optimised sampling distributions, we show that sampling
groups is always sufficient to stably embed the set of -bandlimited signals
but that this number can be smaller -- down to -- depending on the
structure of the groups of nodes. Fast methods to approximate these sampling
distributions are detailed. Second, we consider -bandlimited signals that
are nearly piecewise constant over pre-defined groups of nodes. We show that it
is possible to speed up the reconstruction of such signals by reducing
drastically the dimension of the vectors to reconstruct. When combined with the
proposed structured sampling procedure, we prove that the method provides
stable and accurate reconstruction of the original signal. Finally, we present
numerical experiments that illustrate our theoretical results and, as an
example, show how to combine these methods for interactive object segmentation
in an image using superpixels
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