15,522 research outputs found
Neural Networks for Complex Data
Artificial neural networks are simple and efficient machine learning tools.
Defined originally in the traditional setting of simple vector data, neural
network models have evolved to address more and more difficulties of complex
real world problems, ranging from time evolving data to sophisticated data
structures such as graphs and functions. This paper summarizes advances on
those themes from the last decade, with a focus on results obtained by members
of the SAMM team of Universit\'e Paris
Graphs in machine learning: an introduction
Graphs are commonly used to characterise interactions between objects of
interest. Because they are based on a straightforward formalism, they are used
in many scientific fields from computer science to historical sciences. In this
paper, we give an introduction to some methods relying on graphs for learning.
This includes both unsupervised and supervised methods. Unsupervised learning
algorithms usually aim at visualising graphs in latent spaces and/or clustering
the nodes. Both focus on extracting knowledge from graph topologies. While most
existing techniques are only applicable to static graphs, where edges do not
evolve through time, recent developments have shown that they could be extended
to deal with evolving networks. In a supervised context, one generally aims at
inferring labels or numerical values attached to nodes using both the graph
and, when they are available, node characteristics. Balancing the two sources
of information can be challenging, especially as they can disagree locally or
globally. In both contexts, supervised and un-supervised, data can be
relational (augmented with one or several global graphs) as described above, or
graph valued. In this latter case, each object of interest is given as a full
graph (possibly completed by other characteristics). In this context, natural
tasks include graph clustering (as in producing clusters of graphs rather than
clusters of nodes in a single graph), graph classification, etc. 1 Real
networks One of the first practical studies on graphs can be dated back to the
original work of Moreno [51] in the 30s. Since then, there has been a growing
interest in graph analysis associated with strong developments in the modelling
and the processing of these data. Graphs are now used in many scientific
fields. In Biology [54, 2, 7], for instance, metabolic networks can describe
pathways of biochemical reactions [41], while in social sciences networks are
used to represent relation ties between actors [66, 56, 36, 34]. Other examples
include powergrids [71] and the web [75]. Recently, networks have also been
considered in other areas such as geography [22] and history [59, 39]. In
machine learning, networks are seen as powerful tools to model problems in
order to extract information from data and for prediction purposes. This is the
object of this paper. For more complete surveys, we refer to [28, 62, 49, 45].
In this section, we introduce notations and highlight properties shared by most
real networks. In Section 2, we then consider methods aiming at extracting
information from a unique network. We will particularly focus on clustering
methods where the goal is to find clusters of vertices. Finally, in Section 3,
techniques that take a series of networks into account, where each network i
Magnification Control in Self-Organizing Maps and Neural Gas
We consider different ways to control the magnification in self-organizing
maps (SOM) and neural gas (NG). Starting from early approaches of magnification
control in vector quantization, we then concentrate on different approaches for
SOM and NG. We show that three structurally similar approaches can be applied
to both algorithms: localized learning, concave-convex learning, and winner
relaxing learning. Thereby, the approach of concave-convex learning in SOM is
extended to a more general description, whereas the concave-convex learning for
NG is new. In general, the control mechanisms generate only slightly different
behavior comparing both neural algorithms. However, we emphasize that the NG
results are valid for any data dimension, whereas in the SOM case the results
hold only for the one-dimensional case.Comment: 24 pages, 4 figure
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