7,079 research outputs found
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
Point: From animal models to prevention of colon cancer. Systematic review of chemoprevention in min mice and choice of the model system.
The Apc(Min/+) mouse model and the azoxymethane (AOM) rat model are the main animal models used to study the effect of dietary agents on colorectal cancer. We reviewed recently the potency of chemopreventive agents in the AOM rat model (D. E. Corpet and S. Tache, Nutr. Cancer, 43: 1-21, 2002). Here we add the results of a systematic review of the effect of dietary and chemopreventive agents on the tumor yield in Min mice. The review is based on the results of 179 studies from 71 articles and is displayed also on the internet http://corpet.net/min.(2) We compared the efficacy of agents in the Min mouse model and the AOM rat model, and found that they were correlated (r = 0.66; P < 0.001), although some agents that afford strong protection in the AOM rat and the Min mouse small bowel increase the tumor yield in the large bowel of mutant mice. The agents included piroxicam, sulindac, celecoxib, difluoromethylornithine, and polyethylene glycol. The reason for this discrepancy is not known. We also compare the results of rodent studies with those of clinical intervention studies of polyp recurrence. We found that the effect of most of the agents tested was consistent across the animal and clinical models. Our point is thus: rodent models can provide guidance in the selection of prevention approaches to human colon cancer, in particular they suggest that polyethylene glycol, hesperidin, protease inhibitor, sphingomyelin, physical exercise, epidermal growth factor receptor kinase inhibitor, (+)-catechin, resveratrol, fish oil, curcumin, caffeate, and thiosulfonate are likely important preventive agents
Well-posed lateral boundary conditions for spectral semi-implicit semi-Lagrangian schemes : tests in a one-dimensional model
The aim of this paper is to investigate the feasibility of well-posed lateral boundary conditions in a Fourier spectral semi-implicit semi-Lagrangian one-dimensional model. Two aspects are analyzed: (i) the complication of designing well-posed boundary conditions for a spectral semi-implicit scheme and (ii) the implications of such a lateral boundary treatment for the semi-Lagrangian trajectory computations at the lateral boundaries.
Straightforwardly imposing boundary conditions in the gridpoint-explicit part of the semi-implicit time-marching scheme leads to numerical instabilities for time steps that are relevant in today's numerical weather prediction applications. It is shown that an iterative scheme is capable of curing these instabilities. This new iterative boundary treatment has been tested in the framework of the one-dimensional shallow-water equations leading to a significant improvement in terms of stability.
As far as the semi-Lagrangian part of the time scheme is concerned, the use of a trajectory truncation scheme has been found to be stable in experimental tests, even for large values of the advective Courant number. It is also demonstrated that a well-posed buffer zone can be successfully applied in this spectral context. A promising (but not easily implemented) alternative to these three above-referenced schemes has been tested and is also presented here
Exact ICL maximization in a non-stationary temporal extension of the stochastic block model for dynamic networks
The stochastic block model (SBM) is a flexible probabilistic tool that can be
used to model interactions between clusters of nodes in a network. However, it
does not account for interactions of time varying intensity between clusters.
The extension of the SBM developed in this paper addresses this shortcoming
through a temporal partition: assuming interactions between nodes are recorded
on fixed-length time intervals, the inference procedure associated with the
model we propose allows to cluster simultaneously the nodes of the network and
the time intervals. The number of clusters of nodes and of time intervals, as
well as the memberships to clusters, are obtained by maximizing an exact
integrated complete-data likelihood, relying on a greedy search approach.
Experiments on simulated and real data are carried out in order to assess the
proposed methodology
Exact ICL maximization in a non-stationary time extension of the latent block model for dynamic networks
The latent block model (LBM) is a flexible probabilistic tool to describe
interactions between node sets in bipartite networks, but it does not account
for interactions of time varying intensity between nodes in unknown classes. In
this paper we propose a non stationary temporal extension of the LBM that
clusters simultaneously the two node sets of a bipartite network and constructs
classes of time intervals on which interactions are stationary. The number of
clusters as well as the membership to classes are obtained by maximizing the
exact complete-data integrated likelihood relying on a greedy search approach.
Experiments on simulated and real data are carried out in order to assess the
proposed methodology.Comment: European Symposium on Artificial Neural Networks, Computational
Intelligence and Machine Learning (ESANN), Apr 2015, Bruges, Belgium.
pp.225-230, 2015, Proceedings of the 23-th European Symposium on Artificial
Neural Networks, Computational Intelligence and Machine Learning (ESANN 2015
An asymptotic preserving scheme for strongly anisotropic elliptic problems
In this article we introduce an asymptotic preserving scheme designed to
compute the solution of a two dimensional elliptic equation presenting large
anisotropies. We focus on an anisotropy aligned with one direction, the
dominant part of the elliptic operator being supplemented with Neumann boundary
conditions. A new scheme is introduced which allows an accurate resolution of
this elliptic equation for an arbitrary anisotropy ratio.Comment: 21 page
Block modelling in dynamic networks with non-homogeneous Poisson processes and exact ICL
We develop a model in which interactions between nodes of a dynamic network
are counted by non homogeneous Poisson processes. In a block modelling
perspective, nodes belong to hidden clusters (whose number is unknown) and the
intensity functions of the counting processes only depend on the clusters of
nodes. In order to make inference tractable we move to discrete time by
partitioning the entire time horizon in which interactions are observed in
fixed-length time sub-intervals. First, we derive an exact integrated
classification likelihood criterion and maximize it relying on a greedy search
approach. This allows to estimate the memberships to clusters and the number of
clusters simultaneously. Then a maximum-likelihood estimator is developed to
estimate non parametrically the integrated intensities. We discuss the
over-fitting problems of the model and propose a regularized version solving
these issues. Experiments on real and simulated data are carried out in order
to assess the proposed methodology
The first rational Chebyshev knots
A Chebyshev knot is a knot which has a parametrization
of the form where
are integers, is the Chebyshev polynomial of degree and We show that any two-bridge knot is a Chebyshev knot with and also
with . For every integers ( and , coprime), we
describe an algorithm that gives all Chebyshev knots \cC(a,b,c,\phi). We
deduce a list of minimal Chebyshev representations of two-bridge knots with
small crossing number.Comment: 22p, 27 figures, 3 table
Computing Chebyshev knot diagrams
A Chebyshev curve C(a,b,c,\phi) has a parametrization of the form x(t)=Ta(t);
y(t)=T_b(t) ; z(t)= Tc(t + \phi), where a,b,c are integers, Tn(t) is the
Chebyshev polynomial of degree n and \phi \in \RR. When C(a,b,c,\phi) has no
double points, it defines a polynomial knot. We determine all possible knots
when a, b and c are given.Comment: 8
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