421 research outputs found
Hypergraph Modelling for Geometric Model Fitting
In this paper, we propose a novel hypergraph based method (called HF) to fit
and segment multi-structural data. The proposed HF formulates the geometric
model fitting problem as a hypergraph partition problem based on a novel
hypergraph model. In the hypergraph model, vertices represent data points and
hyperedges denote model hypotheses. The hypergraph, with large and
"data-determined" degrees of hyperedges, can express the complex relationships
between model hypotheses and data points. In addition, we develop a robust
hypergraph partition algorithm to detect sub-hypergraphs for model fitting. HF
can effectively and efficiently estimate the number of, and the parameters of,
model instances in multi-structural data heavily corrupted with outliers
simultaneously. Experimental results show the advantages of the proposed method
over previous methods on both synthetic data and real images.Comment: Pattern Recognition, 201
Mode-Seeking on Hypergraphs for Robust Geometric Model Fitting
In this paper, we propose a novel geometric model fitting method, called
Mode-Seeking on Hypergraphs (MSH),to deal with multi-structure data even in the
presence of severe outliers. The proposed method formulates geometric model
fitting as a mode seeking problem on a hypergraph in which vertices represent
model hypotheses and hyperedges denote data points. MSH intuitively detects
model instances by a simple and effective mode seeking algorithm. In addition
to the mode seeking algorithm, MSH includes a similarity measure between
vertices on the hypergraph and a weight-aware sampling technique. The proposed
method not only alleviates sensitivity to the data distribution, but also is
scalable to large scale problems. Experimental results further demonstrate that
the proposed method has significant superiority over the state-of-the-art
fitting methods on both synthetic data and real images.Comment: Proceedings of the IEEE International Conference on Computer Vision,
pp. 2902-2910, 201
Exploring cooperative game mechanisms of scientific coauthorship networks
Scientific coauthorship, generated by collaborations and competitions among
researchers, reflects effective organizations of human resources. Researchers,
their expected benefits through collaborations, and their cooperative costs
constitute the elements of a game. Hence we propose a cooperative game model to
explore the evolution mechanisms of scientific coauthorship networks. The model
generates geometric hypergraphs, where the costs are modelled by space
distances, and the benefits are expressed by node reputations, i. e. geometric
zones that depend on node position in space and time. Modelled cooperative
strategies conditioned on positive benefit-minus-cost reflect the spatial
reciprocity principle in collaborations, and generate high clustering and
degree assortativity, two typical features of coauthorship networks. Modelled
reputations generate the generalized Poisson parts and fat tails appeared in
specific distributions of empirical data, e. g. paper team size distribution.
The combined effect of modelled costs and reputations reproduces the
transitions emerged in degree distribution, in the correlation between degree
and local clustering coefficient, etc. The model provides an example of how
individual strategies induce network complexity, as well as an application of
game theory to social affiliation networks
Connectivity of Random Geometric Hypergraphs
We consider a random geometric hypergraph model based on an underlying
bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a
node is assigned to those hyperedges that lie with a certain radius. From a
modelling perspective, we explain how the model captures higher order
connections that arise in real data sets. Our main contribution is to study the
connectivity properties of the model. In an asymptotic limit where the number
of nodes and hyperedges grow in tandem we give a condition on the radius that
guarantees connectivity
Advancements in latent space network modelling
The ubiquity of relational data has motivated an extensive literature on network analysis, and over the last two decades the latent space approach has become a popular network modelling framework. In this approach, the nodes of a network are represented in a low-dimensional latent space and the probability of interactions occurring are modelled as a function of the associated latent coordinates. This thesis focuses on computational and modelling aspects of the latent space approach, and we present two main contributions. First, we consider estimation of temporally evolving latent space networks in which interactions among a fixed population are observed through time. The latent coordinates of each node evolve other time and this presents a natural setting for the application of sequential monte carlo (SMC) methods. This facilitates online inference which allows estimation for dynamic networks in which the number of observations in time is large. Since the performance of SMC methods degrades as the dimension of the latent state space increases, we explore the high-dimensional SMC literature to allow estimation of networks with a larger number of nodes. Second, we develop a latent space model for network data in which the interactions occur between sets of the population and, as a motivating example, we consider a coauthorship network in which it is typical for more than two authors to contribute to an article. This type of data can be represented as a hypergraph, and we extend the latent space framework to this setting. Modelling the nodes in a latent space provides a convenient visualisation of the data and allows properties to be imposed on the hypergraph relationships. We develop a parsimonious model with a computationally convenient likelihood. Furthermore, we theoretically consider the properties of the degree distribution of our model and further explore its properties via simulation
The infinite random simplicial complex
We study the Fraisse limit of the class of all finite simplicial complexes.
Whilst the natural model-theoretic setting for this class uses an infinite
language, a range of results associated with Fraisse limits of structures for
finite languages carry across to this important example. We introduce the
notion of a local class, with the class of finite simplicial complexes as an
archetypal example, and in this general context prove the existence of a 0-1
law and other basic model-theoretic results. Constraining to the case where all
relations are symmetric, we show that every direct limit of finite groups, and
every metrizable profinite group, appears as a subgroup of the automorphism
group of the Fraisse limit. Finally, for the specific case of simplicial
complexes, we show that the geometric realisation is topologically surprisingly
simple: despite the combinatorial complexity of the Fraisse limit, its
geometric realisation is homeomorphic to the infinite simplex.Comment: 33 page
Multiple structure recovery with T-linkage
reserved2noThis work addresses the problem of robust fitting of geometric structures to noisy data corrupted by outliers. An extension of J-linkage (called T-linkage) is presented and elaborated. T-linkage improves the preference analysis implemented by J-linkage in term of performances and robustness, considering both the representation and the segmentation steps. A strategy to reject outliers and to estimate the inlier threshold is proposed, resulting in a versatile tool, suitable for multi-model fitting “in the wild”. Experiments demonstrate that our methods perform better than J-linkage on simulated data, and compare favorably with state-of-the-art methods on public domain real datasets.mixedMagri L.; Fusiello A.Magri, L.; Fusiello, A
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