All Years Seminars
[INMA] 2016-11-22 (16:30) : A line-search based proximal algorithm for convex and non-convex optimization, with applications to image processing
At CORE (room C.035)
Speaker :
Ignace Loris (ULB)
Abstract :
A novel iterative algorithm for the solution of convex or non-convex
optimization problems is presented. In particular, the objective
function is assumed to be the sum of a differentiable (possibly
non-convex) part and a convex (possibly non-differentiable) part. The
proposed algorithm is based on an Armijo line-search rule and uses the
gradient of the smooth part and the proximal operator of the non-smooth
part. However, the proximal operator does not have to be computed
exactly and verifiable criteria for its inexact computation are given in
some cases of practical interest.
In general we prove that all limit points of the iterates are
stationary, while in the special case of a convex objective function we
prove the convergence of the whole sequence to a minimizer. In the
non-convex case, we also show convergence if the objective function
satisfies the Kurdyka- Lojasiewicz property at each point of its domain.
Finally, the algorithm is applied to a wide range of image
reconstruction problems.
[INMA] 2016-11-15 (14:00) : Three PhD topics in Applied Mathematics
At Euler building (room A.002)
Speaker :
Cyril De Bodt, Shuyu Dong, Dounia Mulders (UCL)
Abstract :
Three PhD students will explain their topics: "User-centered machine learning" (Cyril De Bodt), "Dictionary learning for graph signals" (Shuyu Dong) and "Human pain connectome identification" (Dounia Mulders)
[INMA] 2016-11-08 (14:00) : Mining Patterns in Data
At Euler building (A002)
Speaker :
Siegfried Nijssen (UCL)
Abstract :
Pattern mining algorithms are algorithms that search for patterns in large collections of data. While initially developed for the discovery of frequently occurring structures in binary databases, nowadays they can be applied on many types of data: on graph databases, numerical databases, sequence databases, time series and heterogeneous databases; they can not only find frequent structures, but also identify interesting subgroups, accurate classifiers and good clusterings. In this talk, I will discuss number of different pattern mining techniques, with a focus on techniques that find patterns in supervised data; these are techniques that can be used to find associations between one particular attribute in a database and the remaining other attributes. I will discuss algorithms, their computational complexity and remaining challenges.
[INMA] 2016-10-25 (14:00) : Continuous opinions and discrete actions in social networks: a multi-agent system approach
At Euler building (A002)
Speaker :
Martin, Samuel
Abstract :
We propose and analyze a novel multi-agent opinion dynamics model in which agents have access to actions which are quantized version of the opinions of their neighbors. The model produces different behaviors observed in social networks such as disensus, clustering, oscillations, opinion propagation, even when the communication network is connected. The main result provides the characterization of preservation and diffusion of actions under general communication topologies. A complete analysis allowing the opinion forecasting is given in the particular cases of complete and ring communication graphs. Numerical examples illustrate the main features of this model.
Joint work with N. R. Chowdhury, I.-C. Morarescu, and S. Srikant.
[INMA] 2016-10-18 (14:00) : Network analysis through invariant subspaces: symmetries, graph partitions, and dynamics
At Euler building (A002)
Speaker :
Schaub, Michael
Abstract :
Many tools used in network analysis are grounded in the spectral decomposition of a matrix Q associated to the network structure, such as the adjacency matrix A, or the (normalized) Laplacian L; or products of such matrices. From an abstract viewpoint, we may thus interpret all these algorithms as assessing a dominant invariant linear subspace with respect to an appropriately chosen network descriptor matrix.
By limiting the subspace to be one-dimensional, we can recover centrality measures including the famous PageRank algorithm, the Katz centrality, and Kleinberg's HITS score (which is based on the SVD of A). Considering dominant subspaces of larger sizes naturally leads to spectral clustering, and other graph partitioning algorithms.
However, instead of looking only at the dominant invariant subspaces, in this talk we will be concerned with a different class of invariant subspaces, namely, those invariant subspaces that can be spanned by the indicator vectors of a graph partition.
Such invariant subspaces are naturally related to so called (external) equitable graph partitions, which are closely associated to the inherent symmetries in the network. As we will show, by analysing these invariant subspaces and the associated graph partitions, we can gain insights about various kinds of cluster synchronization behaviours in consensus dynamics and networks of coupled oscillators, such as Kuramoto oscillators.
Joint work with N. O'Clery, Y.Billeh, R. Lambiotte, J.-C. Delvenne, and M.Barahona
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