A New Heuristic for Feature Selection by Consistent Biclustering

Given a set of data, biclustering aims at finding simultaneous partitions in biclusters of its samples and of the features which are used for representing the samples. Consistent biclusterings allow to obtain correct classifications of the samples from the known classification of the features, and vice versa, and they are very useful for performing supervised classifications. The problem of finding consistent biclusterings can be seen as a feature selection problem, where the features that are not relevant for classification purposes are removed from the set of data, while the total number of features is maximized in order to preserve information. This feature selection problem can be formulated as a linear fractional 0-1 optimization problem. We propose a reformulation of this problem as a bilevel optimization problem, and we present a heuristic algorithm for an efficient solution of the reformulated problem. Computational experiments show that the presented algorithm is able to find better solutions with respect to the ones obtained by employing previously presented heuristic algorithms

Euclidean distance geometry and applications

Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in Euclidean space that realizes the given distances. We survey some of the theory of Euclidean distance geometry and some of the most important applications: molecular conformation, localization of sensor networks and statics.Comment: 64 pages, 21 figure

BINMETA: a new Java package for meta-heuristic searches

International audienceWe present a new Java package, named BINMETA, for the development and the study of meta-heuristic searches for global optimization. The solution space for our optimization problems is based on a discrete representation, but it does not restrict to combinatorial problems, for every representation on computer machines finally reduces to a sequence of bits. We focus on general purpose meta-heuristics, which are not tailored to any specific subclass of problems. Although we are aware that this is not the first attempt to develop one unique tool implementing more than one meta-heuristic search, we are motivated by the following three main research lines on meta-heuristics. First, we plan to collect several implementations of meta-heuristic searches, developed by several programmers under the common interface of the package, where a particular attention is given to the common components of the various meta-heuristics. Second, the discrete representation for the solutions that we employ allows the user to perform a preliminary study on the degrees of freedom that is likely to give a positive impact on the performance of the meta-heuristic searches. Third, the choice of Java as a programming language is motivated by its flexibility and the use of a high-level objective-oriented paradigm. Finally, an important point in the development of BINMETA is that a meta-heuristic search implemented in the package can also be seen as an optimization problem, where its parameters play the role decision variables

An Analysis on the Degrees of Freedom of Binary Representations for Solutions to Discretizable Distance Geometry Problems

International audienceThe degrees of freedom in special binary representations for instances of the Discretizable Distance Geometry Problem (DDGP) are studied in this note article. The focus is on DDGP instances where the underlying graphs, together with their associated vertex orders, are able to satisfy the so-called consecutivity assumption. This additional assumption, in fact, makes it possible to group together subsets of consecutive binary variables, which turn out to strongly depend on each other, so that they can actually be replaced by a smaller subset of binary variables. As a consequence, new binary representations, with reduced degrees of freedom w.r.t the trivial binary representations for DDGP instances, can be introduced and potentially be exploited in DDGP solution methods

DSPP: Deep Shape and Pose Priors of Humans

The prior knowledge of real human body shapes and poses is fundamentalin computer games and animation (e.g. performance capture). Linear subspaces such as the popular SMPL model have a limited capacity to represent the large geometric variations of human shapes and poses. What is worse is that random sampling from them often produces non-realistic humans because the distribution of real humans is more likely to concentrate on a non-linear manifold instead of the full subspace. Towards this problem, we propose to learn human shape and pose manifolds using a more powerful deep generator network, which is trained to produce samples that cannot be distinguished from real humans by a deep discriminator network. In contrast to previous work that learn both the generator and discriminator in the original geometry spaces, we learn them in the more representative latent spaces discovered by a shape and a pose auto-encoder network respectively. Random sampling from our priors produces higher-quality human shapes and poses. The capacity of our priors is best applied to applications such as virtual human synthesis in games

On the Representation of Human Motions and Distance-based Retargeting

International audienceDistance-based motion adaptation leads to the formulation of a dynamical Distance Geometry Problem (dynDGP) where the involved distances simultaneously represent the morphology of the animated character, as well as a possible motion. The explicit use of inter-joint distances allows us to easily verify the presence of joint contacts, which one generally wishes to preserve when adapting a given motion to characters having a different morphology. In this work, we focus our attention on suitable representations of human-like animated characters, and study the advantages (and disadvantages) in using some of them. In the initial works on distance-based motion adaptation, a 3n-dimensional vector was employed for representing the positions of the n joints of the character at a given frame. Here, we investigate the use of another, very popular in computer graphics, representation that basically replaces every joint position in the three-dimensional space with a set of three sorted Euler angles. We show that the latter can in fact be useful for avoiding some of the artifacts that were observed in previous computational experiments, but we argue that this Euler-angle representation, from a motion adaptation point of view, does not seem to be the optimal one. By paying particular attention to the degrees of freedom of the studied representations, it turns out that a novel character representation, inspired by representations used in structural biology for molecules, may allow us to reduce the character degrees of freedom to their minimal value. As a result, statistical analysis on human motion databases, where the motions are given with this new representation, can potentially provide important insights on human motions. This study is an initial step towards the identification of a full set of constraints capable of ensuring that unnatural postures for humans cannot be created while tackling motion adaptation problems

A GPU approach to distance geometry in 1D: an implementation in C/CUDA

International audienceWe present a GPU implementation in C and CUDA of a matrix-by-vector procedure that is particularly tailored to a special class of distance geometry problems in dimension 1, which we name "paradoxical DGP instances". This matrix-byvector reformulation was proposed in previous studies on an optical processor specialized for this kind of computations. Our computational experiments show that a consistent speed-up is observed when comparing our GPU implementation against a standard algorithm for distance geometry, called the Branchand-Prune algorithm. These results confirm that a suitable implementation of the matrix-by-vector procedure in the context of optic computing is very promising. We also remark, however, that the total number of detected solutions grows with the instance size in our implementations, which appears to be an important limitation to the effective implementation of the optical processor