203 research outputs found
Line-distortion, Bandwidth and Path-length of a graph
We investigate the minimum line-distortion and the minimum bandwidth problems
on unweighted graphs and their relations with the minimum length of a
Robertson-Seymour's path-decomposition. The length of a path-decomposition of a
graph is the largest diameter of a bag in the decomposition. The path-length of
a graph is the minimum length over all its path-decompositions. In particular,
we show:
- if a graph can be embedded into the line with distortion , then
admits a Robertson-Seymour's path-decomposition with bags of diameter at most
in ;
- for every class of graphs with path-length bounded by a constant, there
exist an efficient constant-factor approximation algorithm for the minimum
line-distortion problem and an efficient constant-factor approximation
algorithm for the minimum bandwidth problem;
- there is an efficient 2-approximation algorithm for computing the
path-length of an arbitrary graph;
- AT-free graphs and some intersection families of graphs have path-length at
most 2;
- for AT-free graphs, there exist a linear time 8-approximation algorithm for
the minimum line-distortion problem and a linear time 4-approximation algorithm
for the minimum bandwidth problem
Automatic 3D Facial Expression Analysis in Videos
We introduce a novel framework for automatic 3D facial expression analysis in videos. Preliminary results demonstrate editing facial expression with facial expression recognition. We first build a 3D expression database to learn the expression space of a human face. The real-time 3D video data were captured by a camera/projector scanning system. From this database, we extract the geometry deformation independent of pose and illumination changes. All possible facial deformations of an individual make a nonlinear manifold embedded in a high dimensional space. To combine the manifolds of different subjects that vary significantly and are usually hard to align, we transfer the facial deformations in all training videos to one standard model. Lipschitz embedding embeds the normalized deformation of the standard model in a low dimensional generalized manifold. We learn a probabilistic expression model on the generalized manifold. To edit a facial expression of a new subject in 3D videos, the system searches over this generalized manifold for optimal replacement with the 'target' expression, which will be blended with the deformation in the previous frames to synthesize images of the new expression with the current head pose. Experimental results show that our method works effectively
Adaptive Sampling for Nonlinear Dimensionality Reduction Based on Manifold Learning
We make use of the non-intrusive dimensionality reduction method Isomap in order to emulate nonlinear parametric flow problems that are governed by the Reynolds-averaged Navier-Stokes equations. Isomap is a manifold learning approach that provides a low-dimensional embedding space that is approximately isometric to the manifold that is assumed to be formed by the high-fidelity Navier-Stokes flow solutions under smooth variations of the inflow conditions. The focus of the work at hand is the adaptive construction and refinement of the Isomap emulator: We exploit the non-Euclidean Isomap metric to detect and fill up gaps in the sampling in the embedding space. The performance of the proposed manifold filling method will be illustrated by numerical experiments, where we consider nonlinear parameter-dependent steady-state Navier-Stokes flows in the transonic regime
On-line relational SOM for dissimilarity data
International audienceIn some applications and in order to address real world situations better, data may be more complex than simple vectors. In some examples, they can be known through their pairwise dissimilarities only. Several variants of the Self Organizing Map algorithm were introduced to generalize the original algorithm to this framework. Whereas median SOM is based on a rough representation of the prototypes, relational SOM allows representing these prototypes by a virtual combination of all elements in the data set. However, this latter approach suffers from two main drawbacks. First, its complexity can be large. Second, only a batch version of this algorithm has been studied so far and it often provides results having a bad topographic organization. In this article, an on-line version of relational SOM is described and justified. The algorithm is tested on several datasets, including categorical data and graphs, and compared with the batch version and with other SOM algorithms for non vector data
Euclidean Distances, soft and spectral Clustering on Weighted Graphs
We define a class of Euclidean distances on weighted graphs, enabling to
perform thermodynamic soft graph clustering. The class can be constructed form
the "raw coordinates" encountered in spectral clustering, and can be extended
by means of higher-dimensional embeddings (Schoenberg transformations).
Geographical flow data, properly conditioned, illustrate the procedure as well
as visualization aspects.Comment: accepted for presentation (and further publication) at the ECML PKDD
2010 conferenc
Ground-state properties of tubelike flexible polymers
In this work we investigate structural properties of native states of a
simple model for short flexible homopolymers, where the steric influence of
monomeric side chains is effectively introduced by a thickness constraint. This
geometric constraint is implemented through the concept of the global radius of
curvature and affects the conformational topology of ground-state structures. A
systematic analysis allows for a thickness-dependent classification of the
dominant ground-state topologies. It turns out that helical structures,
strands, rings, and coils are natural, intrinsic geometries of such tubelike
objects
Visual Analysis of a Cold Rolling Process Using Data-Based Modeling
International Conference on Engineering Applications of Neural Networks (13th. 2012. Coventry Univ, Otaniemi, Finland
Homotopic Path Planning on Manifolds for Cabled Mobile Robots
We present two path planning algorithms for mobile robots that are connected
by cable to a fixed base. Our algorithms efficiently compute the shortest path
and control strategy that lead the robot to the target location considering cable length
and obstacle interactions. First, we focus on cable-obstacle collisions. We introduce
and formally analyze algorithms that build and search an overlapped configuration
space manifold. Next, we present an extension that considers cable-robot collisions.
All algorithms are experimentally validated using a real robot
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