Multi-Marginal Gromov-Wasserstein Transport and Barycenters

Gromov-Wasserstein (GW) distances are combinations of Gromov-Hausdorff and Wasserstein distances that allow the comparison of two different metric measure spaces (mm-spaces). Due to their invariance under measure- and distance-preserving transformations, they are well suited for many applications in graph and shape analysis. In this paper, we introduce the concept of multi-marginal GW transport between a set of mm-spaces as well as its regularized and unbalanced versions. As a special case, we discuss multi-marginal fused variants, which combine the structure information of an mm-space with label information from an additional label space. To tackle the new formulations numerically, we consider the bi-convex relaxation of the multi-marginal GW problem, which is tight in the balanced case if the cost function is conditionally negative definite. The relaxed model can be solved by an alternating minimization, where each step can be performed by a multi-marginal Sinkhorn scheme. We show relations of our multi-marginal GW problem to (unbalanced, fused) GW barycenters and present various numerical results, which indicate the potential of the concept

Prediction of performance and cutter wear in rock TBM: Application to Koralm tunnel project

Excavation by Tunnel Boring Machines is the tunnelling method most frequently used nowadays in long infrastructural projects, in a wide range of geological conditions. In the last 40 years, many prediction models were developed to estimate TBM performance and cutter wear, using as input geological parameters. The research gives an overview of the existing penetration models for hard rock TBMs, identifies the most frequently used input parameters and summarizes the characteristics of the datasets on which the models are based on. Theoretical background is tested through the example of Koralm tunnel project, a 32.9-km-long base tunnel in Austria, in a 1000-m-long portion of the South tube in the construction lot KAT 2. The outcomes shows that the estimation of the penetration is reasonably accurate when applying models that are based on a database consistent with the project data, especially in terms of geology and typology of machine used in the excavation. The article proposes a design method for a system of TBM data analysis and prediction at the construction stage, based on a back-analysis process about machine data in different geological conditions. The methodology can be applied in any other project and the system is particularly useful in long tunnels, in which a continuous improvement of the ability of prediction can have an effective impact on time and costs

Unbalanced Multi-Marginal Optimal Transport

Entropy regularized optimal transport and its multi-marginal generalization have attracted increasing attention in various applications, in particular due to efficient Sinkhorn-like algorithms for computing optimal transport plans. However, it is often desirable that the marginals of the optimal transport plan do not match the given measures exactly, which led to the introduction of the so-called unbalanced optimal transport. Since unbalanced methods were not examined for the multi-marginal setting so far, we address this topic in the present paper. More precisely, we introduce the unbalanced multi-marginal optimal transport problem and its dual, and show that a unique optimal transport plan exists under mild assumptions. Further, we generalize the Sinkhorn algorithm for regularized unbalanced optimal transport to the multi-marginal setting and prove its convergence. If the cost function decouples according to a tree, the iterates can be computed efficiently. At the end, we discuss three applications of our framework, namely two barycenter problems and a transfer operator approach, where we establish a relation between the barycenter problem and the multi-marginal optimal transport with an appropriate tree-structured cost function

The INTERSPEECH 2013 computational paralinguistics challenge: social signals, conflict, emotion, autism

The INTERSPEECH 2013 Computational Paralinguistics Challenge provides for the first time a unified test-bed for Social Signals such as laughter in speech. It further introduces conflict in group discussions as new tasks and picks up on autism and its manifestations in speech. Finally, emotion is revisited as task, albeit with a broader ranger of overall twelve emotional states. In this paper, we describe these four Sub-Challenges, Challenge conditions, baselines, and a new feature set by the openSMILE toolkit, provided to the participants. \em Bj\"orn Schuller$^1$, Stefan Steidl$^2$, Anton Batliner$^1$, Alessandro Vinciarelli$^{3,4}$, Klaus Scherer$^5$}\\ {\em Fabien Ringeval$^6$, Mohamed Chetouani$^7$, Felix Weninger$^1$, Florian Eyben$^1$, Erik Marchi$^1$, }\\ {\em Hugues Salamin$^3$, Anna Polychroniou$^3$, Fabio Valente$^4$, Samuel Kim$^4$

A survey on perceived speaker traits: personality, likability, pathology, and the first challenge

The INTERSPEECH 2012 Speaker Trait Challenge aimed at a unified test-bed for perceived speaker traits – the first challenge of this kind: personality in the five OCEAN personality dimensions, likability of speakers, and intelligibility of pathologic speakers. In the present article, we give a brief overview of the state-of-the-art in these three fields of research and describe the three sub-challenges in terms of the challenge conditions, the baseline results provided by the organisers, and a new openSMILE feature set, which has been used for computing the baselines and which has been provided to the participants. Furthermore, we summarise the approaches and the results presented by the participants to show the various techniques that are currently applied to solve these classification tasks