Uncertainty-Aware Principal Component Analysis

We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to non-linear methods, linear dimensionality reduction techniques have the advantage that the characteristics of such probability distributions remain intact after projection. We derive a representation of the PCA sample covariance matrix that respects potential uncertainty in each of the inputs, building the mathematical foundation of our new method: uncertainty-aware PCA. In addition to the accuracy and performance gained by our approach over sampling-based strategies, our formulation allows us to perform sensitivity analysis with regard to the uncertainty in the data. For this, we propose factor traces as a novel visualization that enables to better understand the influence of uncertainty on the chosen principal components. We provide multiple examples of our technique using real-world datasets. As a special case, we show how to propagate multivariate normal distributions through PCA in closed form. Furthermore, we discuss extensions and limitations of our approach

Uncertainty-aware Visualization in Medical Imaging - A Survey

Medical imaging (image acquisition, image transformation, and image visualization) is a standard tool for clinicians in order to make diagnoses, plan surgeries, or educate students. Each of these steps is affected by uncertainty, which can highly influence the decision-making process of clinicians. Visualization can help in understanding and communicating these uncertainties. In this manuscript, we aim to summarize the current state-of-the-art in uncertainty-aware visualization in medical imaging. Our report is based on the steps involved in medical imaging as well as its applications. Requirements are formulated to examine the considered approaches. In addition, this manuscript shows which approaches can be combined to form uncertainty-aware medical imaging pipelines. Based on our analysis, we are able to point to open problems in uncertainty-aware medical imaging

Proceedings of the 2011 New York Workshop on Computer, Earth and Space Science

The purpose of the New York Workshop on Computer, Earth and Space Sciences is to bring together the New York area's finest Astronomers, Statisticians, Computer Scientists, Space and Earth Scientists to explore potential synergies between their respective fields. The 2011 edition (CESS2011) was a great success, and we would like to thank all of the presenters and participants for attending. This year was also special as it included authors from the upcoming book titled "Advances in Machine Learning and Data Mining for Astronomy". Over two days, the latest advanced techniques used to analyze the vast amounts of information now available for the understanding of our universe and our planet were presented. These proceedings attempt to provide a small window into what the current state of research is in this vast interdisciplinary field and we'd like to thank the speakers who spent the time to contribute to this volume.Comment: Author lists modified. 82 pages. Workshop Proceedings from CESS 2011 in New York City, Goddard Institute for Space Studie

Bayesian Spatial Modeling of fMRI data: A Multiple-Subject Analysis

The aim of this work is to develop a spatial model for multi-subject fMRI data. While there has been much work on univariate modeling of each voxel for single- and multi-subject data, and some work on spatial modeling for single-subject data, there has been no work on spatial models that explicitly account for intersubject variability in activation location. We use a Bayesian hierarchical spatial model to fit the data. At the first level we model population centers that mark the centers of regions of activation. For a given population center each subject may have zero or more associated individual components . While most previous work uses Gaussian mixtures for the activation shape, we instead use Gaussian mixtures for the probability that a voxel belongs to an activated region, assuming homogeneous mean intensity within a region. Our approach incorporates the unknown number of mixture components into the model as a parameter whose posterior distribution is estimated by reversible jump Markov Chain Monte Carlo. We demonstrate our method with a fMRI study of vi- sual working memory and show dramatically better precision of localization with our method relative to the standard mass-univariate method. Although we are motivated by fMRI data, this model could easily be modified to handle other types of imaging data

SRT3D: A Sparse Region-Based 3D Object Tracking Approach for the Real World

Region-based methods have become increasingly popular for model-based, monocular 3D tracking of texture-less objects in cluttered scenes. However, while they achieve state-of-the-art results, most methods are computationally expensive, requiring significant resources to run in real-time. In the following, we build on our previous work and develop SRT3D, a sparse region-based approach to 3D object tracking that bridges this gap in efficiency. Our method considers image information sparsely along so-called correspondence lines that model the probability of the object's contour location. We thereby improve on the current state of the art and introduce smoothed step functions that consider a defined global and local uncertainty. For the resulting probabilistic formulation, a thorough analysis is provided. Finally, we use a pre-rendered sparse viewpoint model to create a joint posterior probability for the object pose. The function is maximized using second-order Newton optimization with Tikhonov regularization. During the pose estimation, we differentiate between global and local optimization, using a novel approximation for the first-order derivative employed in the Newton method. In multiple experiments, we demonstrate that the resulting algorithm improves the current state of the art both in terms of runtime and quality, performing particularly well for noisy and cluttered images encountered in the real world

Pseudo-Probabilistic Design for High-Resolution Tsunami Simulations in the Southwestern Spanish Coast

The application of simulation software has proven to be a crucial tool for tsunami hazard assessment studies. Understanding the potentially devastating effects of tsunamis leads to the development of safety and resilience measures, such as the design of evacuation plans or the planning of the economic investment necessary to quickly mitigate their consequences. This article introduces a pseudo-probabilistic seismic-triggered tsunami simulation approach to investigate the potential impact of tsunamis in the southwestern coast of Spain, in the provinces of Huelva and Cádiz. Selected faults, probabilistic distributions and sampling methods are presented as well as some results for the nearly 900 Atlantic-origin tsunamis computed along the 250 km-long coast.This work has being carried out under a project funded by a public mutual agreement of understanding between the CN-IGME (CSIC) and the CCS (Law reference: BOE 103, 30/04/2019). This project is supported by an agreement of understanding between CN-IGME and UMA, creating a cooperative entity INGEA (Law reference: BOE 332, 22/12/2020). The numerical results presented in this work have been performed with the computational resources allocated by the Spanish Network for Supercomputing (RES) grants AECT-2020-3-0023 and AECT-2021-2-0018. Further support has also been received from the Spanish Government research project MEGAFLOW (RTI2018-096064-B-C21) and ChEESE project (EU Horizon 2020, grant agreement No. 823844, https://cheese-coe.eu/) due to the synergies found between the projects. Partial funding for open access charge: Universidad de Málag

Multiscale Simulation of Polymeric Fluids using Sparse Grids

The numerical simulation of non-Newtonian fluids is of high practical relevance since most complex fluids developed in the chemical industry are not correctly modeled by classical fluid mechanics. In this thesis, we implement a multiscale multi-bead-spring chain model into the three-dimensional Navier-Stokes solver NaSt3DGPF developed at the Institute for Numerical Simulation, University of Bonn. It is the first implementation of such a high-dimensional model for non-Newtonian fluids into a three-dimensional flow solver. Using this model, we present novel simulation results for a square-square contraction flow problem. We then compare the results of our 3D simulations with experimental measurements from the literature and obtain a very good agreement. Up to now, high-dimensional multiscale approaches are hardly used in practical applications as they lead to computing times in the order of months even on massively parallel computers. This thesis combines two approaches to reduce this enormous computational complexity. First, we use a domain decomposition with MPI to allow for massively parallel computations. Second, we employ a dimension-adaptive sparse grid variant, the combination technique, to reduce the computational complexity of the multiscale model. Here, the combination technique is used in a general formulation that balances not only different discretization errors but also considers the accuracy of the mathematical model