8,243 research outputs found
Locally Learning Biomedical Data Using Diffusion Frames
Diffusion geometry techniques are useful to classify patterns and visualize high-dimensional datasets. Building upon ideas from diffusion geometry, we outline our mathematical foundations for learning a function on high-dimension biomedical data in a local fashion from training data. Our approach is based on a localized summation kernel, and we verify the computational performance by means of exact approximation rates. After these theoretical results, we apply our scheme to learn early disease stages in standard and new biomedical datasets
A deep learning approach to diabetic blood glucose prediction
We consider the question of 30-minute prediction of blood glucose levels
measured by continuous glucose monitoring devices, using clinical data. While
most studies of this nature deal with one patient at a time, we take a certain
percentage of patients in the data set as training data, and test on the
remainder of the patients; i.e., the machine need not re-calibrate on the new
patients in the data set. We demonstrate how deep learning can outperform
shallow networks in this example. One novelty is to demonstrate how a
parsimonious deep representation can be constructed using domain knowledge
Development of method of matched morphological filtering of biomedical signals and images
Formalized approach to the analysis of biomedical signals and images with locally concentrated features is developed on the basis of matched morphological filtering taking into account the useful signal models that allowed generalizing the existing methods of digital processing and analysis of biomedical signals and images with locally concentrated features. The proposed matched morphological filter has been adapted to solve such problems as localization of the searched structural elements on biomedical signals with locally concentrated features, estimation of the irregular background aimed at the visualization quality improving of biological objects on X-ray biomedical images, pathologic structures selection on mammogram. The efficiency of the proposed methods of matched morphological filtration of biomedical signals and images with locally concentrated features is proved by experiments
Graph Signal Processing: Overview, Challenges and Applications
Research in Graph Signal Processing (GSP) aims to develop tools for
processing data defined on irregular graph domains. In this paper we first
provide an overview of core ideas in GSP and their connection to conventional
digital signal processing. We then summarize recent developments in developing
basic GSP tools, including methods for sampling, filtering or graph learning.
Next, we review progress in several application areas using GSP, including
processing and analysis of sensor network data, biological data, and
applications to image processing and machine learning. We finish by providing a
brief historical perspective to highlight how concepts recently developed in
GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE
An Infinitesimal Probabilistic Model for Principal Component Analysis of Manifold Valued Data
We provide a probabilistic and infinitesimal view of how the principal
component analysis procedure (PCA) can be generalized to analysis of nonlinear
manifold valued data. Starting with the probabilistic PCA interpretation of the
Euclidean PCA procedure, we show how PCA can be generalized to manifolds in an
intrinsic way that does not resort to linearization of the data space. The
underlying probability model is constructed by mapping a Euclidean stochastic
process to the manifold using stochastic development of Euclidean
semimartingales. The construction uses a connection and bundles of covariant
tensors to allow global transport of principal eigenvectors, and the model is
thereby an example of how principal fiber bundles can be used to handle the
lack of global coordinate system and orientations that characterizes manifold
valued statistics. We show how curvature implies non-integrability of the
equivalent of Euclidean principal subspaces, and how the stochastic flows
provide an alternative to explicit construction of such subspaces. We describe
estimation procedures for inference of parameters and prediction of principal
components, and we give examples of properties of the model on embedded
surfaces
- …