Search results for "kernel"
showing 10 items of 357 documents
Accelerated Proximal Gradient Descent in Metric Learning for Kernel Regression
2018
The purpose of this paper is to learn a specific distance function for the Nadayara Watson estimator to be applied as a non-linear classifier. The idea of transforming the predictor variables and learning a kernel function based on Mahalanobis pseudo distance througth an low rank structure in the distance function will help us to lead the development of this problem. In context of metric learning for kernel regression, we introduce an Accelerated Proximal Gradient to solve the non-convex optimization problem with better convergence rate than gradient descent. An extensive experiment and the corresponding discussion tries to show that our strategie its a competitive solution in relation to p…
Influence of increasing convolution kernel filtering on plaque imaging with multislice CT using an ex-vivo model of coronary angiography
2005
PURPOSE: To assess the variability in attenuation of coronary plaques with multislice CT-angiography (MSCT-CA) in an ex-vivo model with varying convolution kernels. MATERIALS AND METHODS: MSCT-CA (Sensation 16, Siemens) was performed in three ex-vivo left coronary arteries after instillation of contrast material solution (Iomeprol 400 mgI/ml, dilution: 1/80). The specimens were placed in oil to simulate epicardial fat. Scan parameters: slices 16/0.75 mm, rotation time 375 ms, feed/rotation 3.0 mm, mAs 500, slice thickness 1 mm, and FOV 50 mm. Datasets were reconstructed using 4 different kernels (B30f-smooth, B36f-medium smooth, B46f-medium, and B60f-sharp). Each scan was scored for the pre…
Influence of convolution filtering on coronary plaque attenuation values: observations in an ex vivo model of multislice computed tomography coronary…
2007
Attenuation variability ( measured in Hounsfield Units, HU) of human coronary plaques using multislice computed tomography (MSCT) was evaluated in an ex vivo model with increasing convolution kernels. MSCT was performed in seven ex vivo left coronary arteries sunk into oil followingthe instillation of saline (1/infinity) and a 1/50 solution of contrast material ( 400 mgI/ml iomeprol). Scan parameters were: slices/ collimation, 16/0.75 mm; rotation time, 375 ms. Four convolution kernels were used: b30f-smooth, b36f-medium smooth, b46f-medium and b60f-sharp. An experienced radiologist scored for the presence of plaques and measured the attenuation in lumen, calcified and noncalcified plaques …
Differentiation between acute and chronic myocardial infarction by means of texture analysis of late gadolinium enhancement and cine cardiac magnetic…
2017
[EN] The purpose of this study was to differentiate acute from chronic myocardial infarction using machine learning techniques and texture features extracted from cardiac magnetic resonance imaging (MRI). The study group comprised 22 cases with acute myocardial infarction (AMI) and 22 cases with chronic myocardial infarction (CMI). Cine and late gadolinium enhancement (LGE) MRI were analyzed independently to differentiate AMI from CMI. A total of 279 texture features were extracted from predefined regions of interest (ROIs): the infarcted area on LGE MRI, and the entire myocardium on cine MRI. Classification performance was evaluated by a nested cross-validation approach combining a feature…
Model reduction techniques for the computation of extended Markov parameterizations for generalized Langevin equations
2021
Abstract The generalized Langevin equation is a model for the motion of coarse-grained particles where dissipative forces are represented by a memory term. The numerical realization of such a model requires the implementation of a stochastic delay-differential equation and the estimation of a corresponding memory kernel. Here we develop a new approach for computing a data-driven Markov model for the motion of the particles, given equidistant samples of their velocity autocorrelation function. Our method bypasses the determination of the underlying memory kernel by representing it via up to about twenty auxiliary variables. The algorithm is based on a sophisticated variant of the Prony metho…
ℓ1-Penalized Methods in High-Dimensional Gaussian Markov Random Fields
2016
In the last 20 years, we have witnessed the dramatic development of new data acquisition technologies allowing to collect massive amount of data with relatively low cost. is new feature leads Donoho to define the twenty-first century as the century of data. A major characteristic of this modern data set is that the number of measured variables is larger than the sample size; the word high-dimensional data analysis is referred to the statistical methods developed to make inference with this new kind of data. This chapter is devoted to the study of some of the most recent ℓ1-penalized methods proposed in the literature to make sparse inference in a Gaussian Markov random field (GMRF) defined …
Physics-Aware Gaussian Processes for Earth Observation
2017
Earth observation from satellite sensory data pose challenging problems, where machine learning is currently a key player. In recent years, Gaussian Process (GP) regression and other kernel methods have excelled in biophysical parameter estimation tasks from space. GP regression is based on solid Bayesian statistics, and generally yield efficient and accurate parameter estimates. However, GPs are typically used for inverse modeling based on concurrent observations and in situ measurements only. Very often a forward model encoding the well-understood physical relations is available though. In this work, we review three GP models that respect and learn the physics of the underlying processes …
Iterative Reconstruction of Memory Kernels.
2017
In recent years, it has become increasingly popular to construct coarse-grained models with non-Markovian dynamics to account for an incomplete separation of time scales. One challenge of a systematic coarse-graining procedure is the extraction of the dynamical properties, namely, the memory kernel, from equilibrium all-atom simulations. In this article, we propose an iterative method for memory reconstruction from dynamical correlation functions. Compared to previously proposed noniterative techniques, it ensures by construction that the target correlation functions of the original fine-grained systems are reproduced accurately by the coarse-grained system, regardless of time step and disc…
Sensitivity Maps of the Hilbert-Schmidt Independence Criterion
2018
Abstract Kernel dependence measures yield accurate estimates of nonlinear relations between random variables, and they are also endorsed with solid theoretical properties and convergence rates. Besides, the empirical estimates are easy to compute in closed form just involving linear algebra operations. However, they are hampered by two important problems: the high computational cost involved, as two kernel matrices of the sample size have to be computed and stored, and the interpretability of the measure, which remains hidden behind the implicit feature map. We here address these two issues. We introduce the sensitivity maps (SMs) for the Hilbert–Schmidt independence criterion (HSIC). Sensi…
Explicit Recursive and Adaptive Filtering in Reproducing Kernel Hilbert Spaces
2014
This brief presents a methodology to develop recursive filters in reproducing kernel Hilbert spaces. Unlike previous approaches that exploit the kernel trick on filtered and then mapped samples, we explicitly define the model recursivity in the Hilbert space. For that, we exploit some properties of functional analysis and recursive computation of dot products without the need of preimaging or a training dataset. We illustrate the feasibility of the methodology in the particular case of the $\gamma$ -filter, which is an infinite impulse response filter with controlled stability and memory depth. Different algorithmic formulations emerge from the signal model. Experiments in chaotic and elect…