Search results for "Kernel"

Fundamentals of a Generalized Measure Theory

1999

In this chapter, we try to present a coherent survey on some recent attempts in building a theory of generalized measures. Our main goal is to emphasize a minimal set of axioms both for the measures and their domains, and still to be able to prove significant results. Therefore we start with fairly general structures and enrich them with additional properties only if necessary.

Some Numerical Remarks on a Meshless Approximation Method

2016

In this paper we consider sources of enhancement for the Smoothed Particle Hydrodynamics method in approximating a function and its derivatives. It is well known that the standard formulation is usually poor when scattered data distribution is considered or when the approximation near the boundary occurs. In this paper studies on the accuracy are provided and assessed with gridded and scattered data distribution in the problem domain. The improvements of the method are addressed and supporting numerical experiments are included.

A Novel Time Series Kernel for Sequences Generated by LTI Systems

2017

The recent introduction of Hankelets to describe time series relies on the assumption that the time series has been generated by a vector autoregressive model (VAR) of order p. The success of Hankelet-based time series representations prevalently in nearest neighbor classifiers poses questions about if and how this representation can be used in kernel machines without the usual adoption of mid-level representations (such as codebook-based representations). It is also of interest to investigate how this representation relates to probabilistic approaches for time series modeling, and which characteristics of the VAR model a Hankelet can capture. This paper aims at filling these gaps by: deriv…

On Representing Concepts in High-dimensional Linear Spaces

2017

Producing a mathematical model of concepts is a very important issue in artificial intelligence, because if such a model were found this, besides being a very interesting result in its own right, would also contribute to the emergence of what we could call the ‘mathematics of thought.’ One of the most interesting attempts made in this direction is P. Gardenfors’ theory of conceptual spaces, a ¨ theory which is mostly presented by its author in an informal way. The main aim of the present article is contributing to Gardenfors’ theory of conceptual spaces ¨ by discussing some of the advantages which derive from the possibility of representing concepts in high-dimensional linear spaces.

FUZZY KERNEL REGRESSION FOR REGISTRATION AND OTHER IMAGE WARPING APPLICATIONS

2011

In this dissertation a new approach for non-rigid medical im- age registration is presented. It relies onto a probabilistic framework based on the novel concept of Fuzzy Kernel Regression. The theoric framework, after a formal introduction is applied to develop several complete registration systems, two of them are interactive and one is fully automatic. They all use the composition of local deforma- tions to achieve the final alignment. Automatic one is based onto the maximization of mutual information to produce local affine aligments which are merged into the global transformation. Mutual Information maximization procedure uses gradient descent method. Due to the huge amount of data asso…

Gamma kernel intensity estimation in time point processes

2009

Comparison between nonparametric and parametric estimate of the conditional intensity function of a seismic space-time point process

2008

A seismic gap can be defined as a segment of an active geologic fault that has not produced seismic events for an unusually long time; gaps are often considered susceptible to future strong earthquakes occurrence and therefore their identification may be useful for predictive purposes. In this paper we try to identify gaps in an area of South Tyrrhenian Sea by comparing the observed seismicity, estimated by nonparametric method, and the theoretical one, described by a particular space-time point process (ETAS model).

Active Learning Methods for Efficient Hybrid Biophysical Variable Retrieval

2016

Kernel-based machine learning regression algorithms (MLRAs) are potentially powerful methods for being implemented into operational biophysical variable retrieval schemes. However, they face difficulties in coping with large training data sets. With the increasing amount of optical remote sensing data made available for analysis and the possibility of using a large amount of simulated data from radiative transfer models (RTMs) to train kernel MLRAs, efficient data reduction techniques will need to be implemented. Active learning (AL) methods enable to select the most informative samples in a data set. This letter introduces six AL methods for achieving optimized biophysical variable estimat…

Multi-temporal and Multi-source Remote Sensing Image Classification by Nonlinear Relative Normalization

2016

Remote sensing image classification exploiting multiple sensors is a very challenging problem: data from different modalities are affected by spectral distortions and mis-alignments of all kinds, and this hampers re-using models built for one image to be used successfully in other scenes. In order to adapt and transfer models across image acquisitions, one must be able to cope with datasets that are not co-registered, acquired under different illumination and atmospheric conditions, by different sensors, and with scarce ground references. Traditionally, methods based on histogram matching have been used. However, they fail when densities have very different shapes or when there is no corres…

Causal inference in geosciences with kernel sensitivity maps

2020

Establishing causal relations between random variables from observational data is perhaps the most important challenge in today's Science. In remote sensing and geosciences this is of special relevance to better understand the Earth's system and the complex and elusive interactions between processes. In this paper we explore a framework to derive cause-effect relations from pairs of variables via regression and dependence estimation. We propose to focus on the sensitivity (curvature) of the dependence estimator to account for the asymmetry of the forward and inverse densities of approximation residuals. Results in a large collection of 28 geoscience causal inference problems demonstrate the…