Search results for "Kernel method"
showing 10 items of 79 documents
Kernel methods and their derivatives: Concept and perspectives for the earth system sciences.
2020
Kernel methods are powerful machine learning techniques which implement generic non-linear functions to solve complex tasks in a simple way. They Have a solid mathematical background and exhibit excellent performance in practice. However, kernel machines are still considered black-box models as the feature mapping is not directly accessible and difficult to interpret.The aim of this work is to show that it is indeed possible to interpret the functions learned by various kernel methods is intuitive despite their complexity. Specifically, we show that derivatives of these functions have a simple mathematical formulation, are easy to compute, and can be applied to many different problems. We n…
Kernel Anomalous Change Detection for Remote Sensing Imagery
2020
Anomalous change detection (ACD) is an important problem in remote sensing image processing. Detecting not only pervasive but also anomalous or extreme changes has many applications for which methodologies are available. This paper introduces a nonlinear extension of a full family of anomalous change detectors. In particular, we focus on algorithms that utilize Gaussian and elliptically contoured (EC) distribution and extend them to their nonlinear counterparts based on the theory of reproducing kernels' Hilbert space. We illustrate the performance of the kernel methods introduced in both pervasive and ACD problems with real and simulated changes in multispectral and hyperspectral imagery w…
Randomized kernels for large scale Earth observation applications
2020
Abstract Current remote sensing applications of bio-geophysical parameter estimation and image classification have to deal with an unprecedented big amount of heterogeneous and complex data sources. New satellite sensors involving a high number of improved time, space and wavelength resolutions give rise to challenging computational problems. Standard physical inversion techniques cannot cope efficiently with this new scenario. Dealing with land cover classification of the new image sources has also turned to be a complex problem requiring large amount of memory and processing time. In order to cope with these problems, statistical learning has greatly helped in the last years to develop st…
Randomized Rx For Target Detection
2018
This work tackles the target detection problem through the well-known global RX method. The RX method models the clutter as a multivariate Gaussian distribution, and has been extended to nonlinear distributions using kernel methods. While the kernel RX can cope with complex clutters, it requires a considerable amount of computational resources as the number of clutter pixels gets larger. Here we propose random Fourier features to approximate the Gaussian kernel in kernel RX and consequently our development keep the accuracy of the nonlinearity while reducing the computational cost which is now controlled by an hyperparameter. Results over both synthetic and real-world image target detection…
Consistent Regression of Biophysical Parameters with Kernel Methods
2020
This paper introduces a novel statistical regression framework that allows the incorporation of consistency constraints. A linear and nonlinear (kernel-based) formulation are introduced, and both imply closed-form analytical solutions. The models exploit all the information from a set of drivers while being maximally independent of a set of auxiliary, protected variables. We successfully illustrate the performance in the estimation of chlorophyll content.
A Unified SVM Framework for Signal Estimation
2013
This paper presents a unified framework to tackle estimation problems in Digital Signal Processing (DSP) using Support Vector Machines (SVMs). The use of SVMs in estimation problems has been traditionally limited to its mere use as a black-box model. Noting such limitations in the literature, we take advantage of several properties of Mercer's kernels and functional analysis to develop a family of SVM methods for estimation in DSP. Three types of signal model equations are analyzed. First, when a specific time-signal structure is assumed to model the underlying system that generated the data, the linear signal model (so called Primal Signal Model formulation) is first stated and analyzed. T…
Semisupervised nonlinear feature extraction for image classification
2012
Feature extraction is of paramount importance for an accurate classification of remote sensing images. Techniques based on data transformations are widely used in this context. However, linear feature extraction algorithms, such as the principal component analysis and partial least squares, can address this problem in a suboptimal way because the data relations are often nonlinear. Kernel methods may alleviate this problem only when the structure of the data manifold is properly captured. However, this is difficult to achieve when small-size training sets are available. In these cases, exploiting the information contained in unlabeled samples together with the available training data can si…
Kernel-Based Inference of Functions Over Graphs
2018
Abstract The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting—and prevalent in several fields of study—problem is that of inferring a function defined over the nodes of a network. This work presents a versatile kernel-based framework for tackling this inference problem that naturally subsumes and generalizes the reconstruction approaches put forth recently for the signal processing by the community studying graphs. Both the static and the dynamic settings are considered along with effective modeling approaches for addressing real-world problems. The analytical discussion herein is complement…
Model selection based product kernel learning for regression on graphs
2013
The choice of a suitable graph kernel is intrinsically hard and often cannot be made in an informed manner for a given dataset. Methods for multiple kernel learning offer a possible remedy, as they combine and weight kernels on the basis of a labeled training set of molecules to define a new kernel. Whereas most methods for multiple kernel learning focus on learning convex linear combinations of kernels, we propose to combine kernels in products, which theoretically enables higher expressiveness. In experiments on ten publicly available chemical QSAR datasets we show that product kernel learning is on no dataset significantly worse than any of the competing kernel methods and on average the…
A structural cluster kernel for learning on graphs
2012
In recent years, graph kernels have received considerable interest within the machine learning and data mining community. Here, we introduce a novel approach enabling kernel methods to utilize additional information hidden in the structural neighborhood of the graphs under consideration. Our novel structural cluster kernel (SCK) incorporates similarities induced by a structural clustering algorithm to improve state-of-the-art graph kernels. The approach taken is based on the idea that graph similarity can not only be described by the similarity between the graphs themselves, but also by the similarity they possess with respect to their structural neighborhood. We applied our novel kernel in…