Search results for "Kernel principal component analysis"
showing 10 items of 21 documents
On application of kernel PCA for generating stimulus features for fMRI during continuous music listening
2017
Abstract Background There has been growing interest towards naturalistic neuroimaging experiments, which deepen our understanding of how human brain processes and integrates incoming streams of multifaceted sensory information, as commonly occurs in real world. Music is a good example of such complex continuous phenomenon. In a few recent fMRI studies examining neural correlates of music in continuous listening settings, multiple perceptual attributes of music stimulus were represented by a set of high-level features, produced as the linear combination of the acoustic descriptors computationally extracted from the stimulus audio. New method fMRI data from naturalistic music listening experi…
Reproducing kernel hilbert spaces regression methods for genomic assisted prediction of quantitative traits.
2008
Abstract Reproducing kernel Hilbert spaces regression procedures for prediction of total genetic value for quantitative traits, which make use of phenotypic and genomic data simultaneously, are discussed from a theoretical perspective. It is argued that a nonparametric treatment may be needed for capturing the multiple and complex interactions potentially arising in whole-genome models, i.e., those based on thousands of single-nucleotide polymorphism (SNP) markers. After a review of reproducing kernel Hilbert spaces regression, it is shown that the statistical specification admits a standard mixed-effects linear model representation, with smoothing parameters treated as variance components.…
Sign and Rank Covariance Matrices: Statistical Properties and Application to Principal Components Analysis
2002
In this paper, the estimation of covariance matrices based on multivariate sign and rank vectors is discussed. Equivariance and robustness properties of the sign and rank covariance matrices are described. We show their use for the principal components analysis (PCA) problem. Limiting efficiencies of the estimation procedures for PCA are compared.
Nonlinear PCA for Spatio-Temporal Analysis of Earth Observation Data
2020
Remote sensing observations, products, and simulations are fundamental sources of information to monitor our planet and its climate variability. Uncovering the main modes of spatial and temporal variability in Earth data is essential to analyze and understand the underlying physical dynamics and processes driving the Earth System. Dimensionality reduction methods can work with spatio-temporal data sets and decompose the information efficiently. Principal component analysis (PCA), also known as empirical orthogonal functions (EOFs) in geophysics, has been traditionally used to analyze climatic data. However, when nonlinear feature relations are present, PCA/EOF fails. In this article, we pro…
Optimized Kernel Entropy Components
2016
This work addresses two main issues of the standard Kernel Entropy Component Analysis (KECA) algorithm: the optimization of the kernel decomposition and the optimization of the Gaussian kernel parameter. KECA roughly reduces to a sorting of the importance of kernel eigenvectors by entropy instead of by variance as in Kernel Principal Components Analysis. In this work, we propose an extension of the KECA method, named Optimized KECA (OKECA), that directly extracts the optimal features retaining most of the data entropy by means of compacting the information in very few features (often in just one or two). The proposed method produces features which have higher expressive power. In particular…
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…
A more distinctive representation for 3D shape descriptors using principal component analysis
2015
Many researchers have used the Heat Kernel Signature (or HKS) for characterizing points on non-rigid three-dimensional shapes and Classical Multidimensional Scaling (Classical MDS) method in object classification which we quote, in particular, the example of Jian Sun et al. (2009) [1]. However, in this paper, the main focuses on classification that we propose a concise and provably factorial method by invoking Principal Component Analysis (PCA) as a classifier to improve the scheme of 3D shape classification. To avoid losing or disordering information after extracting features from the mesh, PCA is used instead of the Classical MDS to discriminate-as much as possible-feature points for each…
Learning with the kernel signal to noise ratio
2012
This paper presents the application of the kernel signal to noise ratio (KSNR) in the context of feature extraction to general machine learning and signal processing domains. The proposed approach maximizes the signal variance while minimizes the estimated noise variance in a reproducing kernel Hilbert space (RKHS). The KSNR can be used in any kernel method to deal with correlated (possibly non-Gaussian) noise. We illustrate the method in nonlinear regression examples, dependence estimation and causal inference, nonlinear channel equalization, and nonlinear feature extraction from high-dimensional satellite images. Results show that the proposed KSNR yields more fitted solutions and extract…
Explicit signal to noise ratio in reproducing kernel Hilbert spaces
2011
This paper introduces a nonlinear feature extraction method based on kernels for remote sensing data analysis. The proposed approach is based on the minimum noise fraction (MNF) transform, which maximizes the signal variance while also minimizing the estimated noise variance. We here propose an alternative kernel MNF (KMNF) in which the noise is explicitly estimated in the reproducing kernel Hilbert space. This enables KMNF dealing with non-linear relations between the noise and the signal features jointly. Results show that the proposed KMNF provides the most noise-free features when confronted with PCA, MNF, KPCA, and the previous version of KMNF. Extracted features with the explicit KMNF…
An Introduction to Kernel Methods
2009
Machine learning has experienced a great advance in the eighties and nineties due to the active research in artificial neural networks and adaptive systems. These tools have demonstrated good results in many real applications, since neither a priori knowledge about the distribution of the available data nor the relationships among the independent variables should be necessarily assumed. Overfitting due to reduced training data sets is controlled by means of a regularized functional which minimizes the complexity of the machine. Working with high dimensional input spaces is no longer a problem thanks to the use of kernel methods. Such methods also provide us with new ways to interpret the cl…