Related papers: Optimized Kernel Entropy Components
Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In…
Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…
Many studies of neural activity in behaving animals aim to discover interpretable low-dimensional structure in large-scale neural population recordings. One approach to this problem is demixed principal component analysis (dPCA), a…
We consider the problem of estimating multiple principal components using the recently-proposed Sparse and Functional Principal Components Analysis (SFPCA) estimator. We first propose an extension of SFPCA which estimates several principal…
Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of…
This paper introduces a novel kernel density estimator (KDE) based on the generalised exponential (GE) distribution, designed specifically for positive continuous data. The proposed GE KDE offers a mathematically tractable form that avoids…
In this article, we introduce a kernel-based consensual aggregation method for regression problems. We aim to exibly combine individual regression estimators $r_1, \ldots, r_M$ using a weighted average where the weights are dened based on…
Principal component analysis (PCA) is a key tool in the field of data dimensionality reduction that is useful for various data science problems. However, many applications involve heterogeneous data that varies in quality due to noise…
Principal Component Analysis (PCA) is one of the most important unsupervised methods to handle high-dimensional data. However, due to the high computational complexity of its eigen decomposition solution, it hard to apply PCA to the…
Independent component analysis (ICA) is a method for recovering statistically independent signals from observations of unknown linear combinations of the sources. Some of the most accurate ICA decomposition methods require searching for the…
This paper develops a method to detect model structural changes by applying a Corrected Kernel Principal Component Analysis (CKPCA) to construct the so-called central distribution deviation subspaces. This approach can efficiently identify…
The K-means algorithm is among the most commonly used data clustering methods. However, the regular K-means can only be applied in the input space and it is applicable when clusters are linearly separable. The kernel K-means, which extends…
An efficient computational approach for optimal reconstructing parameters of binary-type physical properties for models in biomedical applications is developed and validated. The methodology includes gradient-based multiscale optimization…
PCA is widely used in health and care research to analyze complex HD datasets, such as patient health records, genetic data, and medical imaging. By reducing dimensionality, PCA helps identify key patterns and trends, which can aid in…
Discrete entropy estimation is a classic information theory problem, wherein the average information content of a discrete random variable is estimated from samples alone. Naive approaches, such as the plugin method, fail to account for the…
Non-Gaussian component analysis (NGCA) is a problem in multidimensional data analysis which, since its formulation in 2006, has attracted considerable attention in statistics and machine learning. In this problem, we have a random variable…
Machine learning methods usually depend on internal parameters -- so called hyperparameters -- that need to be optimized for best performance. Such optimization poses a burden on machine learning practitioners, requiring expert knowledge,…
The Hilbert Schmidt Independence Criterion (HSIC) is a kernel dependence measure that has applications in various aspects of machine learning. Conveniently, the objectives of different dimensionality reduction applications using HSIC often…
Kernel canonical correlation analysis (KCCA) is a nonlinear multi-view representation learning technique with broad applicability in statistics and machine learning. Although there is a closed-form solution for the KCCA objective, it…
A kernel method is proposed to estimate the condensed density of the generalized eigenvalues of pencils of Hankel matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance. These pencils arise when…