Related papers: Sparse Functional Linear Discriminant Analysis
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
We propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data, where both the predictor and response are functions of a covariate such as time. Predictor and response processes have smooth…
We propose a novel framework for sparse functional clustering that also embeds an alignment step. Sparse functional clustering means finding a grouping structure while jointly detecting the parts of the curves' domains where their grouping…
Feature selection and feature transformation, the two main ways to reduce dimensionality, are often presented separately. In this paper, a feature selection method is proposed by combining the popular transformation based dimensionality…
This paper develops a convex approach for sparse one-dimensional deconvolution that improves upon L1-norm regularization, the standard convex approach. We propose a sparsity-inducing non-separable non-convex bivariate penalty function for…
High-dimensional learning problems, where the number of features exceeds the sample size, often require sparse regularization for effective prediction and variable selection. While established for fully supervised data, these techniques…
Many real world practical problems can be formulated as $\ell_{0}$-minimization problems with nonnegativity constraints, which seek the sparsest nonnegative signals to underdetermined linear systems. They have been widely applied in signal…
We suggest a new method, called Functional Additive Regression, or FAR, for efficiently performing high-dimensional functional regression. FAR extends the usual linear regression model involving a functional predictor, $X(t)$, and a scalar…
A new model-based procedure is developed for sparse clustering of functional data that aims to classify a sample of curves into homogeneous groups while jointly detecting the most informative portions of domain. The proposed method is…
We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…
In this paper, a s-difference type regularization for sparse recovery problem is proposed, which is the difference of the normal penalty function R(x) and its corresponding struncated function R (xs). First, we show the equivalent…
Recovering nonlinearly degraded signal in the presence of noise is a challenging problem. In this work, this problem is tackled by minimizing the sum of a non convex least-squares fit criterion and a penalty term. We assume that the…
Sparse functional data frequently arise in real-world applications, posing significant challenges for accurate classification. To address this, we propose a novel classification method that integrates functional principal component analysis…
We compute approximate solutions to L0 regularized linear regression using L1 regularization, also known as the Lasso, as an initialization step. Our algorithm, the Lass-0 ("Lass-zero"), uses a computationally efficient stepwise search to…
The goal of compressed sensing is to reconstruct a sparse signal under a few linear measurements far less than the dimension of the ambient space of the signal. However, many real-life applications in physics and biomedical sciences carry…
In recent years many sparse linear discriminant analysis methods have been proposed for high-dimensional classification and variable selection. However, most of these proposals focus on binary classification and they are not directly…
Linear discriminant analysis (LDA) is a classical method for dimensionality reduction, where discriminant vectors are sought to project data to a lower dimensional space for optimal separability of classes. Several recent papers have…
Regularized variants of Principal Components Analysis, especially Sparse PCA and Functional PCA, are among the most useful tools for the analysis of complex high-dimensional data. Many examples of massive data, have both sparse and…
In this work, we consider a class of linear ill-posed problems with operators that map from the sequence space $ \ell_r $ ($r \ge 1$) into a Banach space and in addition satisfy a conditional stability estimate in the scale of sequence…
Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…