Related papers: High-Dimensional Partial Least Squares: Spectral A…
The least-mean-squares (LMS) algorithm is the most popular algorithm in adaptive filtering. Several variable step-size strategies have been suggested to improve the performance of the LMS algorithm. These strategies enhance the performance…
Partial diffusion scheme is an effective method for reducing computational load and power consumption in adaptive network implementation. The Information is exchanged among the nodes, usually over noisy links. In this paper, we consider a…
In this paper we consider the problem of recovering a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model that can efficiently restrict the degrees of freedom of the problem and is…
There are many practical applications based on the Least Square Error (LSE) approximation. It is based on a square error minimization 'on a vertical' axis. The LSE method is simple and easy also for analytical purposes. However, if data…
Pseudospectral analysis is fundamental for quantifying the sensitivity and transient behavior of nonnormal matrices, yet its computational cost scales cubically with dimension, rendering it prohibitive for large-scale systems. While…
As a popular tool for producing meaningful and interpretable models, large-scale sparse learning works efficiently when the underlying structures are indeed or close to sparse. However, naively applying the existing regularization methods…
We present a non-conforming least squares method for approximating solutions of second order elliptic problems with discontinuous coefficients. The method is based on a general Saddle Point Least Squares (SPLS) method introduced in previous…
Bootstrap methods have long been the cornerstone of ensemble learning in machine learning. This paper presents a theoretical analysis of bootstrap techniques applied to the Least Square Support Vector Machine (LSSVM) ensemble in the context…
We study the problem of stabilizing an unknown partially observable linear time-invariant (LTI) system. For fully observable systems, leveraging an unstable/stable subspace decomposition approach, state-of-art sample complexity is…
In this paper, we establish a unified framework for subspace identification (SID) of linear parameter-varying (LPV) systems to estimate LPV state-space (SS) models in innovation form. This framework enables us to derive novel LPV SID…
Latin hypercube sampling (LHS) is generalized in terms of a spectrum of stratified sampling (SS) designs referred to as partially stratified sample (PSS) designs. True SS and LHS are shown to represent the extremes of the PSS spectrum. The…
Principal Subspace Analysis (PSA) -- and its sibling, Principal Component Analysis (PCA) -- is one of the most popular approaches for dimensionality reduction in signal processing and machine learning. But centralized PSA/PCA solutions are…
Multi-view subspace clustering always performs well in high-dimensional data analysis, but is sensitive to the quality of data representation. To this end, a two stage fusion strategy is proposed to embed representation learning into the…
In hyperspectral remote sensing data mining, it is important to take into account of both spectral and spatial information, such as the spectral signature, texture feature and morphological property, to improve the performances, e.g., the…
In this paper, we study the \emph{sparse integer least squares problem} (SILS), an NP-hard variant of least squares with sparse $\{0, \pm 1\}$-vectors. We propose an $\ell_1$-based SDP relaxation, and a randomized algorithm for SILS, which…
The selection of best variables is a challenging problem in supervised and unsupervised learning, especially in high dimensional contexts where the number of variables is usually much larger than the number of observations. In this paper,…
Spectral methods have been the mainstay in several domains such as machine learning and scientific computing. They involve finding a certain kind of spectral decomposition to obtain basis functions that can capture important structures for…
We study the functional linear regression model with a scalar response and a Hilbert space-valued predictor, a canonical example of an ill-posed inverse problem. We show that the functional partial least squares (PLS) estimator attains…
Uncertainty in estimating the log-law parameters is arguably the greatest obstacle to establishing definitive conclusions regarding their numerical values and universality. This challenge is exacerbated by the limited number of studies that…
In this work, we present a subdomain discontinuous least-squares (SDLS) scheme for neutronics problems. Least-squares (LS) methods are known to be inaccurate for problems with sharp total-cross section interfaces. In addition, the…