Related papers: A Unified Principal Components Analysis for Statio…
Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the…
Principal component analysis (PCA), a ubiquitous dimensionality reduction technique in signal processing, searches for a projection matrix that minimizes the mean squared error between the reduced dataset and the original one. Since…
Data reconciliation (DR) and Principal Component Analysis (PCA) are two popular data analysis techniques in process industries. Data reconciliation is used to obtain accurate and consistent estimates of variables and parameters from…
A novel text data dimension reduction technique, called the tree-structured multi-linear principal component anal- ysis (TMPCA), is proposed in this work. Being different from traditional text dimension reduction methods that deal with the…
Particulate matter data now include various particle sizes, which often manifest as a collection of curves observed sequentially over time. When considering 51 distinct particle sizes, these curves form a high-dimensional functional time…
This paper introduces a novel methodology for Feature Selection for Functional Classification, FSFC, that addresses the challenge of jointly performing feature selection and classification of functional data in scenarios with categorical…
This study presents the development of multivariate functional Moran's I, along with a novel approach termed multivariate functional areal spatial principal component analysis (mfasPCA), specifically designed for analyzing functional areal…
Accurate predictions of pollutant concentrations at new locations are often of interest in air pollution studies on fine particulate matters (PM$_{2.5}$), in which data is usually not measured at all study locations. PM$_{2.5}$ is also a…
In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant…
Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…
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,…
Principal component analysis (PCA) has been widely applied to dimensionality reduction and data pre-processing for different applications in engineering, biology and social science. Classical PCA and its variants seek for linear projections…
This paper proposes a novel global optimization algorithm, Particle Filter-Based Optimization (PFO), designed for a class of stochastic optimization problems in which the objective function lacks an analytical form and is subject to noisy…
Data analysis often requires methods that are invariant with respect to specific transformations, such as rotations in case of images or shifts in case of images and time series. While principal component analysis (PCA) is a widely-used…
Principal component analysis (PCA) is a widely used unsupervised dimensionality reduction technique in machine learning, applied across various fields such as bioinformatics, computer vision and finance. However, when the response variables…
In the era of big data, reducing data dimensionality is critical in many areas of science. Widely used Principal Component Analysis (PCA) addresses this problem by computing a low dimensional data embedding that maximally explain variance…
Monitoring multichannel profiles has important applications in manufacturing systems improvement, but it is non-trivial to develop efficient statistical methods due to two main challenges. First, profiles are high-dimensional functional…
In this study, we propose a function-on-function linear quantile regression model that allows for more than one functional predictor to establish a more flexible and robust approach. The proposed model is first transformed into a…
Functional principal component analysis (FPCA) based on the Karhunen--Lo\`{e}ve decomposition has been successfully applied in many applications, mainly for one sample problems. In this paper we consider common functional principal…
Principal Component Analysis (PCA) finds the best linear representation of data, and is an indispensable tool in many learning and inference tasks. Classically, principal components of a dataset are interpreted as the directions that…