Related papers: Dynamic Functional Principal Component
Principal component analysis (PCA) is a classical and widely used method for dimensionality reduction, with applications in data compression, computer vision, pattern recognition, and signal processing. However, PCA is designed for…
Local field potentials (LFPs) are signals that measure electrical activity in localized cortical regions from implanted tetrodes in the human or animal brain. The LFP signals are curves observed at multiple tetrodes which are implanted…
Intermittency analysis of factorial moments is a promising method used for the detection of power-law scaling in high-energy collision data. In particular, it has been employed in the search of fluctuations characteristic of the critical…
We consider the sampling problem for functional PCA (fPCA), where the simplest example is the case of taking time samples of the underlying functional components. More generally, we model the sampling operation as a continuous linear map…
Dimensionality reduction is a critical step in scaling machine learning pipelines. Principal component analysis (PCA) is a standard tool for dimensionality reduction, but performing PCA over a full dataset can be prohibitively expensive. As…
Two existing approaches to functional principal components analysis (FPCA) are due to Rice and Silverman (1991) and Silverman (1996), both based on maximizing variance but introducing penalization in different ways. In this article we…
The Principal Component Analysis (PCA) is a data dimensionality reduction technique well-suited for processing data from sensor networks. It can be applied to tasks like compression, event detection, and event recognition. This technique is…
As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale…
Multivariate Functional Principal Component Analysis (MFPCA) is a valuable tool for exploring relationships and identifying shared patterns of variation in multivariate functional data. However, controlling the roughness of the extracted…
Sequential or online dimensional reduction is of interests due to the explosion of streaming data based applications and the requirement of adaptive statistical modeling, in many emerging fields, such as the modeling of energy end-use…
The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the…
Between 2011 and 2014 NHANES collected objectively measured physical activity data using wrist-worn accelerometers for tens of thousands of individuals for up to seven days. In this study, we analyze minute-level indicators of being active,…
Principal component analysis (PCA) is a widely used dimension reduction method, but its performance is known to be non-robust to outliers. Recently, product-PCA (PPCA) has been shown to possess the efficiency-loss free ordering-robustness…
Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and thus, various robust PCA methods have been proposed.…
Principal component analysis (PCA) is an essential algorithm for dimensionality reduction in many data science domains. We address the problem of performing a federated PCA on private data distributed among multiple data providers while…
We consider Fair Principal Component Analysis (FPCA) and search for a low dimensional subspace that spans multiple target vectors in a fair manner. FPCA is defined as a non-concave maximization of the worst projected target norm within a…
We propose a novel class of prior distributions for sequences of orthogonal functions, which are frequently required in various statistical models such as functional principal component analysis (FPCA). Our approach constructs priors…
Multidimensional functional data streams arise in diverse scientific fields, yet their analysis poses significant challenges. We propose a novel online framework for functional principal component analysis that enables efficient and…
Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…
We propose a time domain approach to define dynamic principal components (DPC) using a reconstruction of the original series criterion. This approach to define DPC was introduced by Brillinger, who gave a very elegant theoretical solution…