Functional Data Analysis
TLDR
In this article, the authors provide an overview of FDA, starting with simple statistical notions such as mean and covariance functions, then covering some core techniques, the most popular of which is functional principal component analysis (FPCA).Abstract:
With the advance of modern technology, more and more data are being recorded continuously during a time interval or intermittently at several discrete time points. These are both examples of functional data, which has become a commonly encountered type of data. Functional data analysis (FDA) encompasses the statistical methodology for such data. Broadly interpreted, FDA deals with the analysis and theory of data that are in the form of functions. This paper provides an overview of FDA, starting with simple statistical notions such as mean and covariance functions, then covering some core techniques, the most popular of which is functional principal component analysis (FPCA). FPCA is an important dimension reduction tool, and in sparse data situations it can be used to impute functional data that are sparsely observed. Other dimension reduction approaches are also discussed. In addition, we review another core technique, functional linear regression, as well as clustering and classification of functional d...read more
Citations
More filters
Journal ArticleDOI
Cooperative Filtering and Parameter Identification for Advection–Diffusion Processes Using a Mobile Sensor Network
TL;DR: In this article , a constrained cooperative Kalman filter is developed to provide estimates of the field values and gradients along the trajectories of the mobile sensors so that the temporal variations in field values can be estimated.
Journal ArticleDOI
From multivariate to functional data analysis: Fundamentals, recent developments, and emerging areas
TL;DR: Functional data analysis (FDA) is a branch of statistics on modeling infinite dimensional random vectors residing in functional spaces as discussed by the authors , which has become a major research area for Journal of Multivariate Analysis .
Book ChapterDOI
Estimating Parameters in Complex Systems with Functional Outputs: A Wavelet-Based Approximate Bayesian Computation Approach
TL;DR: A wavelet-based approximate Bayesian computation (wABC) approach that is likelihood-free and computationally scalable to functional data measured on a dense, high-dimensional grid and provides the joint posterior distribution of all underlying parameters, which is otherwise intractable using existing analytical methods.
Journal ArticleDOI
Truncated estimation in functional generalized linear regression models
Abdulaziz A. Alodhayani , Raghad A. Almansour , Jawaher J. Alotaibi , Ebtehaj G. Alghamdi , Mai S. …
TL;DR: In this article , a truncated likelihood estimator is formulated by combining a structured variable selection method with a localized B-spline expansion of the regression coefficient function, and a nested group lasso penalty is also included which guarantees the sequential entering of Bsplines and thus induces the desired truncation on the estimator.
Journal ArticleDOI
A calibration-free method for biosensing in cell manufacturing
TL;DR: A novel calibration-free statistical framework is proposed to effectively deduce critical quality attributes under the patient-to-patient variability ofimeric antigen receptor T-cell therapy, and can deduce the critical quality attribute of interest, free from the calibration parameter.
References
More filters
Journal ArticleDOI
Nonlinear dimensionality reduction by locally linear embedding.
Sam T. Roweis,Lawrence K. Saul +1 more
TL;DR: Locally linear embedding (LLE) is introduced, an unsupervised learning algorithm that computes low-dimensional, neighborhood-preserving embeddings of high-dimensional inputs that learns the global structure of nonlinear manifolds.
Journal ArticleDOI
A global geometric framework for nonlinear dimensionality reduction.
TL;DR: An approach to solving dimensionality reduction problems that uses easily measured local metric information to learn the underlying global geometry of a data set and efficiently computes a globally optimal solution, and is guaranteed to converge asymptotically to the true structure.
Journal ArticleDOI
Dynamic programming algorithm optimization for spoken word recognition
TL;DR: This paper reports on an optimum dynamic progxamming (DP) based time-normalization algorithm for spoken word recognition, in which the warping function slope is restricted so as to improve discrimination between words in different categories.
Journal ArticleDOI
Generalized Additive Models
Trevor Hastie,Robert Tibshirani +1 more
TL;DR: The class of generalized additive models is introduced, which replaces the linear form E fjXj by a sum of smooth functions E sj(Xj), and has the advantage of being completely auto- matic, i.e., no "detective work" is needed on the part of the statistician.