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
Multivariate Functional Regression Via Nested Reduced-Rank Regularization
Xiaokang Liu,Shujie Ma,Kun Chen +2 more
TL;DR: In this paper, a nested reduced-rank regression (NRRR) approach is proposed to fit a regression model with multivariate functional responses and predictors to achieve tailored dimension reduction and facilitat...
Posted Content
Trajectory Functional Boxplots
TL;DR: Wang et al. as discussed by the authors proposed two informative exploratory tools, the trajectory functional boxplot, and the modified simplicial band depth versus Wiggliness of Directional Outlyingness (WO) plot, to visualize the centrality of trajectory functional data.
Journal ArticleDOI
Functional Fuzzy System: A Nonlinear Regression Model and Its Learning Algorithm for Function-on-Function Regression
TL;DR: In this article , the authors proposed a functional fuzzy regression model known as functional fuzzy system (FFS) and its learning method from data, which is a general nonlinear functional regression model, which has inputs and outputs are functions in infinite dimensional spaces.
A wavelet-based method in aggregated functional data analysis
TL;DR: In this article , a bayesian wavelet shrinkage rule based on a mixture of a point mass function at zero and the logistic distribution as prior to wavelet coefficients is proposed to estimate mean curves of components.
Journal ArticleDOI
On functional processes with multiple discontinuities
TL;DR: In this paper , the authors consider the problem of estimating multiple change points for a functional data process and propose a half-kernel approach that addresses the inference of the total number, locations and jump sizes of the changes.
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.