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
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Journal ArticleDOI
Learning the properties of adaptive regions with functional data analysis.
TL;DR: An approach termed SURFDAWave is presented, which translates measures of genetic diversity calculated in genomic windows to functional data, and identifies BNC2 in Europeans as a target of adaptive introgression, and predicts that it harbors a beneficial mutation that arose in an archaic human population that split from modern humans within the hypothesized modern human-Neanderthal divergence range.
Journal ArticleDOI
Estimating Truncated Functional Linear Models With a Nested Group Bridge Approach
TL;DR: In this paper, a scalar-on-function truncated linear regression model is proposed, where the functional predictor does not influence the response when the time passes a certain cutoff point.
Journal ArticleDOI
Modeling double time-scale travel time processes with application to assessing the resilience of transportation systems
TL;DR: The proposed double time-scale model can be used to evaluate short-term to long-term effects of new transport policies and construction of critical infrastructures, and to analyze the resilience of road networks under disruptions, to capture the day-to-day evolution along with the within-day variability of travel time.
Journal ArticleDOI
Heterogeneous Aging Effects on Functional Connectivity in Different Cortical Regions: A Resting-State Functional MRI Study Using Functional Data Analysis
Pin-Yu Chen,Jeng-Min Chiou,Ya-Fang Yang,Yu-Ting Chen,Hsin-Long Hsieh,Yu-Ling Chang,Wen-Yih Isaac Tseng +6 more
TL;DR: Functional correlation analysis enables differentiation of changes in functional connectivities and characterizes the heterogeneous aging effects in different cortical regions.
Journal ArticleDOI
Analyzing speech in both time and space: Generalized additive mixed models can uncover systematic patterns of variation in vocal tract shape in real-time MRI
Christopher Carignan,Phil Hoole,Esther Kunay,Marianne Pouplier,Arun A. Joseph,Dirk Voit,Jens Frahm,Jonathan Harrington +7 more
TL;DR: It is proposed that GAMMs are a robust, powerful, and interpretable method of simultaneously analyzing both temporal and spatial effects in rt-MRI video of speech.
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.