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Optimally weighted L(2) distance for functional data.

ABSTRACT: Many techniques of functional data analysis require choosing a measure of distance between functions, with the most common choice being L2 distance. In this article we show that using a weighted L2 distance, with a judiciously chosen weight function, can improve the performance of various statistical methods for functional data, including k-medoids clustering, nonparametric classification, and permutation testing. Assuming a quadratically penalized (e.g., spline) basis representation for the functional data, we consider three nontrivial weight functions: design density weights, inverse-variance weights, and a new weight function that minimizes the coefficient of variation of the resulting squared distance by means of an efficient iterative procedure. The benefits of weighting, in particular with the proposed weight function, are demonstrated both in simulation studies and in applications to the Berkeley growth data and a functional magnetic resonance imaging data set.

SUBMITTER: Chen H

PROVIDER: S-EPMC4652579 | biostudies-literature | 2014 Sep

REPOSITORIES: biostudies-literature

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Optimally weighted L(2) distance for functional data.

Chen Huaihou H Reiss Philip T PT Tarpey Thaddeus T

Biometrics 20140313 3

Many techniques of functional data analysis require choosing a measure of distance between functions, with the most common choice being L2 distance. In this article we show that using a weighted L2 distance, with a judiciously chosen weight function, can improve the performance of various statistical methods for functional data, including k-medoids clustering, nonparametric classification, and permutation testing. Assuming a quadratically penalized (e.g., spline) basis representation for the fun ...[more]

PMID: 26228660

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Project description:Alzheimer's disease (AD) is increasingly recognized as a disconnection syndrome, which leads to cognitive impairment due to the disruption of functional activity across large networks or systems of interconnected brain regions. We explored abnormal functional magnetic resonance imaging (fMRI) resting-state dynamics, functional connectivity, and weighted functional networks, in a sample of patients with severe AD (N = 18) and age-matched healthy volunteers (N = 21). We found that patients had reduced amplitude and regional homogeneity of low-frequency fMRI oscillations, and reduced the strength of functional connectivity, in several regions previously described as components of the default mode network, for example, medial posterior parietal cortex and dorsal medial prefrontal cortex. In patients with severe AD, functional connectivity was particularly attenuated between regions that were separated by a greater physical distance; and loss of long distance connectivity was associated with less efficient global and nodal network topology. This profile of functional abnormality in severe AD was consistent with the results of a comparable analysis of data on 2 additional groups of patients with mild AD (N = 17) and amnestic mild cognitive impairment (MCI; N = 18). A greater degree of cognitive impairment, measured by the mini-mental state examination across all patient groups, was correlated with greater attenuation of functional connectivity, particularly over long connection distances, for example, between anterior and posterior components of the default mode network, and greater reduction of global and nodal network efficiency. These results indicate that neurodegenerative disruption of fMRI oscillations and connectivity in AD affects long-distance connections to hub nodes, with the consequent loss of network efficiency. This profile was evident also to a lesser degree in the patients with less severe cognitive impairment, indicating that the potential of resting-state fMRI measures as biomarkers or predictors of disease progression in AD.

Dataset Information

Optimally weighted L(2) distance for functional data.

Publications

Optimally weighted L(2) distance for functional data.

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