Degrees of Freedom in Functional Principal Components Analysis

This paper develops the analytical form of the degrees of freedom in functional principal components analysis. Under the framework of unbiased risk estimation, we derive an unbiased estimator with a clear analytical formula for the degrees of freedom in the one-way penalized functional principal components analysis paradigm. Specifically, a new analytical formula incorporating binary smoothing parameters is also derived based on the singular value decomposition and half-smoothed method regarding the two-way penalized functional principal components analysis framework. The performance of our procedures is demonstrated by simulation studies.

An Animated Functional Data Analysis Interface to Cluster Rapid Lung Function Decline and Enhance Center-Level Care in Cystic Fibrosis

Identifying disease progression through enhanced decision support tools is key to chronic management in cystic fibrosis at both the patient and care center level. Rapid decline in lung function relative to patient level and center norms is an important predictor of outcomes. Our objectives were to construct and utilize center-level classification of rapid decliners to develop an animated dashboard for comparisons within patients over time, multiple patients within centers, or between centers. A functional data analysis technique known as functional principal components analysis was applied to lung function trajectories from 18,387 patients across 247 accredited centers followed through the United States Cystic Fibrosis Foundation Patient Registry, in order to cluster patients into rapid decline phenotypes. Smaller centers (<30 patients) had older patients with lower baseline lung function and less severe rates of decline and had maximal decline later, compared to medium (30–150 patients) or large (>150 patients) centers. Small centers also had the lowest prevalence of early rapid decliners (17.7%, versus 24% and 25.7% for medium and large centers, resp.). The animated functional data analysis dashboard illustrated clustering and center-specific summaries of the rapid decline phenotypes. Clinical scenarios and utility of the center-level functional principal components analysis (FPCA) approach are considered and discussed.

Tracking the New Zealand English NEAR/SQUARE merger using functional principal components analysis

Copyright © 2019 ISCA The focus of the study is the application of functional principal components analysis (FPCA) to a sound change in progress in which the SQUARE and NEAR falling diphthongs are merging in New Zealand English. FPCA approximated the trajectory shapes of the first two formant frequencies (F1/F2) in a large acoustic database of read New Zealand English speech spanning three different age groups and two regions. The derived FPCA parameters showed a greater degree of centralisation and monophthongisation in SQUARE than in NEAR. Compatibly with the evidence of an ongoing sound change in which SQUARE is shifting towards NEAR, these shape differences were more marked for older than for younger/mid-age speakers. There was no effect of region nor of place of articulation of the preceding consonant; there was a trend for the merger to be more advanced in low frequency words. The study underlines the benefits of FPCA for quantifying the many types of sound changes involving subtle shifts in speech dynamics. In particular, multi-dimensional trajectory shape differences can be quantified without the need for vowel targets nor for determining the influence of the parameters - in this case of the first two formant frequencies - independently of each other.

Tracking the New Zealand English NEAR/SQUARE merger using functional principal components analysis

Copyright © 2019 ISCA The focus of the study is the application of functional principal components analysis (FPCA) to a sound change in progress in which the SQUARE and NEAR falling diphthongs are merging in New Zealand English. FPCA approximated the trajectory shapes of the first two formant frequencies (F1/F2) in a large acoustic database of read New Zealand English speech spanning three different age groups and two regions. The derived FPCA parameters showed a greater degree of centralisation and monophthongisation in SQUARE than in NEAR. Compatibly with the evidence of an ongoing sound change in which SQUARE is shifting towards NEAR, these shape differences were more marked for older than for younger/mid-age speakers. There was no effect of region nor of place of articulation of the preceding consonant; there was a trend for the merger to be more advanced in low frequency words. The study underlines the benefits of FPCA for quantifying the many types of sound changes involving subtle shifts in speech dynamics. In particular, multi-dimensional trajectory shape differences can be quantified without the need for vowel targets nor for determining the influence of the parameters - in this case of the first two formant frequencies - independently of each other.

ANALIZA WSKAŹNIKA ZATRUDNIENIA W KRAJACH NOWEJ UE Z WYKORZYSTANIEM FPCA

In the paper new countries of UE are compared with respect to employment rate in 2004-2016. Functional principal components analysis was applied. On the basis of results of this analysis the groups of countries of similar employment rate were determined.