Dataset Information

Structured functional principal component analysis.

ABSTRACT: Motivated by modern observational studies, we introduce a class of functional models that expand nested and crossed designs. These models account for the natural inheritance of the correlation structures from sampling designs in studies where the fundamental unit is a function or image. Inference is based on functional quadratics and their relationship with the underlying covariance structure of the latent processes. A computationally fast and scalable estimation procedure is developed for high-dimensional data. Methods are used in applications including high-frequency accelerometer data for daily activity, pitch linguistic data for phonetic analysis, and EEG data for studying electrical brain activity during sleep.

SUBMITTER: Shou H

PROVIDER: S-EPMC4383722 | biostudies-literature | 2015 Mar

REPOSITORIES: biostudies-literature

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Structured functional principal component analysis.

Shou Haochang H Zipunnikov Vadim V Crainiceanu Ciprian M CM Greven Sonja S

Biometrics 20141018 1

Motivated by modern observational studies, we introduce a class of functional models that expand nested and crossed designs. These models account for the natural inheritance of the correlation structures from sampling designs in studies where the fundamental unit is a function or image. Inference is based on functional quadratics and their relationship with the underlying covariance structure of the latent processes. A computationally fast and scalable estimation procedure is developed for high- ...[more]

PMID: 25327216

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Project description:Principal component analysis is used to summarize matrix data, such as found in transcriptome, proteome or metabolome and medical examinations, into fewer dimensions by fitting the matrix to orthogonal axes. Although this methodology is frequently used in multivariate analyses, it has disadvantages when applied to experimental data. First, the identified principal components have poor generality; since the size and directions of the components are dependent on the particular data set, the components are valid only within the data set. Second, the method is sensitive to experimental noise and bias between sample groups. It cannot reflect the experimental design that is planned to manage the noise and bias; rather, it estimates the same weight and independence to all the samples in the matrix. Third, the resulting components are often difficult to interpret. To address these issues, several options were introduced to the methodology. First, the principal axes were identified using training data sets and shared across experiments. These training data reflect the design of experiments, and their preparation allows noise to be reduced and group bias to be removed. Second, the center of the rotation was determined in accordance with the experimental design. Third, the resulting components were scaled to unify their size unit.The effects of these options were observed in microarray experiments, and showed an improvement in the separation of groups and robustness to noise. The range of scaled scores was unaffected by the number of items. Additionally, unknown samples were appropriately classified using pre-arranged axes. Furthermore, these axes well reflected the characteristics of groups in the experiments. As was observed, the scaling of the components and sharing of axes enabled comparisons of the components beyond experiments. The use of training data reduced the effects of noise and bias in the data, facilitating the physical interpretation of the principal axes.Together, these introduced options result in improved generality and objectivity of the analytical results. The methodology has thus become more like a set of multiple regression analyses that find independent models that specify each of the axes.

Dataset Information

Structured functional principal component analysis.

Publications

Structured functional principal component analysis.

Similar Datasets

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