Wavelet‐Based Clustering for Mixed‐Effects Functional Models in High Dimension

Abstract

Summary We propose a method for high‐dimensional curve clustering in the presence of interindividual variability. Curve clustering has longly been studied especially using splines to account for functional random effects. However, splines are not appropriate when dealing with high‐dimensional data and can not be used to model irregular curves such as peak‐like data. Our method is based on a wavelet decomposition of the signal for both fixed and random effects. We propose an efficient dimension reduction step based on wavelet thresholding adapted to multiple curves and using an appropriate structure for the random effect variance, we ensure that both fixed and random effects lie in the same functional space even when dealing with irregular functions that belong to Besov spaces. In the wavelet domain our model resumes to a linear mixed‐effects model that can be used for a model‐based clustering algorithm and for which we develop an EM‐algorithm for maximum likelihood estimation. The properties of the overall procedure are validated by an extensive simulation study. Then, we illustrate our method on mass spectrometry data and we propose an original application of functional data analysis on microarray comparative genomic hybridization (CGH) data. Our procedure is available through the R package curvclust which is the first publicly available package that performs curve clustering with random effects in the high dimensional framework (available on the CRAN).

Functional Clustering of Accelerometer Data Via Transformed Input Variables

“…shows the mean curves of subgroups identified by funclust of Jacques and Preda () and curvclust of Giacofci et al . (), with the number of clusters fixed at 2. funclust is a model‐based clustering method based on the Gaussian mixture modelling of functional principal component scores, which is implemented by R package funcy. For the curvclust method, Giacofci et al .…”

“…For the curvclust method, Giacofci et al . () proposed a model‐based clustering method based on wavelet decomposition of the signal for both fixed and random effects. For this, they considered an efficient dimension reduction by wavelet thresholding and a linear mixed effects model in the wavelet domain.…”

“…Moreover, Giacofci et al . () implemented their method in R package curvclust for wavelet‐based functional mixed model clustering. Both methods identify two subgroups with different mean activity levels especially in the afternoon hours.…”

“…1 shows the mean curves of subgroups identified by funclust of Jacques and Preda (2013) and curvclust of Giacofci et al (2013), with the number of clusters fixed at 2. funclust is a model-based clustering method based on the Gaussian mixture modelling of functional principal component scores, which is implemented by R package funcy. For the curvclust method, Giacofci et al (2013) proposed a model-based clustering method based on wavelet decomposition of the signal for both fixed and random effects. For this, they considered an efficient dimension reduction by wavelet thresholding and a linear mixed effects model in the wavelet domain.…”

“…For this, they considered an efficient dimension reduction by wavelet thresholding and a linear mixed effects model in the wavelet domain. Moreover, Giacofci et al (2013) implemented their method in R package curvclust for wavelet-based functional mixed model clustering. Both methods identify two subgroups with different mean activity levels especially in the afternoon hours.…”