bandSelect: Penalized multi-band learning function

In PML: Penalized Multi-Band Learning for Circadian Rhythm Analysis Using Actigraphy

Description

In a group of individuals with physcial activity data, this function utilize Fast Fourier Transform (FFT) and L-1/L-2 penalties to select significant harmonics/periodicities and describe the main activity pattern (circadian rhythm) among the population.

Usage

bandSelect(df, Nlength, Nlambda = 100, alpha = 1, Ntop = 5,
  cross = FALSE, Ncross = NULL, plot = TRUE)

Arguments

df	the tbl_df data frame containing at least two variables: subject ID and activity. The function form can help prepare the data frame.
Nlength	the length of observations necessary for each individual, note that it should be consistent among all
Nlambda	λ's take values from 0 to 2max(||X_k||^2), as 0 gives no penalty and the latter suppresses all θ's to 0. Therefore, we divide 2max(||X_k||^2) into Nlambda (default to be 100) λ's to pick frequencies/harmonics/periodicities.
alpha	the tuning parameter controlling the balance between L-1 and L-2 penalty. The default is 1, using complete Lasso/ L-1 penalty.
Ntop	the number of frequencies/harmonics/periodicities picked for the population. The default is 5.
cross	whether to perform cross-validation. The default is FALSE.
Ncross	the number of groups of data for cross-validation. If cross=TRUE, the data shall be divided into Ncross groups.
plot	whether to plot: MSE against the number of nonzero θ's, and only the points at which the number of nonzero θ's changes (as λ changes) are be plotted. The default is TRUE.

Value

if no cross-validation is conducted, return a list; if cross-validation, return a list of lists, with the last list consisting of all FFT results and cross-validation groups (showing the subject IDs leave-out /NOT used each time).

topfreq	vector of length Ntop: top frequencies selected.
mse	vector of length Nlambda: mean squared error for each lambda (penalty). If no cross-validation, mse is calculated based on all available data; if cross-validation, mse is calculated based on the rest observations.
nonzero	vector of length Nlambda: the number of nonzero θ's (frequencies) for each lambda (penalty).
deltazero	vector of length Nlambda: the change in the number of nonzero θ's (frequencies) for each lambda (penalty).
lambda	vector of length Nlambda: the value of lambda.
theta	Nfreq by Nlambda matrix: estimated θ's (frequencies) at each lambda (penalty). Nfreq is the total number of frequencies given by FFT.
xscore	Nind by Nfreq matrix: the original FFT scores for each individual. Nind is the number of individuals in the population, and Nfreq is the total number of frequencies given by FFT.
xprop	Nind by Nfreq matrix: the original FFT results expressed as the proportion of variances explained by each frequency for each individual. Nind is the number of individuals in the population, and Nfreq is the total number of frequencies given by FFT.
freq	vector of length Nfreq: list of frequencies in FFT results.

References

Li, X. , Kane, M. , Zhang, Y. , Sun, W. , Song, Y. , Dong, S. , Lin, Q. , Zhu, Q. , Jiang, F. & Zhao, H. (2019). Penalized Selection of Periodicities Characterizes the Consolidation of Sleep-Wake Circadian Rhythms During Early Childhood Development. Submitted.

See Also

form

Examples

data(pa3)
re <- bandSelect(df=pa3,Nlength=1440*3,Nlambda=100,alpha=1,Ntop=5,
                 cross=FALSE,Ncross=NULL,plot=TRUE)

PML documentation built on Feb. 12, 2020, 1:17 a.m.