- Direct Known Subclasses:
AverageImplicitModelPCA
public class ExplicitImplicitModelPCA
extends Object
Given a time series of vectored observations, we decompose them
into a reduced dimension of linear sum of both explicit/specified and
implicit factors. The implicit factors are orthogonal. The user specifies the
time series of observations and th explicit factor values over time.
Specifically, we have
\(R = Γ'G + \bar{R} + {B}'F + E\)
R is the time series of vectored observation. Its size is N x
T.
G is the time series of the explicit factor values. Its size is M x
T, where M is the number of implicit factors.
Γ' is the matrix of factor loadings for explicit factors. Its size is
N x M. Each row is the explicit factor loadings for each subject.
R_bar is the average of each subject's value over time, one entry per
subject. It size is N. We copy the vector T times by columns to
form a matrix for computation.
F is the time series of the implicit factor values. Its size is K x
T, where K is the number of implicit factors.
B' is the matrix of implicit factor loadings. Its size is N x
K. Each row is the implicit factor loadings for each subject.
E is the residual matrix.