From the > menu, you can select to perform Robust Principal Component Analysis (RPCA). RPCA is an algorithm for statistical pre-filtering of outliers in measurements. The objective is to separate correlations between field design from outliers. While traditional Principal Component Analysis (PCA) is very sensitive to data corruption or outliers, RPCA is robust to data corruption under surprisingly broad conditions.
RPCA attempts to split a given matrix (M) into two matrices
(S and L):
M = L + S
where L is a low-rank matrix and S
is a sparse matrix of random errors (of arbitrary magnitude and random sign). In the
context of oSP3D, each column vector of M might be a
particular field design. Without any prior knowledge about outliers, RPCA is then
able to separate correlations between field designs (L) from
outliers (S).
Security camera footage is a good example. Following the M
= L + S data model,
L represents the slowly changing background, while
S represents movement (the people who are walking). For
more examples and a precise definition of the conditions for RPCA to deliver good
results, see https://arxiv.org/abs/0912.3599.
By default, ComputeRPCA creates two new quantity
identifiers named RPCA[quantityIdent]
(L) and RPCAError[quantityIdent]
(S). The algorithm attempts to recover
L and S by running the Principal
Component Pursuit bi-objective optimization program:
where 
denotes the nuclear norm of Y (the sum of the singular values of
L) and 
denotes the 
-norm of S seen as a long vector.
The recommended value is 
.