  High throughput biomedical measurements normally capture multiple overlaid
biologically relevant signals and often also signals representing different
types of technical artefacts like e.g. batch effects. Signal identification and
decomposition are accordingly main objectives in statistical biomedical
modeling and data analysis. Existing methods, aimed at signal reconstruction
and deconvolution, in general, are either supervised, contain parameters that
need to be estimated or present other types of ad hoc features. We here
introduce SubMatrix Selection SingularValue Decomposition (SMSSVD), a
parameter-free unsupervised signal decomposition and dimension reduction
method, designed to reduce noise, adaptively for each low-rank-signal in a
given data matrix, and represent the signals in the data in a way that enable
unbiased exploratory analysis and reconstruction of multiple overlaid signals,
including identifying groups of variables that drive different signals.
  The Submatrix Selection Singular Value Decomposition (SMSSVD) method produces
a denoised signal decomposition from a given data matrix. The SMSSVD method
guarantees orthogonality between signal components in a straightforward manner
and it is designed to make automation possible. We illustrate SMSSVD by
applying it to several real and synthetic datasets and compare its performance
to golden standard methods like PCA (Principal Component Analysis) and SPC
(Sparse Principal Components, using Lasso constraints). The SMSSVD is
computationally efficient and despite being a parameter-free method, in
general, outperforms existing statistical learning methods.
  A Julia implementation of SMSSVD is openly available on GitHub
(https://github.com/rasmushenningsson/SMSSVD.jl).
