SMSSVD - SubMatrix Selection Singular Value Decomposition
This provides a tool for biomedical researchers to perform unbiased exploratory analysis and signal reconstruction, though it appears incremental as an enhancement to existing decomposition methods.
The authors tackled the problem of decomposing multiple overlaid signals in high-throughput biomedical data, introducing SMSSVD, a parameter-free unsupervised method that outperforms standard techniques like PCA and Sparse PCA on real and synthetic datasets.
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).