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Generalized simultaneous component analysis of binary and quantitative data
Author(s) -
Song Yipeng,
Westerhuis Johan A.,
Aben Nanne,
Wessels Lodewyk F. A.,
Groenen Patrick J. F.,
Smilde Age K.
Publication year - 2021
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.3312
Subject(s) - binary number , binary data , computer science , component (thermodynamics) , subspace topology , data mining , algorithm , mathematics , artificial intelligence , physics , arithmetic , thermodynamics
In the current era of systems biology research, there is a need for the integrative analysis of binary and quantitative genomics data sets measured on the same objects. One standard tool of exploring the underlying dependence structure present in multiple quantitative data sets is the simultaneous component analysis (SCA) model. However, it does not have any provisions when a part of the data are binary. To this end, we propose the generalized SCA (GSCA) model, which takes into account the distinct mathematical properties of binary and quantitative measurements in the maximum likelihood framework. Like in the SCA model, a common low‐dimensional subspace is assumed to represent the shared information between these two distinct types of measurements. To achieve a low rank solution, we propose to use a concave variant of the nuclear norm penalty. An efficient majorization algorithm is developed to fit this model with different concave penalties. Realistic simulations (low signal‐to‐noise ratio and highly imbalanced binary data) are used to evaluate the performance of the proposed model in recovering the underlying structure. Also, a missing value based cross‐validation procedure is implemented for model selection. We illustrate the usefulness of the GSCA model for exploratory data analysis of quantitative gene expression and binary copy number aberration measurements obtained from the GDSC1000 data sets.