In contrast, the alternative ARF matrix approximation method performed poorer in the E-MAP dataset, regardless of whether or not the preprocessing option was used (Figure S3).
In particular, our QMA decomposition method was found out to be essential in the detection of positive interaction pairs (Figure 1A), whereas the alternative ARF matrix approximation method showed good performance in the negative interaction classes only (Figure S1).
In this work, we develop a novel and efficient rank-one matrix approximation method, named QMA, to address the problem of detecting accurately also the positive end of interactions, yet being simple enough for the large-data interaction datasets.
In the identification of the most distinctive negative pairs, the QMA estimation parameters shared by both the positive and negative categories performed relatively well, compared to the parameters adjusted specifically to the three negative categories (Figures 1B D), indicating that the matrix approximation method can be made relatively robust using the fixed mode.
The matrix approximation method is conceptually similar to the Tukey's median polish procedure [60], except that QMA uses multiplicative model instead of additive model, division in place of subtraction, arbitrary quantile points instead of fixed medians, and performs one iteration only rather than continuing until convergence or pre-defined number of iteration steps.
ROL and VPE developed and implemented the matrix approximation method.
In the present work, the estimation of x and y was performed using a robust, rank-one matrix approximation method, named quantile-based matrix approximation (QMA) [ 31].
The quantile-based matrix approximation (QMA) is an efficient rank-one matrix approximation method, which is conceptually similar to the Tukey's median polish procedure, except that QMA uses multiplicative model instead of additive model and quantiles instead of medians [ 31].
The presumption was that such a data preprocessing could potentially make the null model for the non-interacting genes more distinctive, and therefore facilitate its estimation by means of matrix-approximation methods, especially in those datasets, such as SGA and GIM, in which the original double-mutant fitness measurements were available.
The proposed sparse CCA seeks to obtain iteratively a sparse pair of canonical projectors by solving a penalized rank-1 matrix approximation via a sparse coding method.
In this section, we will propose the sparse CCA method based on rank-1 matrix approximation by penalizing the optimization problem (18).
