A best matrix approximation technique for updating the analytical model is developed using the known modal parameters.
Low-rank matrix approximation problem is a field which arises in a number of applications in model selection, system identification, complexity theory, and optics.
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.
A piecewise linear approximation model is shown.
The matrix approximation approach is based on the concept that most gene pairs in the large-scale genetic interaction screens have no significant interaction with each other, suggesting that the double-mutant fitness matrix W alone should carry enough information for the estimation of the vector w of single-mutant fitness effects under an appropriate null model (see Methods for details).
Recent work on fast matrix approximation may help speed up these calculations and save memory capacities [34], [35].
ROL and VPE developed and implemented the matrix approximation method.
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].
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 underlying idea of the matrix approximation it to decompose the original fitness matrix into separate components, W = x ⊗ y, where the m and n-dimensional vectors x and y model the variability across the array and query mutants, respectively [ 31, 34].
