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In the present work, we developed a sequential matrix approximation procedure, which uses increasingly larger subsets of mutation pairs in W to provide a series of estimates for w as solutions of the weighted least squares problem [16].
To evaluate the performance of the sequential matrix approximation procedure in practice, we applied it to a recent high-resolution genetic interaction study of St Onge et al. [10].
The purpose of the data transformation is to improve the scoring of the various interaction classes using the double-mutant fitness measurements together with the single-mutant fitness estimates, obtained through the matrix approximation procedure.
The matrix approximation procedure has been made available to support the design and analysis of the future screening studies.
The filtered and normalized double-mutant fitness data matrix, with median close to unity, was used in the matrix approximation procedure.
To promote its widespread usage in the future screening studies, we have made publicly available an efficient, stand-alone R-implementation of the quantile-based matrix approximation procedure (QMAP).
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We invite those participating in the genetic interaction mapping effort to try out the matrix approximation-based procedure and to give us input and suggestions for its further improvements.
NMF is an approximation procedure to the original matrix in a distance metric.
In case the dimensionality of the double-mutant fitness matrix W is moderate, the matrix approximation problem can be treated using iterative procedures, which solve the weighted least-squares optimization problem, in which binary weights can be employed to ignore the effects of missing entries [58].
Throughout the operation of the approximation procedure, we ensured that the weight matrix remained symmetric.
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.
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