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Fig. 1 | BMC Bioinformatics

Fig. 1

From: Trade-off between conservation of biological variation and batch effect removal in deep generative modeling for single-cell transcriptomics

Fig. 1

Panel A shows the Pareto front for an example bi-objective minimization problem. Point A and point B are non-dominated points on the Pareto front, while point C is dominated by both A and B. Panel B shows example Pareto candidates that can be discovered by the scalarization method for a convex (left) and a non-convex (right) Pareto front. In theory, scalarization cannot recover Pareto candidates in the non-convex part of a non-convex (right) Pareto front, such as Point C [9]. Panel C is a schematic of the Pareto MTL method [8], which first decomposes the bi-objective space into subregions according to a set of preference vectors \(c_k\), and then seeks a Pareto candidate within each subregion

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BMC Bioinformatics

ISSN: 1471-2105

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