scrnaseq – Understanding regularization step in Meta-cell pre processing

I’m reading through this paper: Baran, Y., Bercovich, A., Sebe-Pedros, A., Lubling, Y., Giladi, A., Chomsky, E., … & Tanay, A. (2019). MetaCell: analysis of single-cell RNA-seq data using K-nn graph partitions. Genome biology, 20(1), 1-19.

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Maybe I am not familiar with this notation but I don’t understand the regularization procedure as follows:

  1. What is happening in these max functions? What does the 0 indicate? They have some terms $x$ and then in the max function they write $max( x, 0)$.
  2. I assume $K$ is some regularization parameter, like a cost. Is $s_{ij} * s_{ji}$ the rank product? I.e. the geometric mean?

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