How to reduce filesize of pdf extracted from pheatmap

Hi!

I'm creating heatmaps using pheatmap, to show an overview and clustering of differentially expressed genes.
In my experiment I have tons of DEGs (18000 genes across 132 samples), so the heatmap is.. well.. pretty huge!

The problem I'm running into is that the exported file is about 11MB; which makes it impossible to process afterwards in illustrator for publication.

I tried exporting using the filename= argument of pheatmap, and using the pdf() function.

Does anyone know a solution to reduce the filesize?

Thanks in advance,
Peter