CRISPR-Cas9 screens facilitate the discovery of gene functional relationships and phenotype-specific dependencies. The Cancer Dependency Map (DepMap) is the largest compendium of whole-genome CRISPR screens aimed at identifying cancer-specific genetic dependencies across human cell lines. A mitochondria-associated bias has been previously reported to mask signals for genes involved in other functions, and thus, methods for normalizing this dominant signal to improve co-essentiality networks are of interest. In this study, we explore three unsupervised dimensionality reduction methods - autoencoders, robust, and classical principal component analyses (PCA) - for normalizing the DepMap to improve functional networks extracted from these data. We propose a novel "onion" normalization technique to combine several normalized data layers into a single network. Benchmarking analyses reveal that robust PCA combined with onion normalization outperforms existing methods for normalizing the DepMap. Our work demonstrates the value of removing low-dimensional signals from the DepMap before constructing functional gene networks and provides generalizable dimensionality reduction-based normalization tools.