What is effect on PCA of having too many zeros in the data? I want to use Principal Components Analysis to derive dietary patterns. However, my data have many zeros (no intakes) for many observations. I'm unable to find relevant literature to know how biased my results would be as result. There are some papers related to environmental sciences that have described this, but my data are food intakes. Zero intake means no intake. It cannot be substituted by other numbers in contrast to the way it's done in other fields. 
 A: In case others would find this old post, I do not think this concern is unfounded. Several studies, both in environmental (species counts for example) and non-environmental fields, highlighted issues due to zero-inflated data in standard PCA. Here is an memo on the assumptions of PCA that I find useful: http://alexhwilliams.info/itsneuronalblog/2016/03/27/pca/
Plus some other resources with solutions that do not include substituting zeros by other numbers:
Hellton et al. 2021. The Truth behind the Zeros: A New Approach to Principal Component Analysis of the Neuropsychiatric Inventory. Multivariate Behav Res. 56(1):70-85. https://pubmed.ncbi.nlm.nih.gov/32329370/
Pierson & Yau 2015. ZIFA: Dimensionality reduction for zero-inflated single-cell gene expression analysis. Genome Biol 16, 241. https://doi.org/10.1186/s13059-015-0805-z
Modelling Data with Many Zeros - Principal Component Analysis vs Zero Inflated Models
A: I assume you have non-negative data, as you say (in a comments, should have been in the post itself):

... to derive patterns of food intake and see association of these patterns with health outcomes.

For such data some variant of multiple correspondence analysis might be better. For a paper on this see Use of Multiple Correspondence Analysis and Cluster Analysis to Study Dietary Behaviour: Food Consumption Questionnaire in the SU.VI.MAX. Cohort
Maybe also look into some other ideas for non-negative matrix factorization nnmf?
