Typical data analysis systems involving FPGAs work better with low-dimensional low-precision (LDLP) data than with high-dimensional high-precision (HDHP) ones due to limitations on data bandwidth and on-chip resources. However, data sources usually offer HDHP data matrices. It is possible to obtain LDLP data that approximate HDHP data by applying dimensionality reduction and quantisation. However, this straightforward workflow incurs significant information loss that reduces the accuracy of data analysis on FPGAs. This paper proposes that the information loss in the straightforward workflow is due to the dimensionality reduction algorithm's unawareness of quantisation. To address this problem, the paper introduces Quadir, a novel algorithm that supports quantisation-aware dimensionality reduction. In particular, Quadir is an alternating direction optimisation algorithm that finds a transformation to project an HDHP data matrix to an LDHP one so that the LDLP matrix after quantisation can reconstruct the original HDHP matrix with optimised approximation. Our experimental evaluation in data reconstruction shows that the LDHP data matrices produced by Quadir preserve more information from the original data than principal component analysis (PCA) after quantisation.