Quantitative treatment of microstructure data is the first step in establishing the structure–property linkages using materials informatics. However, the microstructure data are often huge and require dimensionality reduction techniques to use it in a computationally meaningful way. In this paper, we present a simple and unique approach to estimate the intrinsic dimensionality of microstructure data. By using principal component analysis (PCA) and multi-dimensional scaling (MDS), we demonstrate the effects of global and local metrics on various classes of 2D and 3D synthetic two-phase microstructure data on the intrinsic dimensionality (ID). Further, we establish the influence of the phase fraction and the inherent stochastic nature of the microstructure on ID estimation. It is observed that 2-point spatial correlation statistics greatly influence intrinsic dimensionality. A change in the intrinsic dimensionality is observed with an increase in the volume fraction of the phase. Considerable variation is observed in metric values for MDS compared to PCA, with an increase in dimensions. We also provide a reduced-order phase fraction benchmark of intrinsic dimensionality (ID) for high dimensional microstructure data. The presented framework is based on a simple and effective trade-off between property preservation and complexity reduction. © 2021, The Minerals, Metals & Materials Society.