Recently, a general analytical formula to extract all the Rotation Invariant Features (RIFs) of the diffusion Magnetic Resonance Imaging (dMRI) signal was proposed. The features extracted using this formula represent a generalisation of the usual second degree RIFs such as the mean diffusivity. In this work, we study the usefulness of all the 12 algebraically independent RIFs extracted from 4th degree spherical harmonics that model the dMRI signal per voxel in the context of Alzheimer Disease (AD) identification. To do so, and since we are working with imbalanced data sets, we first introduce a non-linear metric to evaluate the performance of the models, the (B-score). This proposed metric allows high score only when both classes are distinguished correctly. We use the proposed metric in conjunction with a deep Convolutional Neural Network that operates on subject slices to identify if a subject has AD or not. We find that micro-structure information communicated by RIFs is indeed useful to AD identification and that not all RIFs are equivalently useful. We also identify the two best RIF combinations for the ADNI-SIEMENS and the ADNI-GE medical data sets respectively. The combination of these RIFs achieves a classification B-score of 73.62% and 72.31% on the previous data sets respectively. We note the importance of combining high degree RIFs with low degree ones to improve the classification performance.