The clustering of fibers into bundles is an important task in studying the structure and function of white matter. Existing technology mostly relies on geometrical features, such as the shape of fibers, and thus only provides very limited information about the neuroanatomical function of the brain. We advance this issue by proposing a multinomial representation of fibers decoding their connectivity to gray matter regions. We then simplify the clustering task by first deriving a compact encoding of our representation via the logit transformation. Furthermore, we define a distance between fibers that is in theory invariant to parcellation biases and is equivalent to a family of Riemannian metrics on the simplex of multinomial probabilities. We apply our method to longitudinal scans of two healthy subjects showing high reproducibility of the resulting fiber bundles without needing to register the corresponding scans to a common coordinate system. We confirm these qualitative findings via a simple statistical analyse of the fiber bundles.