Understanding the geometrical organization of the white matter fibers is one of the current challenges in neuroimaging. White matter fiber clustering technique appears to a corner stone to solve this problem. In this paper, we propose a rapid and efficient unsupervised white matter fiber tracts clustering methodology based on a novel fiber tract similarity metric and an approximation of the k-means algorithm. In this approach, we first define a distance metric capable to quantify the intrinsic geometry of the fiber tracts. This metric is based on a combination of the symmetric Chamfer distance and mean local orientation measures between fiber tracts. Second, we perform the randomized feature selection algorithm proposed for the k-means problem to reduce the dimensionality of the distance data matrix generated from all the fiber tracts using the defined metric. The k-means algorithm is then performed on the reduced distance matrix to cluster the fiber tracts. Finally, we evaluate the method on the synthetic data and in vivo adult brain dataset.