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This letter presents a clustering algorithm for high dimensional data that comes from a union of lower dimensional subspaces of equal and known dimensions. The algorithm estimates a local subspace for each data point, and computes the distances between the local subspaces and the points to convert the problem to a one-dimensional data clustering problem. The algorithm is reliable in the presence of noise, and applied to the Hopkins 155 Dataset, it generates the best results to date for motion segmentation. The two motion, three motion, and overall segmentation rates for the video sequences are 99.43%, 98.69%, and 99.24%, respectively.