Clustering a union of low-rank subspaces of different dimensions with missing data

We derive fundamental conditions for clustering a union of low-rank subspaces with missing data. In particular, given an incomplete matrix, assuming its columns are drawn from K different subspaces with different dimensions, the subspace clustering problem is to cluster the columns that belong to the same subspace. We derive a lower bound on the number of columns from each subspace such that the columns can be clustered correctly with high probability. The analysis focuses on the subspace with the lowest dimension and is a generalization of the corresponding results in [18] that assumes the subspaces are independent and with the same dimension. (C) 2019 Elsevier B.V. All rights reserved.