  This paper focuses on the Matrix Factorization based Clustering (MFC) method
which is one of the few closed form algorithms for the subspace clustering
problem. Despite being simple, closed-form, and computation-efficient, MFC can
outperform the other sophisticated subspace clustering methods in many
challenging scenarios. We reveal the connection between MFC and the Innovation
Pursuit (iPursuit) algorithm which was shown to be able to outperform the other
spectral clustering based methods with a notable margin especially when the
span of clusters are close. A novel theoretical study is presented which sheds
light on the key performance factors of both algorithms (MFC/iPursuit) and it
is shown that both algorithms can be robust to notable intersections between
the span of clusters. Importantly, in contrast to the theoretical guarantees of
other algorithms which emphasized on the distance between the subspaces as the
key performance factor and without making the innovation assumption, it is
shown that the performance of MFC/iPursuit mainly depends on the distance
between the innovative components of the clusters.
