  In this paper, we consider clustering data that is assumed to come from one
of finitely many pointed convex polyhedral cones. This model is referred to as
the Union of Polyhedral Cones (UOPC) model. Similar to the Union of Subspaces
(UOS) model where each data from each subspace is generated from a (unknown)
basis, in the UOPC model each data from each cone is assumed to be generated
from a finite number of (unknown) \emph{extreme rays}.To cluster data under
this model, we consider several algorithms - (a) Sparse Subspace Clustering by
Non-negative constraints Lasso (NCL), (b) Least squares approximation (LSA),
and (c) K-nearest neighbor (KNN) algorithm to arrive at affinity between data
points. Spectral Clustering (SC) is then applied on the resulting affinity
matrix to cluster data into different polyhedral cones. We show that on an
average KNN outperforms both NCL and LSA and for this algorithm we provide the
deterministic conditions for correct clustering. For an affinity measure
between the cones it is shown that as long as the cones are not very coherent
and as long as the density of data within each cone exceeds a threshold, KNN
leads to accurate clustering. Finally, simulation results on real datasets
(MNIST and YaleFace datasets) depict that the proposed algorithm works well on
real data indicating the utility of the UOPC model and the proposed algorithm.
