Not the same, yet similar? - On commonalities and differences between VQPCA and ORCLUS

VQPCA and ORCLUS are two algorithms addressing two different tasks: the former is a method for nonlinear dimensionality reduction through learning a manifold via piece-wise linear manifolds while the latter is an algorithm for discovering clusters that reside in their respective arbitrarily oriented (linear) subspaces, hence manifolds. At first glance both seem to be distinct, however, on a more low-level scale, one can see similarities concerning certain aspects such as their objective functions, their algorithmic approach, and their input parameters. This work investigates the commonalities and differences of VQPCA and ORCLUS on both formal and empirical levels. The results show that although both algorithms can reproduce each other’s results, this is not guaranteed and strongly depends on certain properties of the data.