Selecting landmark points for sparse manifold learning

There has been a surge of interest in learning non-linear manifold models to approximate high-dimensional data. Both for computational complex-ity reasons and for generalization capability, sparsity is a desired feature in such models. This usually means dimensionality reduction, which naturally implies estimating the intrinsic dimension, but it can also mean selecting a subset of the data to use as landmarks, which is especially im-portant because many existing algorithms have quadratic complexity in the number of observations. This paper presents an algorithm for select-ing landmarks, based on LASSO regression, which is well known to fa-vor sparse approximations because it uses regularization with an l1 norm. As an added benefit, a continuous manifold parameterization, based on the landmarks, is also found. Experimental results with synthetic and real data illustrate the algorithm.