Robust neighborhood embedding for unsupervised feature selection Abstract   Unsupervised feature selection is an efficient approach of dimensionality reduction for alleviating the curse of dimensionality in the countless unlabeled highdimensional data. In view of the sparseness of the highdimensional data, we propose a robust neighborhood embedding (RNE) method for unsupervised feature selection. First, with the fact that each data point and its neighbors are close to a locally linear patch of some underlying manifold, we obtain the feature weight matrix through the locally linear embedding (LLE) algorithm. Second, we use      l    1     norm to describe reconstruction error minimization, i.e., loss function to suppress the impact of outlier and noises in the dataset. As the RNE model is convex but nonsmooth, we exploit alternation direction method of multipliers (ADMM) to solve it. Finally, extensive experimental results on benchmark datasets validate that the RNE method is effective and superior to the stateoftheart unsupervised feature selection algorithms in terms of clustering performance.

Local Convex Representation with Pruning for Manifold Clustering Highdimensional data in many applications can be considered as samples drawn from a union of multiple lowdimensional manifolds. Assigning data points into their own manifolds is referred to manifold clustering. Inspired by recent advances in subspace clustering, in this paper, we present an efficient approach for manifold clustering, called Local Convex Representation (LCR), in which each data point is represented as a convex combination of other points in the local neighborhood and under some mild conditions the nonzero coefficients are guaranteed to correspond to the data points lying on the same manifold. Moreover, we incorporate the estimated intrinsic dimension of the manifold to prune the minor nonzero coefficients and validate that the pruning step helps LCR yield remarkable improvements. Experiments on synthetic data as well as real world data demonstrate promising performance.