Sharif Digital Repository

The problem of extracting low-dimensional structure from high-dimensional data arises in many applications such as machine learning, statistical pattern recognition, wireless sensor networks, and data compression. If the data is restricted to a lower dimensional subspace, then simple algorithms using linear projections can find the subspace and consequently estimate its dimensionality. However, if the data lies on a low-dimensional but nonlinear space (e.g., manifolds), then its structure may be highly nonlinear and, hence, linear methods are doomed to fail. In this paper, we introduce a new technique for dimensionality reduction based on point-wise operators. More precisely, let $ {bf A} n...