Locally adaptive nonlinear dimensionality reduction
HE Pi-lian · Journal of Computer Applications · 2006
Popular nonlinear dimensionality reduction algorithms, such as SIE and Isomap suffer a difficulty in common: global neighborhood parameters often fail in tackling data sets with high variation in local manifold. To improve the availability of nonlinear dimensionality reduction algorithms in the field of machine learning, an adaptive neighbors selection scheme based on locally principal direction reconstruction was proposed.The method involves two main computation steps. First, it selects an appropriate neighborhood set for each data points such that all neighbors in a neighborhood set form a d-dimensionality linear subspace approximatively and computes locally principal directions for each neighborhood set respectively. Secondly, it fits each neighbor by means of locally principal directions of corresponding neighborhood set and deletes the neighbors whose fitting error exceed a predefined threshold. The simulation show that the method can deal with data set with high variation in local manifold effectively. Moreover, comparing with other adaptive neighbors selection strategy,this method can circumvent false connectivity introduced by noise or high local curvature.