Locally Linear Embedded Eigenspace Analysis

The existing nonlinear local methods for dimensionality reduction yield impressive results in data embedding and manifold visualization. However, they also open up the problem of how to define a unified projection from new data to the embedded subspace constructed by the training samples. Thinking globally and fitting locally, we present a new linear embedding approach, called Locally Embedded Analysis (LEA), for dimensionality reduction and feature selection. LEA can be viewed as the linear approximation of the Locally Linear Embedding (LLE). By solving a linear eigenspace problem in closed-form, LEA automatically learns the local neighborhood characteristic and discovers the compact linear subspace, which optimally preserves the intrinsic manifold structure. Given a new highdimensional data point, LEA finds the corresponding low-dimensional point in the subspace via the linear projection. This embedding process concentrates the adjacent data points into the same dense cluster, which is effective for discriminant analysis, supervised classification and unsupervised clustering. We test the proposed LEA algorithm on several benchmark databases. Experimental results show that LEA provides better data representation and more efficient dimensionality reduction than the classical linear methods.