Unsupervised Locally Linear Embedding for Dimension Reduction

In this paper, Locally Linear Embedding (LLE) has been implemented for unsupervised non-linear dimension reduction that computes low dimensional, neighborhood preserving embeddings of high dimensional data. Inputs are mapped into a single global coordinate system of lower dimensionality, and its optimizations though capable of generating highly nonlinear embeddings but local minima are not involved. The proposed method was implemented and its performance was verified on images of different poses of Brendan faces, ORL data faces and computer generated images like S-curve and Swiss roll. LLE has performed very well on high dimension data set which exhibits manifold structure. Number of attractive features has been observed that an iterative algorithm is not required and only two parameters are needed to set. In proposed method dimensionality is reduced with learning structures of the manifolds formed by data points and images are embedded into two dimensions. This helps in analyzing the basic relationships between features in various images. Index Terms — LLE, Dimensionality Reduction, Multidimensional, Manifold, Feature Extraction