Non‐linear dimensionality reduction using fuzzy lattices

Abstract

The proposed method is based on extraction of non‐linearity from the nearest neighbourhood elements of image. To detect non‐linearity, relation between the nearest neighbourhood elements of the image, have been expressed in terms of Gaussian membership functions. All the elements of the image are connected with the nearest neighbourhood elements with some membership degree of the Gaussian functions. It results in the formation of number of fuzzy lattices. The lattices have been expressed in the form of Schrödinger equation, to find the kinetic energy (KE) used, corresponding to change occurring in the facial activity of a person. Finally, the KE embedded in three dimension space is used to distinguish non‐linear changes during occurrence of various facial activities. Experimental results show that proposed method is effective in recognition of facial expression as it focuses on extracting the non‐linear features corresponding to contours of maximum energy which are appearing because of different expressions.

Keywords

• nonlinear dimensionality reduction
• fuzzy lattices
• nearest neighbourhood elements
• Gaussian membership functions
• Schrodinger equation
• kinetic energy