Morphological mapping for non‐linear dimensionality reduction

Abstract

Recently, much research has been carried out on dimensionality reduction techniques that summarise a large set of features into a smaller set, leading to much less redundancy. Among the various non‐linear dimensionality reduction techniques, Isomap and local linear embedding are the most popular techniques. However, these techniques require optimisation on the size of the neighbourhood set, reducing their computational efficiency. To overcome this limitation, a computational efficient algorithm, which is not dependent on size of the neighbourhood set, has been proposed in this study. In the proposed algorithm, morphological mapping (Morphmap) has been used for visualising an image in three dimensions. Then neighbourhood graph construction is done using intensity attenuation function. The pixels in the layer which comes under the angle of divergence can form a part of group vectors and other vectors are removed. In the proposed method, neighbourhood graph construction is not dependent on size of neighbourhood set and removes all the redundant data that reduces complexity to a great extent. Various facial expression datasets have been used to evaluate the performance of the proposed method. Finally, improvement in recognition accuracy with reduced number of computations using the Morphomap algorithm has been shown in the study.

Keywords

• morphological mapping
• nonlinear dimensionality reduction
• Isomap
• local linear embedding
• neighbourhood set
• computational efficiency reduction