ONPPn: Orthogonal Neighborhood Preserving Projection with Normalization and its applications

Subspace analysis or dimensionality reduction techniques are becoming very popular for many computer vision tasks such as image recognition. Most of such techniques deal with optimizing a cost function based on some criteria imposed on either projections of data or on the basis of projection space. NPP and ONPP are such linear methods that preserve local linear relationship within the neighborhood, with two different constraints, normalized projection and orthogonal basis of subspace respectively. This article proposes a method, ONPPn, that finds a subspace which satisfies two constraints namely, normalization and orthogonality. The article also provides two-dimensional variant of ONPPn. Experiments show that ONPPn outperforms its NPP and ONPP versions in image recognition tasks, whereas 2D-ONPPn outperforms 2D-ONPP by huge margin but does not perform as good as 2D-NPP. 2D-NPP as well as 2D-ONPP are not suitable for reconstruction task, but the proposed method 2D-ONPPn overcomes drawbacks of existing methods and is best suited for image reconstruction, too.