In recent times most of the face recognition algorithms are based on subspace analysis. High dimensional image data are being transformed into lower dimensional subspace thus leading towards recognition by embedding a new image into the lower dimensional space. Starting from Principle Component Analysis (PCA) many such dimensionality reduction procedures have been utilized for face recognition. Recent edition is Neighborhood Preserving Projection (NPP). All such methods lead towards creating an orthogonal transformation based on some criteria. Orthogonal NPP builds a linear relation within a small neighborhood of the data and then assumes its validity in the lower dimension space. However, the assumption of linearity could be invalid in some applications. With this aim in mind, current paper introduces an approximate non-linearity. In particular piecewise linearity, within the small neighborhood which gives rise to a more compact data representation that could be utilized for recognition. The proposed scheme is implemented on synthetic as well as real data. Suitability of the proposal is tested on a set of face images and a significant improvement in recognition is observed.
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