Orthogonal isometric projection for face recognition

Isometric projection (IsoProjection) is a linear dimensionality reduction method, which explicitly takes into account the manifold structure embedded in the data. However, IsoProjection is non-orthogonal, which makes it extremely sensitive to the dimensions of reduced space and difficult to estimate the intrinsic dimensionality. The non-orthogonality also distorts the metric structure embedded in the data. This paper proposes a new method called orthogonal isometric projection (O-IsoProjection), which shares the same linear character as IsoProjection and overcomes the metric distortion problem of IsoProjection. Similar to IsoProjection, O-IsoProjection firstly constructs an adjacency graph which can reflect the manifold structure embedded in the data and the class relationship between the sample points of face space, and then obtains the projections by preserving such a graph structure. Different from IsoProjection, O-IsoProjection requires the basis vectors to be orthogonal, and the orthogonal basis vectors can be calculated by iterative way. Experimental results on ORL and Yale databases show that O-IsoProjection has better recognition rate for face recognition than Eigenface, Fisherface and IsoProjection.