Image classification via nearest subspace and two-dimensional underdetermined random projection

We consider the problem of classification via two-dimensional underdetermined random projection and sparse representation. We contend that the two-dimensional underdetermine random projection has a natural relationship with deterministic underdetermined projections, such as 2DPCA and (2D)²PCA but is more efficient in terms of the computational complexity for feature extraction. The proposed projection technique, called 2DCS, can be regarded as an extension of the compressive sampling technique which conveniently employs the same ℓ₁-norm minimization technique for exact data reconstruction. The proposed method can be favorably used for feature extraction in pattern recognition. Due to its computational efficiency and independence on training data, 2DCS feature has its own advantages for image classification. Our experiments on the publicly available ORL database have shown the effectiveness of the proposed method.