Higher-order random projection for tensor object recognition

In this paper, the higher-order random projection (HORP) is proposed to directly project the higher-order tensor object from high-dimensional space to low-dimensional space for recognition task. In traditional random projection framework, the projection matrix does not depend on the training data hence it can avoid the principal classification problems such as over-fitting, Small Sample Size (SSS), and singularity problems. However, the tensor object must be transformed to vectors before projection. In this way, the size of projection matrix will depend on the product of all dimensions in all orders, that is very large and consumes lots of memory and computation time to process. Instead of the traditional projection, our method uses n-mode projection for a tensor object directly, which applies the random projection matrices to matrix unfolding in each mode simultaneously. Thus, the size of each projection matrix will depend on only a dimension of each order. The memory and computation time of this method will be substantially reduced. After projection, we investigate the results of HORP by the nearest neighbor classifier. Our experiments on well-known face databases demonstrate the significant of our proposed method.