Objects features extraction by singular projections of data tensor to matrices

The problem of multidimensional tensor objects features extraction in a manner of matrices is considered. The tensor’ elements Higher Order Singular Value Decomposition (SVD) is presented as the d-SVD which includes SVD of the tensor reshaped as a matrix and SVDs of reduced size of the previous SVDs vectors reshaped as matrices. The decomposition allows to create Singular Projections of tensor to a sum of one-rank tensors in selected dimensions. The projections of tensor to matrices by weighted and direct averaging in SVD’ vectors subspace is investigated numerically. The extracted by projection features of a series of image objects are used to develop the optimized Inverse Feature Filters for the objects recognition.