In this paper we present a method for continuous EEG classification, where we employ nonnegative tensor factorization (NTF) to determine discriminative spectral features and use the Viterbi algorithm to continuously classify multiple mental tasks. This is an extension of our previous work on the use of nonnegative matrix factorization (NMF) for EEG classification. Numerical experiments with two...

1 Laboratory for Advanced Brain Signal Processing, RIKEN Brain Science Institute, Saitama 351-0198, Japan 2Department of Informatics and Mathematical Modeling, Technical University of Denmark, Richard Petersens Plads, Building 321, 2800 Lyngby, Denmark 3Advanced Technology Labs, Adobe Systems Inc., 275 Grove Street, Newton, MA 02466, USA 4Centre for Vision, Speech, and Signal Processing, Univer...

Nonnegative Tensor Factorization (NTF) is an emerging technique in multidimensional signal analysis and it can be used to find partsbased representations of high-dimensional data. Inmany applications such as multichannel spectrogram processing or multiarray spectra analysis, the unknown features have locally smooth temporal or spatial structure. In this paper, we incorporate to an objective fun...

This paper addresses Cheeger and Gromoll’s question of which vector bundles admit a complete metric of nonnegative curvature, and relates their question to the issue of which sphere bundles admit a metric of positive curvature. We show that any vector bundle which admits a metric of nonnegative curvature must admit a connection, a tensor, and a metric on the base space which together satisfy a ...

In this paper, we study the sparse nonnegative tensor factorization and completion problem from partial noisy observations for third-order tensors. Because of sparsity nonnegativity, underlying is decomposed into tensor-tensor product one tensor. We propose to minimize sum maximum likelihood estimation with nonnegativity constraints <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML"...

The completely positive (CP) tensor verification and decomposition are essential in tensor analysis and computation due to the wide applications in statistics, computer vision, exploratory multiway data analysis, blind source separation, and polynomial optimization. However, it is generally NP-hard as we know from its matrix case. To facilitate the CP tensor verification and decomposition, more...

Some prosperities of matrix product are presented in the paper, Kronecker product, Khatri-Rao product, Hadamard product and outer product are involved. And we get some results that a multilinear tensor can be represented by the product of matrix product for a three order tensor. For higher tensor, we conjure that the same results also hold. By the representation of matrix, we give an iterative ...