The Schmidt-Eckart-Young theorem for matrices states that the optimal rank-r approximation to a matrix is obtained by retaining the first r terms from the singular value decomposition of that matrix. This work considers a generalization of this optimal truncation property to the CANDECOMP/PARAFAC decomposition of tensors and establishes a necessary orthogonality condition. We prove that this co...

In this paper, we exploit the advantages of tensor representations and propose a Supervised Multilinear Learning Model for regression. The model is based on the Canonical (CANDECOMP)/Parallel Factors (PARAFAC) decomposition of tensors of multiple modes and allows the simultaneous projection of an input tensor to more than one discriminative directions along each mode. These projection weights a...

Due to health-related environmental regulations, the detection of volatile organic compounds (VOCs) is becoming increasingly important. Normal VOCs are benzene, naphthalene, formaldehyde, and tetra chloroethylene; however, there a lot more in climate application. They can cause skin irritation respiratory infections if you exposed them. Interest filling as late guideline scent builds having dir...

In this paper we present a powerful technique for the blind extraction of Direct-Sequence Code-Division Multiple Access (DS-CDMA) signals from convolutive mixtures received by an antenna array. The technique is based on a generalization of the Canonical or Parallel Factor Decomposition (CANDECOMP/PARAFAC) in multilinear algebra. We present a bound on the number of users under which blind separa...

In this paper we investigate the uniqueness of the 4-way CANDECOMP/PARAFAC (CP) model in the case where the only possible linear dependencies between the columns of the loading matrices take the form of collinear loadings. For this special configuration we state a necessary and sufficient condition for having full column rank of the Khatri-Rao product of two loading matrices. This allows to der...

How can we efficiently decompose a tensor into sparse factors, when the data does not fit in memory? Tensor decompositions have gained a steadily increasing popularity in data mining applications, however the current state-of-art decomposition algorithms operate on main memory and do not scale to truly large datasets. In this work, we propose PARCUBE, a new and highly parallelizable method for ...