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Recognition of real world scenes can be efficiently solved based on global features termed the Spatial Envelope. Such features indeed comprise multiple modes such as orientations, scales, sparsity profiles. In order to extract features and classify multiway samples, most approaches vectorize data tensors to convert the classification of multiway data into the one of 1-D samples. This common approach...
In this paper, we propose a tensorial approach to single trial recognition in a EEG-based BCI system related to movement related potentials. In this approach input data are considered as tensors instead of more conventional vector or matrix representations. Feature extraction for multiway EEG spectral tensors is solved by using tensor (multi-array) decompositions. For the same EEG motor imagery dataset,...
Nonnegative Matrix/Tensor factorization (NMF/NTF) have been used in the study of EEG, and the fit (explained variation) is often used to evaluate the performance of a nonnegative decomposition algorithm. However, this parameter only reveals the information derived from the mathematical model and just exhibits the reliability of the algorithms, and the property of EEG can not be reflected. If fits...
Parallel factor analysis (PARAFAC) is a multi-way decomposition method which allows to find hidden factors from the raw tensor data. Recently, the nonnegative tensor factorization (NTF), a variant of the model with nonnegativity constraints imposed on hidden factors has attracted interesting due to meaningful representation with many potential applications in neuroscience, bioinformatics, chemometrics...
Nonnegative parallel factor analysis (PARAFAC) (also called nonnegative tensor factorization - NTF) allows to find nonnegative factors hidden under the raw tensor data which have many potential applications in neuroscience, bioinformatics, chemometrics etc. NTF algorithms can be easily established based on the unfolding tensor and Khatri-Rao products of factors. This kind of algorithms leads to large...
In this paper we present, discuss and compare new methods for the reconstruction of tensors by partial sampling, i.e. based on the information contained only in a subset of their entries. As a generalization of the CUR matrix decomposition, which approximates a matrix from a subset of its rows and columns, we present two methods called Tree-CUR and FSTD (Fiber Sampling Tensor Decomposition) for estimating...
The common spatial patterns (CSP) algorithm has been widely used in EEG classification and brain computer interface (BCI). In this paper, we propose a multilinear formulation of the CSP, termed as TensorCSP or common tensor discriminant analysis (CTDA) for high-order tensor data. As a natural extension of CSP, the proposed algorithm uses the analogous optimization criteria in CSP and a new framework...
In this paper we propose a family of new algorithms for non-negative matrix/tensor factorization (NMF/NTF) and sparse nonnegative coding and representation that has many potential applications in computational neuroscience, multi-sensory, multidimensional data analysis and text mining. We have developed a class of local algorithms which are extensions of hierarchical alternating least squares (HALS)...
In these lecture notes, the authors have outlined several approaches to solve a NMF/NTF problem. The following main conclusions can be drawn: 1) Multiplicative algorithms are not necessary the best approaches for NMF, especially if data representations are not very redundant or sparse. 2) Much better performance can be achieved using the FP-ALS (especially for large-scale problems), IPC, and QN methods...
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