MisMatch Negativity (MMN) is a small event-related potential (ERP) that provide an index of sensory learning and perceptual accuracy for the cognitive research. Group-level analysis plays an important role for detecting differences at group or condition level, especially when the signal-to-noise ratio is low. Tensor factorization has provided a framework for group-level analysis of ERPs by exploiting more information of brain responses in more domains simultaneously. A 4-way ERP tensor of time × frequency × channel × subjects/condition is generated and decomposed via PARAFAC. A crucial step after PARAFAC decomposition is to select the component that corresponds to the event of interest and moreover differentiates the two groups\conditions. This is usually done manually, which is tedious when the number of components is high. Here we propose a technique to select the multi-domain feature of an ERP among all extracted features by a template matching approach, that uses the MMN temporal and spectral signatures. Following a statistical test, the selected feature significantly discriminated subjects for the two experimental conditions.

This paper presents a new way for automatic detection of SSVEPs through correlation analysis between tensor models. 3-way EEG tensor of channel × frequency × time is decomposed into constituting factor matrices using PARAFAC model. PARAFAC analysis of EEG tensor enables us to decompose multichannel EEG into constituting temporal, spectral and spatial signatures. SSVEPs characterized with localized spectral and spatial signatures are then detected exploiting a correlation analysis between extracted signatures of the EEG tensor and the corresponding simulated signatures of all target SSVEP signals. The SSVEP that has the highest correlation is selected as the intended target. Two flickers blinking at 8 and 13 Hz were used as visual stimuli and the detection was performed based on data packets of 1 second without overlapping. Five subjects participated in the experiments and the highest classification rate of 83.34% was achieved, leading to the Information Transfer Rate (ITR) of 21.01 bits/min.

Electroencephalogram (EEG) is widely used for monitoring, diagnosis purposes and also for study of brain's physiological, mental and functional abnormalities. Processing of information by the brain is reflected in dynamical changes of the electrical activity in time, frequency, and space. EEG signal processing tends to describe and quantify these variations in such a way that they are localized in temporal, spectral and spatial domain. Here we use multi-way (Tensor) analysis for localizing the EEG events. We used EMD process for decomposing EEG into distinct oscillatory modes, which are then mapped to TF plane using the near optimal Reassigned Spectrogram. Temporal, Spatial and Spectral information of the Multichannel EEG are then used to generate a three-way Frequency-Time-Space EEG tensor. Exploiting EMD also enables us to detrend the EEG recordings. Simulation results on both synthetic and real EEG data show that tensor analysis greatly improve separation and localization of overlapping events in EEG and it could be effectively exploited for detecting and characterizing the evoked potentials.

Canonical Decomposition (CANDECOMP) also known as Parallel Factor Analysis (PARAFAC) is a well-known multiway model in high-dimensional data modeling. Approaches that use CANDECOMP/PARAFAC for parametric modeling of a noisy observation require an estimate of the number of signal components (rank) of the data as well. In real applications, the true model of data is unknown and model order selection is a challenging step of these algorithms. In addition, considering noise samples with correlation in different dimensions makes the model order selection even more challenging. Model order selection methods generally minimize a criterion to find the optimum model order. In this paper, we propose using the Reconstruction error, which is the error between the reconstructed data and the unavailable noiseless data, for a range of possible ranks, and use an estimate of this error as the desired criterion for order selection. Furthermore, we propose using the CORCONDIA measure for determining the range of possible model orders. In the presence of the colored noise with Kronecker structure, our proposed algorithm performs the multidimensional prewhitening prior to the model order selection. In addition, our method is able to estimate the noise covariance through an iterative algorithm when no prior information about the noise covariance is available. Simulation results show that the proposed method can be effectively exploited for robustly detecting the true rank of the observed tensor even in mid and low SNRs (i.e. 0–10 dB). It also has an advantage over the state-of-the-art methods, such as different variants of CORCONDIA, by having a better Probability of Detection (PoD) with almost no extra computational overhead after the CANDECOMP/PARAFAC decomposition.

The lp-norm regularized least square technique has been effectively exploited for sparse reconstruction problems. However, the choice of an optimum regularization parameter in the optimization routine still remains a challenge. In this paper we propose a new criterion which is based on MNDL, a new method for optimum subspace selection in data representation, to select the optimum regularization parameter utilizing lp-regularized least-squares. Simulations are done for combined model order selection and parameter estimation for the ubiquitous sinusoids-in-noise model. The results show that the MNDL based regularization parameter selection outperforms the state of the art methods that use MDL for the correct estimation of number of components in the signal.