Search

In this paper, we extend the Discrete Empirical Interpolation Method (DEIM) to the third-order tensor case based on the t-product and use it to select important/significant lateral and horizontal slices/features. The proposed Tubal DEIM (TDEIM) is investigated both theoretically and numerically. In particular, the details of the error bounds of the proposed TDEIM method are derived. The experimental results show that the TDEIM can provide more accurate approximations than the existing methods. An application of the proposed method to the supervised classification task is also presented. [ABSTRACT FROM AUTHOR]

Efficient and fast computation of a tensor singular value decomposition (t-SVD) with a few passes over the underlying data tensor is crucial because of its many potential applications. The current/existing subspace randomized algorithms need (2 q + 2) passes over the data tensor to compute a t-SVD, where q is a non-negative integer number (power iteration parameter). In this paper, we propose an efficient and flexible randomized algorithm that can handle any number of passes q, which not necessary need be even. The flexibility of the proposed algorithm in using fewer passes naturally leads to lower computational and communication costs. This advantage makes it particularly appropriate when our task calls for several tensor decompositions or when the data tensors are huge. The proposed algorithm is a generalization of the methods developed for matrices to tensors. The expected/average error bound of the proposed algorithm is derived. Extensive numerical experiments on random and real-world data sets are conducted, and the proposed algorithm is compared with some baseline algorithms. The extensive computer simulation experiments demonstrate that the proposed algorithm is practical, efficient, and in general outperforms the state of the arts algorithms. We also demonstrate how to use the proposed method to develop a fast algorithm for the tensor completion problem. [ABSTRACT FROM AUTHOR]

Multi-channel electroencephalography (EEG) is used to capture features associated with motor imagery (MI) based brain-computer interface (BCI) with a wide spatial coverage across the scalp. However, redundant EEG channels are not conducive to improving BCI performance. Therefore, removing irrelevant channels can help improve the classification performance of BCI systems. We present a new method for identifying relevant EEG channels. Our method is based on the assumption that useful channels share related information and that this can be measured by inter-channel connectivity. Specifically, we treat all candidate EEG channels as a graph and define channel selection as the problem of node classification on a graph. Then we design a graph convolutional neural network (GCN) model for channels classification. Channels are selected based on the outputs of our GCN model. We evaluate our proposed GCN-based channel selection (GCN-CS) method on three MI datasets. On three datasets, GCN-CS achieves performance improvements by reducing the number of channels. Specifically, we achieve classification accuracies of 79.76% on Dataset 1, 89.14% on Dataset 2 and 87.96% on Dataset 3, which outperform competing methods significantly. [ABSTRACT FROM AUTHOR]

With the popularity of smartphones and the pervasion of mobile apps, people spend more and more time to interact with a diversity of apps on their smartphones, especially for young population. This raises a question: how people allocate attention to interfaces of apps during using them. To address this question, we, in this study, designed an experiment with two sessions (i.e., Session1: browsing original interfaces; Session 2: browsing interfaces after removal of colors and background) integrating with an eyetracking system. Attention fixation durations were recorded by an eye-tracker while participants browsed app interfaces. The whole screen of smartphone was divided into four even regions to explore fixation durations. The results revealed that participants gave significantly longer total fixation duration on the bottom left region compared to other regions in the session (1) Longer total fixation duration on the bottom was preserved, but there is no significant difference between left side and right side in the session2. Similar to the finding of total fixation duration, first fixation duration is also predominantly paid on the bottom area of the interface. Moreover, the skill in the use of mobile phone was quantified by assessing familiarity and accuracy of phone operation and was investigated in the association with the fixation durations. We found that first fixation duration of the bottom left region is significantly negatively correlated with the smartphone operation level in the session 1, but there is no significant correlation between them in the session (2) According to the results of ratio exploration, the ratio of the first fixation duration to the total fixation duration is not significantly different between areas of interest for both sessions. The findings of this study provide insights into the attention allocation during browsing app interfaces and are of implications on the design of app interfaces and advertisements as layout can be optimized according to the attention allocation to maximally deliver information. [ABSTRACT FROM AUTHOR]

Objective The stimulus color of P300-BCI systems has been successfully modified. However, the effects of different color combinations have not been widely investigated. In this study, we designed new stimulus patterns to evaluate the influence of color modulation on the BCI performance and waveforms of the evoked related potential (ERP).Methods Comparison was performed for three new stimulus patterns consisting of red face and colored block-shape, namely, red face with a white rectangle (RFW), red face with a blue rectangle (RFB), and red face with a red rectangle (RFR). Bayesian linear discriminant analysis (BLDA) was used to construct the individual classifier model. Repeated-measures ANOVA and Bonferroni correction were applied for statistical analysis. Results The RFW pattern obtained the highest average online accuracy with 96.94%, and those of RFR and RFB patterns were 93.61% and of 92.22% respectively. Significant differences in online accuracy and information transfer rate (ITR) were found between RFW and RFR patterns (p < 0.05). Conclusion Compared with RFR and RFB patterns, RFW yielded the best performance in P300-BCI. These new stimulus patterns with different color combinations have considerable importance to BCI applications and user-friendliness. [ABSTRACT FROM AUTHOR]

During the acquisition of electroencephalographic (EEG) signals, data may be missing or corrupted by noise and artifacts. To reconstruct the incomplete data, EEG signals are firstly converted into a three-order tensor (multi-dimensional data) of shape time × channel × trial. Then, the missing data can be efficiently recovered by applying a tensor completion method (TCM). However, there is not a unique way to organize channels and trials in a tensor, and different numbers of channels are available depending on the EEG setting used, which may affect the quality of the tensor completion results. The main goal of this paper is to evaluate the robustness of EEG completion methods with several designed parameters such as the ordering of channels and trials, the number of channels, and the amount of missing data. In this work, the results of completing missing data by several TCMs were compared. To emulate different scenarios of missing data, three different patterns of missing data were designed. Firstly, the amount of missing data on completion effects was analyzed, including the time lengths of missing data and the number of channels or trials affected by missing data. Secondly, the numerical stability of the completion methods was analyzed by shuffling the indices along channels or trials in the EEG data tensor. Finally, the way that the number of electrodes of EEG tensors influences completion effects was assessed by changing the number of channels. Among all the applied TCMs, the simultaneous tensor decomposition and completion (STDC) method achieves the best performance in providing stable results when the amount of missing data or the electrode number of EEG tensors is changed. In other words, STDC proves to be an excellent choice of TCM, since permutations of trials or channels have almost no influence on the complete results. The STDC method can efficiently complete the missing EEG signals. The designed simulations can be regarded as a procedure to validate whether or not a completion method is useful enough to complete EEG signals. [ABSTRACT FROM AUTHOR]

Tensor decomposition methods have been widely applied to big data analysis as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations of data. Unfortunately most existing approaches are not designed to meet the challenges posed by big data dilemma. This paper attempts to improve the scalability of tensor decompositions and makes two contributions: A flexible and fast algorithm for the CP decomposition (FFCP) of tensors based on their Tucker compression; A distributed randomized Tucker decomposition approach for arbitrarily big tensors but with relatively low multilinear rank. These two algorithms can deal with huge tensors, even if they are dense. Extensive simulations provide empirical evidence of the validity and efficiency of the proposed algorithms. [ABSTRACT FROM AUTHOR]

A novel algorithm to solve the quadratic programming (QP) problem over ellipsoids is proposed. This is achieved by splitting the QP problem into two optimisation sub-problems, (1) quadratic programming over a sphere and (2) orthogonal projection. Next, an augmented-Lagrangian algorithm is developed for this multiple constraint optimisation. Benefitting from the fact that the QP over a single sphere can be solved in a closed form by solving a secular equation, we derive a tighter bound of the minimiser of the secular equation. We also propose to generate a new positive semidefinite matrix with a low condition number from the matrices in the quadratic constraint, which is shown to improve convergence of the proposed augmented-Lagrangian algorithm. Finally, applications of the quadratically constrained QP to bounded linear regression and tensor decomposition paradigms are presented. [ABSTRACT FROM AUTHOR]

Presurgical investigations for categorizing focal patterns are crucial, leading to localization and surgical removal of the epileptic focus. This paper presents a machine learning approach using information theoretic features extracted from high-frequency subbands to detect the epileptic focus from interictal intracranial electroencephalogram (iEEG). It is known that high-frequency subbands (>80 Hz) include important biomarkers such as high-frequency oscillations (HFOs) for identifying epileptic focus commonly referred to as the seizure onset zone (SOZ). In this analysis, the multi-channel interictal iEEG signals were splitted into segments and each segment was decomposed into multiple high-frequency subbands. The different types of entropy were calculated for each of the subbands and the sparse linear discriminant analysis (sLDA) was applied to select the prominent entropy features. Due to the imbalance of SOZ and non-SOZ channels in iEEG data, the use of machine learning techniques is always tricky. To deal with the imbalanced learning problem, an adaptive synthetic oversampling approach (ADASYN) with radial basis function kernel-based SVM was used to detect the focal segments. Finally, the epileptic focus was identified based on detection of focal segments on SOZ and non-SOZ channels. Eight patients were examined to observe the efficiency of the automatic detector. The experimental results and statistical tests indicate that the proposed automatic detector can identify the epileptic focus accurately and efficiently. [ABSTRACT FROM AUTHOR]

Motor imagery (MI) is a mental representation of motor behavior and has been widely used in electroencephalogram based brain–computer interfaces (BCIs). Several studies have demonstrated the efficacy of MI-based BCI-feedback training in post-stroke rehabilitation. However, in the earliest stage of the training, calibration data typically contain insufficient discriminability, resulting in unreliable feedback, which may decrease subjects' motivation and even hinder their training. To improve the performance in the early stages of MI training, a novel hybrid BCI paradigm based on MI and P300 is proposed in this study. In this paradigm, subjects are instructed to imagine writing the Chinese character following the flash order of the desired Chinese character displayed on the screen. The event-related desynchronization/synchronization (ERD/ERS) phenomenon is produced with writing based on one's imagination. Simultaneously, the P300 potential is evoked by the flash of each stroke. Moreover, a fusion method of P300 and MI classification is proposed, in which unreliable P300 classifications are corrected by reliable MI classifications. Twelve healthy naïve MI subjects participated in this study. Results demonstrated that the proposed hybrid BCI paradigm yielded significantly better performance than the single-modality BCI paradigm. The recognition accuracy of the fusion method is significantly higher than that of P300 (p < 0.05) and MI (p < 0.01). Moreover, the training data size can be reduced through fusion of these two modalities. [ABSTRACT FROM AUTHOR]

We discuss extended definitions of linear and multilinear operations such as Kronecker, Hadamard, and contracted products, and establish links between them for tensor calculus. Then we introduce effective low-rank tensor approximation techniques including Candecomp/Parafac, Tucker, and tensor train (TT) decompositions with a number of mathematical and graphical representations. We also provide a brief review of mathematical properties of the TT decomposition as a low-rank approximation technique. With the aim of breaking the curse-of-dimensionality in large-scale numerical analysis, we describe basic operations on large-scale vectors, matrices, and high-order tensors represented by TT decomposition. The proposed representations can be used for describing numerical methods based on TT decomposition for solving large-scale optimization problems such as systems of linear equations and symmetric eigenvalue problems. [ABSTRACT FROM AUTHOR]

Visual brain-computer interfaces (BCIs) are not suitable for people who cannot reliably maintain their eye gaze. Considering that this group usually maintains audition, an auditory based BCI may be a good choice for them. In this paper, we explore two auditory patterns: (1) a pattern utilizing symmetrical spatial cues with multiple frequency beeps [called the high low medium (HLM) pattern], and (2) a pattern utilizing non-symmetrical spatial cues with six tones derived from the diatonic scale [called the diatonic scale (DS) pattern]. These two patterns are compared to each other in terms of accuracy to determine which auditory pattern is better. The HLM pattern uses three different frequency beeps and has a symmetrical spatial distribution. The DS pattern uses six spoken stimuli, which are six notes solmizated as 'do', 're', 'mi', 'fa', 'sol' and 'la', and derived from the diatonic scale. These six sounds are distributed to six, spatially distributed, speakers. Thus, we compare a BCI paradigm using beeps with another BCI paradigm using tones on the diatonic scale, when the stimuli are spatially distributed. Although no significant differences are found between the ERPs, the HLM pattern performs better than the DS pattern: the online accuracy achieved with the HLM pattern is significantly higher than that achieved with the DS pattern ( p = 0.0028). [ABSTRACT FROM AUTHOR]