We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized da-ta points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approxi-mation for the tangent space at each point, and those tangent spaces are then aligned to give the global coordinates of the data pointswith respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can bequite small in some cases. We illustrate our algorithm using curves and surfaces both in 2D/3D Euclidean spaces and higher dimension-al Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.

Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment

Canonical correlation analysis (CCA) between recorded electroencephalogram (EEG) and designed reference signals of sine-cosine waves usually works well for steady-state visual evoked potential (SSVEP) recognition in brain-computer interface (BCI) application. However, using the reference signals of sine- cosine waves without subject-specific and inter-trial information can hardly give the optimal recognition accuracy, due to possible overfitting, especially within a short time window length. This paper introduces an L1-regularized multiway canonical correlation analysis (L1-MCCA) for reference signal optimization to improve the SSVEP recognition performance further. A multiway extension of the CCA, called MCCA, is first presented, in which collaborative CCAs are exploited to optimize the reference signals in correlation analysis for SSVEP recognition alternatingly from the channel-way and trial-way arrays of constructed EEG tensor. L1-regularization is subsequently imposed on the trial-way array optimization in the MCCA, and hence results in the more powerful L1-MCCA with function of effective trial selection. Both the proposed MCCA and L1-MCCA methods are validated for SSVEP recognition with EEG data from 10 healthy subjects, and compared to the ordinary CCA without reference signal optimization. Experimental results show that the MCCA significantly outperforms the CCA for SSVEP recognition. The L1-MCCA further improves the recognition accuracy which is significantly higher than that of the MCCA.

L1-Regularized Multiway Canonical Correlation Analysis for SSVEP-Based BCI

Epilepsy is a health problem that seriously affects the quality of humans for many years. Therefore, it is important to accurately analyze and recognize epilepsy based on EEG signals, and for a long time, researchers have attempted to extract new features from the signals for epilepsy recognition. However, it is very difficult to select useful features from a large number of them in this diagnostic application. As the development of artificial intelligence progresses, unsupervised feature learning based on the deep learning model can obtain features that can better describe identified objects from unlabeled data. In this paper, the deep convolution network and autoencoders-based model, named as AE-CDNN, is constructed in order to perform unsupervised feature learning from EEG in epilepsy. We extract features by AE-CDNN model and classify the features based on two public EEG data sets. Experimental results showed that the classification results of features obtained by AE-CDNN are more optimal than features obtained by principal component analysis and sparse random projection. Using several common classifiers to classify features obtained by AE-CDNN model results in high accuracy and not inferior to the research results from most recent studies. The results also showed that the features of AE-CDNN model are clear, effective, and easy to learn. These features can speed up the convergence and reduce the training times of classifiers. Therefore, the AE-CDNN model can be effectively applied to feature extraction of EEG in epilepsy.

Deep Convolution Neural Network and Autoencoders-Based Unsupervised Feature Learning of EEG Signals

Electroencephalogram (EEG), boasting the advantages of portability, low cost, and high-temporal resolution, is a non-invasive brain-imaging modality that can be used to measure different brain states. However, EEG recordings are always contaminated with artifacts from different sources other than neurons, which renders EEG data analysis more difficult, and which potentially results in misleading findings. Therefore, it is essential for many medical and practical applications to remove these artifacts in the preprocessing stage before analyzing EEG data. In the last thirty years, various methods have been developed to remove different types of artifacts from contaminated EEG data; still though, there is no standard method that can be used optimally, and therefore, the research remains attractive as well as challenging. This paper presents an extensive overview of the existing methods for ocular, muscle, and cardiac artifact identification and removal with their comparative advantages and limitations. We also reviewed the schemes developed for validating the performances of algorithms with simulated and real EEG data. In future studies, researchers should focus not only on the combining of different methods with multiple processing stages for efficient removal of artifactual interferences but also on the development of standard criteria for validation of recorded EEG signals.

Identification and Removal of Physiological Artifacts From Electroencephalogram Signals: A Review

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 classily 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 data sets in BCI competition, confirm the useful behavior of the method for continuous EEG classification.

Nonnegative Tensor Factorization for Continuous EEG Classification

In this study, we utilize a special visual stimulation protocol, called motion reversal, to present a novel steady-state motion visual evoked potential (SSMVEP)-based BCI paradigm that relied on human perception of motions oscillated in two opposite directions. Four Newton's rings with the oscillating expansion and contraction motions served as visual stimulators to elicit subjects' SSMVEPs. And four motion reversal frequencies of 8.1, 9.8, 12.25 and 14 Hz were tested. According to Canonical Correlation Analysis (CCA), the offline accuracy and ITR (mean ± standard deviation) over six healthy subjects were 86.56±9.63% and 15.93±3.83 bits/min, respectively. All subjects except one exceeded the level of 80% mean accuracy. Circular Hotelling's T-Squared test () also demonstrated that most subjects exhibited significantly strong stimulus-locked SSMVEP responses. The results of declining exponential fittings exhibited low-adaptation characteristics over the 100-s stimulation sequences in most experimental conditions. Taken together, these results suggest that the proposed paradigm can provide comparable performance with low-adaptation characteristic and less visual discomfort for BCI applications.

https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0039707&type=printable

Steady-State Motion Visual Evoked Potentials Produced by Oscillating Newton's Rings: Implications for Brain-Computer Interfaces

Performance reliability estimation method based on adaptive failure threshold

An automatic patient-specific seizure onset detection method in intracranial EEG based on incremental nonlinear dimensionalityreduction

With the increment of lifetimes of functional components in complex system, it is difficult or costly to monitor the degradation process for these components directly. In this paper, we propose a novel method to indirectly track the degradation process. The continuous failure time data of associated components is considered as a time series with implications of potential performance degradation information of the long-lifetime functional components (LLFC), which are connected with these associated components. Firstly, in order to compute the mean time-to-failure (MTTF), we present a dynamic probability model based on nonparametric kernel estimator. In this model, the sliding time-window technique is used to extract statistical samples, and conditional probability function of failure time is acquired by kernel estimation, subsequently the MTTF is calculated. Secondly, we apply the elementary renewal theorem to present a mapping model between the cumulative degradation degree of LLFC and the MTTF of the associated component are described. Thirdly, in order to quantitatively evaluate the degradation level of LLFC, we introduce two indicators, probability entropy and relative degradation rate. We apply our method to evaluate the performance degradation of the crystallizer vibro-bench. Results show that the method is available to evaluate the degrees of performance degradation of LLFC even though the degradation data cannot be obtained directly. Meanwhile, the method can auto-adjust itself to meet the different statistical sample to overcome the limitation of parameter distribution model. Furthermore, the method can help us to identify the main reason of breakdown and make correct maintenance decision.

Long-term potential performance degradation analysis method based on dynamical probability model

Feature extraction is of great importance in condition monitoring and fault diagnosis of rolling machinery. Nonlinear Dimensionality Reduction (NDR) theories brought a new idea for recognizing and predicting the underlying nonlinear behavior. In this paper, we propose a NDR based feature extraction method for fault classification of rolling element bearing. Original feature spaces are constructed by time- and frequency-domain feature selection method, NDR based feature exaction scheme is proposed to acquire the lowdimensional embeddings from feature space, which provide a more truthful low-dimensional representation compared to the linear DR methods. In order to systematically and quantitatively investigate the performance of NDR method, we compare the three nonlinear DR methods: Isometric Mapping(Isomap), Locally Linear Embedding (LLE), and Local Tangent Space Alignment(LTSA) with the intent of determining a reduced subspace representation in which the fault classes of rolling element bearing are more easily discriminable. Evaluation of the classification performance is done by Support Vector Machine (SVM), a supervised classifiers. Additionally, with optimal neighborhood size, binary code combinations based on NDR embedded results are given for fault recognition. Experiments on 6 fault data sets are used for fault and severity classification. Quantitative evaluation results suggest that NDR methods are superior in identifying potential novel classes within the data.

Yizhuo Zhang

Papers

Steady-State Motion Visual Evoked Potentials Produced by Oscillating Newton's Rings: Implications for Brain-Computer Interfaces

Performance reliability estimation method based on adaptive failure threshold

An automatic patient-specific seizure onset detection method in intracranial EEG based on incremental nonlinear dimensionalityreduction

Long-term potential performance degradation analysis method based on dynamical probability model

Feature Extraction Methods for Fault Classification of Rolling Element Bearing Based on Nonlinear Dimensionality Reduction and SVMs