Discriminant Analysis via Joint Euler Transform and ℓ2,1-norm

Capped L21-norm-based common spatial patterns for EEG signals classification applicable to BCI systems

The common spatial patterns (CSP) technique is an effective strategy for the classification of multichannel electroencephalogram (EEG) signals. However, the objective function expression of the conventional CSP algorithm is based on the L2-norm, which makes the performance of the method easily affected by outliers and noise. In this paper, we consider a new extension to CSP, which is termed capped L21-norm-based common spatial patterns (CCSP-L21), by using the capped L21-norm rather than the L2-norm for robust modeling. L21-norm considers the L1-norm sum which largely alleviates the influence of outliers and noise for the sake of robustness. The capped norm is further used to mitigate the effects of extreme outliers whose signal amplitude is much higher than that of the normal signal. Moreover, a non-greedy iterative procedure is derived to solve the proposed objective function. The experimental results show that the proposed method achieves the highest average recognition rates on the three real data sets of BCI competitions, which are 91.67%, 85.07%, and 82.04%, respectively. Capped L21-norm-based common spatial patterns-a robust model for EEG signals classification.

Euler common spatial patterns for EEG classification

The technique of common spatial patterns (CSP) is a widely used method in the field of feature extraction of electroencephalogram (EEG) signals. Motivated by the fact that a cosine distance can enlarge the distance between samples of different classes, we propose the Euler CSP (e-CSP) for the feature extraction of EEG signals, and it is then used for EEG classification. The e-CSP is essentially the conventional CSP with the Euler representation. It includes the following two stages: each sample value is first mapped into a complex space by using the Euler representation, and then the conventional CSP is performed in the Euler space. Thus, the e-CSP is equivalent to applying the Euler representation as a kernel function to the input of the CSP. It is computationally as straightforward as the CSP. However, it extracts more discriminative features from the EEG signals. Extensive experimental results illustrate the discrimination ability of the e-CSP.

Learning Robust Discriminant Subspace Based on Joint L₂,ₚ- and L₂,ₛ-Norm Distance Metrics

Recently, there are many works on discriminant analysis, which promote the robustness of models against outliers by using L₁- or L_2,1-norm as the distance metric. However, both of their robustness and discriminant power are limited. In this article, we present a new robust discriminant subspace (RDS) learning method for feature extraction, with an objective function formulated in a different form. To guarantee the subspace to be robust and discriminative, we measure the within-class distances based on [Formula: see text]-norm and use [Formula: see text]-norm to measure the between-class distances. This also makes our method include rotational invariance. Since the proposed model involves both [Formula: see text]-norm maximization and [Formula: see text]-norm minimization, it is very challenging to solve. To address this problem, we present an efficient nongreedy iterative algorithm. Besides, motivated by trace ratio criterion, a mechanism of automatically balancing the contributions of different terms in our objective is found. RDS is very flexible, as it can be extended to other existing feature extraction techniques. An in-depth theoretical analysis of the algorithm's convergence is presented in this article. Experiments are conducted on several typical databases for image classification, and the promising results indicate the effectiveness of RDS.

Multi-view graph embedding clustering network: Joint self-supervision and block diagonal representation

Multi-view clustering has become an active topic in artificial intelligence. Yet, similar investigation for graph-structured data clustering has been absent so far. To fill this gap, we present a Multi-View Graph embedding Clustering network (MVGC). Specifically, unlike traditional multi-view construction methods, which are only suitable to describe Euclidean structure data, we leverage Euler transform to augment the node attribute, as a new view descriptor, for non-Euclidean structure data. Meanwhile, we impose block diagonal representation constraint, which is measured by the ℓ_1,2-norm, on self-expression coefficient matrix to well explore the cluster structure. By doing so, the learned view-consensus coefficient matrix well encodes the discriminative information. Moreover, we make use of the learned clustering labels to guide the learnings of node representation and coefficient matrix, where the latter is used in turn to conduct the subsequent clustering. In this way, clustering and representation learning are seamlessly connected, with the aim to achieve better clustering performance. Extensive experimental results indicate that MVGC is superior to 11 state-of-the-art methods on four benchmark datasets. In particular, MVGC achieves an Accuracy of 96.17% (53.31%) on the ACM (IMDB) dataset, which is an up to 2.85% (1.97%) clustering performance improvement compared with the strongest baseline.

Generalized Centered 2-D Principal Component Analysis

Most existing robust principal component analysis (PCA) and 2-D PCA (2DPCA) methods involving the l₂ -norm can mitigate the sensitivity to outliers in the domains of image analysis and pattern recognition. However, existing approaches neither preserve the structural information of data in the optimization objective nor have the robustness of generalized performance. To address the above problems, we propose two novel center-weight-based models, namely, centered PCA (C-PCA) and generalized centered 2DPCA with l_2,p -norm minimization (GC-2DPCA), which are developed for vector- and matrix-based data, respectively. The C-PCA can preserve the structural information of data by measuring the similarity between the data points and can also retain the PCA's original desirable properties such as the rotational invariance. Furthermore, GC-2DPCA can learn efficient and robust projection matrices to suppress outliers by utilizing the variations between each row of the image matrix and employing power p of l_2,1 -norm. We also propose an efficient algorithm to solve the C-PCA model and an iterative optimization algorithm to solve the GC-2DPCA model, and we theoretically analyze their convergence properties. Experiments on three public databases show that our models yield significant improvements over the state-of-the-art PCA and 2DPCA approaches.