Epileptic focus localization in patients with epileptic seizures is essential when surgery is needed. Recent studies show that this can be done automatically using machine learning approaches. However, well-designed feature extraction methods are often computationally demanding, requiring a large amount of data labeled by physicians, which is time consuming and impractical. In this paper, we firstly introduce a one-dimensional convolutional neural network (1D-CNN) model for epileptic seizure focus detection which avoids the manual, time-consuming feature extraction Moreover, to reduce the necessary number of training samples, we introduce an approach for data augmentation. The experimental results demonstrate the efficiency of the proposed method, with a nearly 3% improvement in performance using the data enhancement method compared to the best result obtained using the traditional feature extraction method.

Low-rank tensor recovery has been widely applied to computer vision and machine learning. Recently, tubal nuclear norm (TNN) based optimization is proposed with superior performance as compared to other tensor nuclear norms. However, one major limitation is its orientation sensitivity due to low-rankness strictly defined along tubal orientation and it cannot simultaneously model spectral low-rankness in multiple orientations. To this end, we introduce two new tensor norms called OITNN-O and OITNN-L to exploit multi-orientational spectral low-rankness for an arbitrary K-way (K ≥ 3) tensors. We further formulate two robust tensor decomposition models via the proposed norms and develop two algorithms as the solutions. Theoretically, we establish non-asymptotic error bounds which can predict the scaling behavior of the estimation error. Experiments on real-world datasets demonstrate the superiority and effectiveness of the proposed norms.

In many applications, data organized in tensor form contains noise and missing entries. In this paper, the goal is to complete a tensor from its partial noisy observations. Specifically, we consider low-tubal-rank tensors sampled by element-wise Bernoulli sampling with additive sub-exponential noise. Algorithmically, a soft-impute-like algorithm, namely iterative singular tube thresholding (ISTT), is proposed. Statistically, bound on the estimation error of ISTT is explored. First, the estimation error is upper bounded non-asymptotically. Then, the minimax optimal lower bound of the estimation error for tensors with limited tubal-rank and bounded l _∞ -norm is established, indicating that the proposed upper bound is order optimal up to a logarithm factor. Numerical simulations show that the proposed upper bound can precisely predict the scaling behavior of the estimation error of ISTT. Compared with several state-of-the-art convex algorithms, the effectiveness of ISTT is demonstrated through experiments on real-world data sets.

Real multi-way data may suffer from missing entries, noise and outliers simultaneously. The recently proposed tubal nuclear norm (TNN) has shown its superiority in tensor completion. However, statistical analysis of TNN based models is still deficient. This paper aims to robustly recover a polluted incomplete tensor with rigorous statistical guarantee. Specifically, an estimator based on a weighed variant of TNN is proposed to complete a low-tubal-rank tensor corrupted by element sparse errors or slice sparse sample outliers from partial noisy observations. Non-asymptotic upper bounds on the estimation error are established and further proved to be minimax optimal up to a log factor. Sharpness of the upper bounds is verified on synthetic datasets and superiority of the proposed estimator is demonstrated through robust video inpainting.