Complex-valued Adaptive System Identification via Low-Rank Tensor Decomposition

Machine learning (ML) and tensor-based methods have been of significant interest for the scientific community for the last few decades. In a previous work we presented a novel tensor-based system identification framework to ease the computational burden of tensor-only architectures while still being able to achieve exceptionally good performance. However, the derived approach only allows to process real-valued problems and is therefore not directly applicable on a wide range of signal processing and communications problems, which often deal with complex-valued systems. In this work we therefore derive two new architectures to allow the processing of complex-valued signals, and show that these extensions are able to surpass the trivial, complex-valued extension of the original architecture in terms of performance, while only requiring a slight overhead in computational resources to allow for complex-valued operations

Enhanced Nonlinear System Identification by Interpolating Low-Rank Tensors

Function approximation from input and output data is one of the most investigated problems in signal processing. This problem has been tackled with various signal processing and machine learning methods. Although tensors have a rich history upon numerous disciplines, tensor-based estimation has recently become of particular interest in system identification. In this paper we focus on the problem of adaptive nonlinear system identification solved with interpolated tensor methods. We introduce three novel approaches where we combine the existing tensor-based estimation techniques with multidimensional linear interpolation. To keep the reduced complexity, we stick to the concept where the algorithms employ a Wiener or Hammerstein structure and the tensors are combined with the well-known LMS algorithm. The update of the tensor is based on a stochastic gradient decent concept. Moreover, an appropriate step size normalization for the update of the tensors and the LMS supports the convergence. Finally, in several experiments we show that the proposed algorithms almost always clearly outperform the state-of-the-art methods with lower or comparable complexity.Comment: 12 pages, 4 figures, 3 table

Nonconvulsive Epileptic Seizure Detection in Scalp EEG Using Multiway Data Analysis

Nonconvulsive status epilepticus is a condition where the patient is exposed to abnormally prolonged epileptic seizures without evident physical symptoms. Since these continuous seizures may cause permanent brain damage, it constitutes a medical emergency. This paper proposes a method to detect nonconvulsive seizures for a further nonconvulsive status epilepticus diagnosis. To differentiate between the normal and seizure electroencephalogram (EEG), a K-Nearest Neighbor, a Radial Basis Support Vector Machine, and a Linear Discriminant Analysis classifier are used. The classifier features are obtained from the Canonical Polyadic Decomposition (CPD) and Block Term Decomposition (BTD) of the EEG data represented as third order tensor. To expand the EEG into a tensor, Wavelet or Hilbert-Huang transform are used. The algorithm is tested on a scalp EEG database of 139 seizures of different duration. The experimental results suggest that a Hilbert-Huang tensor representation and the CPD analysis provide the most suitable framework for nonconvulsive seizure detection. The Radial Basis Support Vector Machine classifier shows the best performance with sensitivity, specificity, and accuracy values over 98%. A rough comparison with other methods proposed in the literature shows the superior performance of the proposed method for nonconvulsive epileptic seizure detection

Adaptive System Identification via Low-Rank Tensor Decompositi

Tensor-based estimation has been of particular interest of the scientific community for several years now. While showing promising results on system estimation and other tasks, one big downside is the tremendous amount of computational power and memory required – especially during training – to achieve satisfactory performance. We present a novel framework for different classes of nonlinear systems, that allows to significantly reduce the complexity by introducing a least-mean-squares block before, after, or between tensors to reduce the necessary dimensions and rank required to model a given system. Our simulations show promising results that outperform traditional tensor models, and achieve equal performance to comparable algorithms for all problems considered while requiring significantly less operations per time step than either of the state-of-the-art architectures