Learning task-agnostic and interpretable subsequence-based representation of time series and its applications in fMRI analysis

The recent success of sequential learning models, such as deep recurrent neural networks, is largely due to their superior representation-learning capability for learning the informative representation of a targeted time series. The learning of these representations is generally goal-directed, resulting in their task-specific nature, giving rise to excellent performance in completing a single downstream task but hindering between-task generalisation. Meanwhile, with increasingly intricate sequential learning models, learned representation becomes abstract to human knowledge and comprehension. Hence, we propose a unified local predictive model based on the multi-task learning paradigm to learn the task-agnostic and interpretable subsequence-based time series representation, allowing versatile use of learned representations in temporal prediction, smoothing, and classification tasks. The targeted interpretable representation could convey the spectral information of the modelled time series to the level of human comprehension. Through a proof-of-concept evaluation study, we demonstrate the empirical superiority of learned task-agnostic and interpretable representation over task-specific and conventional subsequence-based representation, such as symbolic and recurrent learning-based representation, in solving temporal prediction, smoothing, and classification tasks. These learned task-agnostic representations can also reveal the ground-truth periodicity of the modelled time series. We further propose two applications of our unified local predictive model in functional magnetic resonance imaging (fMRI) analysis to reveal the spectral characterisation of cortical areas at rest and reconstruct more smoothed temporal dynamics of cortical activations in both resting-state and task-evoked fMRI data, giving rise to robust decoding.

A Deep Fourier Neural Network for Seizure Prediction Using Convolutional Neural Network and Ratios of Spectral Power

Epileptic seizure prediction is one of the most used therapeutic adjuvant strategies for drug-resistant epilepsy. Conventional methods usually adopt handcrafted features and manual parameter setting. The over-reliance on the expertise of specialists may lead to weak exploitation of features and low popularization of clinical application. This paper proposes a novel parameterless patient-specific method based on Fourier Neural Network (FNN), where the Fourier transform and backpropagation learning are synthesized to make the predictor more efficient and practical. The employment of FNN is the first attempt in the field of seizure prediction due to its automatic extraction of immanent spectra in epileptic signals. Despite the self-adaptive superiority of FNN, we introduce Convolutional Neural Network (CNN) to further improve its search capability in high-dimensional feature spaces. The study also develops a multi-layer module to estimate spectral power ratios of raw recordings, which optimizes the prediction by enhancing feature diversity. Based on these modules, this paper proposes a two-channel deep neural network: Fourier Ratio Convolutional Neural Network (FRCNN). To demonstrate the reliability of the model, we explain the mathematical meaning of hidden-layer neurons in FRCNN theoretically. This approach is evaluated on both intracranial and scalp EEG datasets. It shows that the predictor achieved a sensitivity of 91.2% and a false prediction rate (FPR) of 0.06[Formula: see text]h[Formula: see text] across intracranial subjects and a sensitivity of 85.4% and an FPR of 0.14[Formula: see text]h[Formula: see text] over scalp subjects. The results indicate that FRCNN enables the convenience of epilepsy treatments while preserving a high degree of precision. In the end, a detailed comparison with the previous methods demonstrates that FRCNN has achieved higher performance and generalization ability.

Fourier neural networks: A comparative study

We review neural network architectures which were motivated by Fourier series and integrals and which are referred to as Fourier neural networks. These networks are empirically evaluated in synthetic and real-world tasks. Neither of them outperforms the standard neural network with sigmoid activation function in the real-world tasks. All neural networks, both Fourier and the standard one, empirically demonstrate lower approximation error than the truncated Fourier series when it comes to approximation of a known function of multiple variables.

An NN-based SRD decomposition algorithm and its application in nonlinear compensation

In this study, a neural network-based square root of descending (SRD) order decomposition algorithm for compensating for nonlinear data generated by sensors is presented. The study aims at exploring the optimized decomposition of data 1.00,0.00,0.00 and minimizing the computational complexity and memory space of the training process. A linear decomposition algorithm, which automatically finds the optimal decomposition N and reduces the training time to 1/√N and memory cost to 1/N has been implemented on nonlinear data obtained from an encoder. Particular focus is given to the theoretical access of estimating the numbers of hidden nodes and the precision of varying the decomposition method. Numerical experiments are designed to evaluate the effect of this algorithm. Moreover, a designed device for angular sensor calibration is presented. We conduct an experiment that samples the data of an encoder and compensates for the nonlinearity of the encoder to testify this novel algorithm.

Application of IFT and SPSA to servo system control

This paper treats the application of two data-based model-free gradient-based stochastic optimization techniques, i.e., iterative feedback tuning (IFT) and simultaneous perturbation stochastic approximation (SPSA), to servo system control. The representative case of controlled processes modeled by second-order systems with an integral component is discussed. New IFT and SPSA algorithms are suggested to tune the parameters of the state feedback controllers with an integrator in the linear-quadratic-Gaussian (LQG) problem formulation. An implementation case study concerning the LQG-based design of an angular position controller for a direct current servo system laboratory equipment is included to highlight the pros and cons of IFT and SPSA from an application's point of view. The comparison of IFT and SPSA algorithms is focused on an insight into their implementation.