Adversarial Spectral Kernel Matching for Unsupervised Time Series Domain Adaptation

Unsupervised domain adaptation (UDA) has been received increasing attention since it does not require labels in target domain. Most existing UDA methods learn domain-invariant features by minimizing discrepancy distance computed by a certain metric between domains. However, these discrepancy-based methods cannot be robustly applied to unsupervised time series domain adaptation (UTSDA). That is because discrepancy metrics in these methods contain only low-order and local statistics, which have limited expression for time series distributions and therefore result in failure of domain matching. Actually, the real-world time series are always non-local distributions, i.e., with non-stationary and non-monotonic statistics. In this paper, we propose an Adversarial Spectral Kernel Matching (AdvSKM) method, where a hybrid spectral kernel network is specifically designed as inner kernel to reform the Maximum Mean Discrepancy (MMD) metric for UTSDA. The hybrid spectral kernel network can precisely characterize non-stationary and non-monotonic statistics in time series distributions. Embedding hybrid spectral kernel network to MMD not only guarantees precise discrepancy metric but also benefits domain matching. Besides, the differentiable architecture of the spectral kernel network enables adversarial kernel learning, which brings more discriminatory expression for discrepancy matching. The results of extensive experiments on several real-world UTSDA tasks verify the effectiveness of our proposed method.

A Discriminative Multi-Output Gaussian Processes Scheme for Brain Electrical Activity Analysis

The study of brain electrical activity (BEA) from different cognitive conditions has attracted a lot of interest in the last decade due to the high number of possible applications that could be generated from it. In this work, a discriminative framework for BEA via electroencephalography (EEG) is proposed based on multi-output Gaussian Processes (MOGPs) with a specialized spectral kernel. First, a signal segmentation stage is executed, and the channels from the EEG are used as the model outputs. Then, a novel covariance function within the MOGP known as the multispectral mixture kernel (MOSM) allows us to find and quantify the relationships between different channels. Several MOGPs are trained from different conditions grouped in bi-class problems, and the discrimination is performed based on the likelihood score of the test signals against all the models. Finally, the mean likelihood is computed to predict the correspondence of new inputs with each class’s existing models. Results show that this framework allows us to model the EEG signals adequately using generative models and allows analyzing the relationships between channels of the EEG for a particular condition. At the same time, the set of trained MOGPs is well suited to discriminate new input data.

BaKer-Nets: Bayesian Random Kernel Mapping Networks

Recently, deep spectral kernel networks (DSKNs) have attracted wide attention. They consist of periodic computational elements that can be activated across the whole feature spaces. In theory, DSKNs have the potential to reveal input-dependent and long-range characteristics, and thus are expected to perform more competitive than prevailing networks. But in practice, they are still unable to achieve the desired effects. The structural superiority of DSKNs comes at the cost of the difficult optimization. The periodicity of computational elements leads to many poor and dense local minima in loss landscapes. DSKNs are more likely stuck in these local minima, and perform worse than expected. Hence, in this paper, we propose the novel Bayesian random Kernel mapping Networks (BaKer-Nets) with preferable learning processes by escaping randomly from most local minima. Specifically, BaKer-Nets consist of two core components: 1) a prior-posterior bridge is derived to enable the uncertainty of computational elements reasonably; 2) a Bayesian learning paradigm is presented to optimize the prior-posterior bridge efficiently. With the well-tuned uncertainty, BaKer-Nets can not only explore more potential solutions to avoid local minima, but also exploit these ensemble solutions to strengthen their robustness. Systematical experiments demonstrate the significance of BaKer-Nets in improving learning processes on the premise of preserving the structural superiority.

Aflatoxin Reduction in Maize by Industrial-Scale Cleaning Solutions

Different batches of biomass/feed quality maize contaminated by aflatoxins were processed at the industrial scale (a continuous process and separate discontinuous steps) to evaluate the effect of different cleaning solutions on toxin reduction. The investigated cleaning solutions included: (i) mechanical size separation of coarse, small and broken kernels, (ii) removal of dust/fine particles through an aspiration channel, (iii) separation of kernels based on gravity and (iv) optical sorting of spatial and spectral kernel defects. Depending on the sampled fraction, dynamic or static sampling was performed according to the Commission Regulation No. 401/2006 along the entire cleaning process lines. Aflatoxin analyses of the water–slurry aggregate samples were performed according to the AOAC Official Method No. 2005.008 based on high-performance liquid chromatography and immunoaffinity column cleanup of the extracts. A significant reduction in aflatoxin content in the cleaned products, ranging from 65% to 84% with respect to the uncleaned products, was observed when continuous cleaning lines were used. Additionally, an overall aflatoxin reduction from 55% to 94% was obtained by combining results from separate cleaning steps. High levels of aflatoxins (up to 490 µg/kg) were found in the rejected fractions, with the highest levels in dust and in the rejected fractions from the aspirator and optical sorting. This study shows that a cleaning line combining both mechanical and optical sorting technologies provides an efficient solution for reducing aflatoxin contamination in maize.

Automated Spectral Kernel Learning

The generalization performance of kernel methods is largely determined by the kernel, but spectral representations of stationary kernels are both input-independent and output-independent, which limits their applications on complicated tasks. In this paper, we propose an efficient learning framework that incorporates the process of finding suitable kernels and model training. Using non-stationary spectral kernels and backpropagation w.r.t. the objective, we obtain favorable spectral representations that depends on both inputs and outputs. Further, based on Rademacher complexity, we derive data-dependent generalization error bounds, where we investigate the effect of those factors and introduce regularization terms to improve the performance. Extensive experimental results validate the effectiveness of the proposed algorithm and coincide with our theoretical findings.

Deep Spectral Kernel Learning

Recently, spectral kernels have attracted wide attention in complex dynamic environments. These advanced kernels mainly focus on breaking through the crucial limitation on locality, that is, the stationarity and the monotonicity. But actually, owing to the inefficiency of shallow models in computational elements, they are more likely unable to accurately reveal dynamic and potential variations. In this paper, we propose a novel deep spectral kernel network (DSKN) to naturally integrate non-stationary and non-monotonic spectral kernels into elegant deep architectures in an interpretable way, which can be further generalized to cover most kernels. Concretely, we firstly deal with the general form of spectral kernels by the inverse Fourier transform. Secondly, DSKN is constructed by embedding the preeminent spectral kernels into each layer to boost the efficiency in computational elements, which can effectively reveal the dynamic input-dependent characteristics and potential long-range correlations by compactly representing complex advanced concepts. Thirdly, detailed analyses of DSKN are presented. Owing to its universality, we propose a unified spectral transform technique to flexibly extend and reasonably initialize domain-related DSKN. Furthermore, the representer theorem of DSKN is given. Systematical experiments demonstrate the superiority of DSKN compared to state-of-the-art relevant algorithms on varieties of standard real-world tasks.