nils-herrmann/clean_scirepeval huggingface dataset:
Estimation of periodicity in non-uniformly sampled astronomical data using a 2D kernel in correntropy

Estimation of periodicity in non-uniformly sampled time series data is frequently a goal in astronomical data analysis. There are various problems faced: Firstly, data is sampled non-uniformly which makes it difficult to use simple Fourier transform for performing spectral analysis. Secondly, there are large gaps in data which makes it difficult to interpolate the signal for re-sampling. Thirdly, in data sets with smaller time periods the non-uniformity in sampling and noise in data pose even greater problems because of the lesser number of samples per period. Finally, recent use of CCD technology has enabled collection of vast amounts of data from various sources. In order to process this huge amount of data we also need to remove human intervention from the process of periodicity estimation to make the algorithm more efficient. In the present work we focus on correntropy and design a new spatio-temporal kernel to accurately estimate the time period of the data without any human intervention.
Parzen particle filters

Using a Parzen density estimator, any distribution can be approximated arbitrarily close by a sum of kernels. In particle filtering, this fact is utilized to estimate a probability density function with Dirac delta kernels; when the distribution is discretized it becomes possible to solve an otherwise intractable integral. In this work, we propose to extend the idea and use any kernel to approximate the distribution. The extra work involved in propagating small kernels through the nonlinear function can be made up for by decreasing the number of kernels needed, especially for high dimensional problems. A further advantage of using kernels with nonzero width is that the density estimate becomes continuous.
Quantized mixture kernel least mean square

Use of multiple kernels in the conventional kernel algorithms is gaining much popularity as it addresses the kernel selection problem as well as improves the performance. Kernel least mean square (KLMS) has been extended to multiple kernels recently using different approaches, one of which is mixture kernel least mean square (MxKLMS). Although this method addresses the kernel selection problem, and improves the performance, it suffers from a problem of linearly growing dictionary like in KLMS. In this paper, we present the quantized MxKLMS (QMxKLMS) algorithm to achieve sub-linear growth in dictionary. This method quantizes the input space based on the conventional criteria using Euclidean distance in input space as well as a new criteria using Euclidean distance in RKHS induced by the sum kernel. The empirical results suggest that QMxKLMS using the latter metric is suitable in a non-stationary environment with abruptly changing modes as they are able to utilize the information regarding the relative importance of kernels. Moreover, the QMxKLMS using both metrics are compared with the QKLMS and the existing multi-kernel methods MKLMS and MKNLMS-CS, showing an improved performance over these methods.
Life detection based on Correntropy Spectral Density

A life detection method based on Correntropy Spectral Density (CSD) is proposed. Because correntropy contains second and higher-order moments of the probability density function due to the nonlinearty of the kernel, it is capable of yielding higher output Signal to Noise Ratio (SNR) in non-Gaussian background when compared with traditional life detection algorithm based on the Power Spectral Density (PSD). The simulation with synthetic data and experimental results illustrate the superiority of the method.
Target discrimination in synthetic aperture radar using artificial neural networks

This paper addresses target discrimination in synthetic aperture radar (SAR) imagery using linear and nonlinear adaptive networks. Neural networks are extensively used for pattern classification but here the goal is discrimination. We show that the two applications require different cost functions. We start by analyzing with a pattern recognition perspective the two-parameter constant false alarm rate (CFAR) detector which is widely utilized as a target detector in SAR. Then we generalize its principle to construct the quadratic gamma discriminator (QGD), a nonparametrically trained classifier based on local image intensity. The linear processing element of the QCD is further extended with nonlinearities yielding a multilayer perceptron (MLP) which we call the NL-QGD (nonlinear QGD). MLPs are normally trained based on the L(2) norm. We experimentally show that the L(2) norm is not recommended to train MLPs for discriminating targets in SAR. Inspired by the Neyman-Pearson criterion, we create a cost function based on a mixed norm to weight the false alarms and the missed detections differently. Mixed norms can easily be incorporated into the backpropagation algorithm, and lead to better performance. Several other norms (L(8), cross-entropy) are applied to train the NL-QGD and all outperformed the L(2) norm when validated by receiver operating characteristics (ROC) curves. The data sets are constructed from TABILS 24 ISAR targets embedded in 7 km(2) of SAR imagery (MIT/LL mission 90).
A robust maximum correntropy criterion for dictionary learning

We introduce a method that incorporates robustness to one of the main building blocks of sparse modeling: dictionary learning. Particularly, we exploit correntropy to compute the principal components in cases where outliers might be detrimental without proper care. This is further added to one of the most utilized dictionary learning tools: K-SVD; the result is Correntropy K-SVD, or CK-SVD, a method that is based on a Maximum Correntropy Criterion (MCC) instead of the somewhat limited Minimum Squared Error (MSE) approach. The optimization is performed using the well-known Half-Quadratic (HQ) technique, which allows a fast and efficient implementation. The results show the importance of this work not only by outperforming K-SVD, but also by circumventing one of the main assumptions during learning overcomplete representations: the availability of untampered, noiseless and outlier-free samples for training stages.
Multivariate density estimation with optimal marginal parzen density estimation and gaussianization

Multivariate density estimation is an important problem that is frequently encountered in statistical learning and signal processing. One of the most popular techniques is Parzen windowing, also referred to as kernel density estimation. Gaussianization is a procedure that allows one to estimate multivariate densities efficiently from the marginal densities of the individual random variables. In this paper, we present an optimal density estimation scheme that combines the desirable properties of Parzen windowing and Gaussianization, using minimum Kullback-Leibler divergence as the optimality criterion for selecting the kernel size in the Parzen windowing step. The performance of the estimate is illustrated in a classifier design example
Automatic plant identification using stem automata

In this paper, we propose a novel approach to automatically identify plant species using dynamics of plant growth and development or spatiotemporal evolution model (STEM). The online kernel adaptive autoregressive-moving-average (KAARMA) algorithm, a discrete-time dynamical system in the kernel reproducing Hilbert space (RKHS), is used to learn plant-development syntactic patterns from feature-vector sequences automatically extracted from 2D plant images, generated by stochastic L-systems. Results show multiclass KAARMA STEM can automatically identify plant species based on growth patterns. Furthermore, finite state machines extracted from trained KAARMA STEM retains competitive performance and are robust to noise. Automatically constructing an L-system or formal grammar to replicate a spatiotemporal structure is an open problem. This is an important first step to not only identify plants but also to generate realistic plant models automatically from observations.
Interpreting neural activity through linear and nonlinear models for brain machine interfaces

Brain machine interface (BMI) design can be achieved by training linear and nonlinear models with simultaneously recorded cortical neural activity and behavior (typically the hand position of a primate). We propose the use of optimized BMI models for analyzing neural activity to assess the role of individual neurons and cortical areas in generating the performed movement. Two models (linear-feedforward and nonlinear-feedback) are trained to predict the hand position of a primate from neural recordings in a reaching task. Qualitative and quantitative investigation of the effect of neurons and their corresponding cortical areas through both models yields conclusions consistent with neurophysiologic knowledge. In addition, this analysis revealed the role of these areas and the importance of the neurons in terms of BMI design.
A complex Echo State Network for nonlinear adaptive filtering

The operation of echo state networks (ESNs) is extended to the complex domain, in order to perform nonlinear complex valued adaptive filtering of nonlinear and nonstationary signals. This is achieved by introducing a nonlinear output layer into an ESN, whereby full adaptivity is provided by introducing an adaptive amplitude into the nonlinear activation function within the output layer of ESN. This allows us to control and track the degree of nonlinearity, which facilitates real-world adaptive filtering applications. Learning algorithms for such ESN are derived, and the benefits of the combination of sparse connections and nonlinear adaptive output layer are illustrated by simulations of both benchmark and real world signals.
Complex Correntropy: Probabilistic Interpretation and Application to Complex-Valued Data

Recent studies have demonstrated that correntropy is an efficient tool for analyzing higher order statistical moments in non-Gaussian noise environments. Although correntropy has been used with complex data, no theoretical study was pursued to elucidate its properties, nor how to best use it for optimization. By using a probabilistic interpretation, this work presents a novel similarity measure between two complex random variables, which is defined as complex correntropy. A new recursive solution for the maximum complex correntropy criterion is introduced based on a fixed-point solution. This technique is applied to a system identification, and the results demonstrate prominent advantages when compared against three other algorithms: the complex least mean square, complex recursive least squares, and least absolute deviation. By the aforementioned probabilistic interpretation, correntropy can now be applied to solve several problems involving complex data in a more straightforward way.
Neural network classification of event related potentials for the design of a new computer interface

A discussion is presented of the classification of single event-related potentials (ERP) with a neural network classifier. The purpose is to discriminate the YES and NO answers thought by a computer user in response to words flashed on the computer display and to assess the feasibility of building a computer interface called the cortical mouse. The performance of the neural network is compared with a classifier using an eigenvector-based extraction method. The neural network outperformed the other classifier. For some subjects the classification is above 90%, but the introspected variability is still large
Real-Time Monitoring of Epileptic Seizures through Recurrence Time Analysis of EEGs

We propose a recurrence time based approach to characterize brain electrical activity. Unlike many other nonlinear methods, the proposed approach does not require that the EEG data be either chaotic or stationary. It works well on clean signals and is robust to noise. Furthermore, it only contains a few parameters that are largely signal-independent, and hence, is very easy to use. By analyzing single channel as well as multiple channel human EEG data, it is shown that the method is able to accurately detect epileptic seizures and effectively reveal seizure propagation information in the brain. Most critically, the method is very fast - it can real-time on-line process about 100 channel EEG data with a typical PC. Therefore, it has the potential to be an excellent candidate for real-time monitoring of the occurrence and propagation of epileptic seizures in a clinical setting.
Computing with transiently stable states

Stability is an essential constraint in the design of linear dynamical systems. Similar stability restrictions on nonlinear dynamical systems, such as echo state network, have been enforced in order to use them for reliable computation. In this paper we introduce a novel computational mode for nonlinear systems with sigmoidal nonlinearity, which does not require global stability. In this mode, although the autonomous system is unstable, the input signal forces the system dynamics to become "transiently stable". We demonstrate with a function approximation experiment that the transiently stable system can still do useful computation. We explain the principles of computation with the stability of local dynamics obtained from linearization of the system at the operating point.
Adaptive Inverse Control of Neural Spatiotemporal Spike Patterns With a Reproducing Kernel Hilbert Space (RKHS) Framework

The precise control of spiking in a population of neurons via applied electrical stimulation is a challenge due to the sparseness of spiking responses and neural system plasticity. We pose neural stimulation as a system control problem where the system input is a multidimensional time-varying signal representing the stimulation, and the output is a set of spike trains; the goal is to drive the output such that the elicited population spiking activity is as close as possible to some desired activity, where closeness is defined by a cost function. If the neural system can be described by a time-invariant (homogeneous) model, then offline procedures can be used to derive the control procedure; however, for arbitrary neural systems this is not tractable. Furthermore, standard control methodologies are not suited to directly operate on spike trains that represent both the target and elicited system response. In this paper, we propose a multiple-input multiple-output (MIMO) adaptive inverse control scheme that operates on spike trains in a reproducing kernel Hilbert space (RKHS). The control scheme uses an inverse controller to approximate the inverse of the neural circuit. The proposed control system takes advantage of the precise timing of the neural events by using a Schoenberg kernel defined directly in the space of spike trains. The Schoenberg kernel maps the spike train to an RKHS and allows linear algorithm to control the nonlinear neural system without the danger of converging to local minima. During operation, the adaptation of the controller minimizes a difference defined in the spike train RKHS between the system and the target response and keeps the inverse controller close to the inverse of the current neural circuit, which enables adapting to neural perturbations. The results on a realistic synthetic neural circuit show that the inverse controller based on the Schoenberg kernel outperforms the decoding accuracy of other models based on the conventional rate representation of neural signal (i.e., spikernel and generalized linear model). Moreover, after a significant perturbation of the neuron circuit, the control scheme can successfully drive the elicited responses close to the original target responses.
Feasibility of fixed-point transversal adaptive filters in FPGA devices with embedded DSP blocks

Transversal adaptive filters for digital signal processing have traditionally been implemented into DSP processors due to their ability to perform fast floating-point arithmetic. However, with its growing die size as well as incorporating the embedded DSP block, the FPGA devices have become a serious contender in the signal processing market. Although it is not yet feasible to use floating-point arithmetic in modern FPGAs, it is sufficient to use fixed-point arithmetic and still achieve tap-weight convergence for adaptive filters. This paper examines the feasibility of implementing an adaptive algorithm, namely the LMS algorithm, based on fixed-point arithmetic, using the Altera Stratix device.
Error Entropy, Correntropy and M-Estimation

Minimization of the error entropy (MEE) cost function was introduced for nonlinear and non-Gaussian signal processing. In this paper, we show that this cost function has a close relation to a introduced correntropy criterion and M-estimation, thus it also theoretically explains the robustness of MEE to outliers. Based on this understanding, we propose a modification to the MEE cost function named minimization of error entropy with fiducial points, which sets the bias for MEE in an elegant and robust way. The performance of this new criterion is compared with the original MEE and the mean square error criterion (MSE) in robust regression and short-term prediction of a chaotic time series.
Hardware implementation of adder for pulse signal processing

Analog to pulse converter (APC) converts continuous time signals into train of pulses such that each pulse interval represents a constant area. Recently, it was theoretically shown that arithmetic can be performed with pulse trains. In this paper, we examine the hardware design challenges in pulse signal processing when compared with conventional digital processing techniques and propose an architecture for implementation of pulse adders. The proposed architecture is validated for accuracy and we study the tradeoffs associated with the design parameters. Synthesis results show that a 16bit pulse adder occupies an area of 0374mm2 and consumes power of 3.06mW at 100MHz in SMIC 0.18ßm CMOS technology.
Online entropy manipulation: stochastic information gradient

Entropy has found significant applications in numerous signal processing problems including independent components analysis and blind deconvolution. In general, entropy estimators require O(N/sup 2/) operations, N being the number of samples. For practical online entropy manipulation, it is desirable to determine a stochastic gradient for entropy, which has O(N) complexity. In this paper, we propose a stochastic Shannon's entropy estimator. We determine the corresponding stochastic gradient and investigate its performance. The proposed stochastic gradient for Shannon's entropy can be used in online adaptation problems where the optimization of an entropy-based cost function is necessary.
A marked point process approach for identifying neural correlates of tics in Tourette Syndrome

We propose a novel interpretation of local field potentials (LFP) based on a marked point process (MPP) framework that models relevant neuromodulations as shifted weighted versions of prototypical temporal patterns. Particularly, the MPP samples are categorized according to the well known oscillatory rhythms of the brain in an effort to elucidate spectrally specific behavioral correlates. The result is a transient model for LFP. We exploit data-driven techniques to fully estimate the model parameters with the added feature of exceptional temporal resolution of the resulting events. We utilize the learned features in the alpha and beta bands to assess correlations to tic events in patients with Tourette Syndrome (TS). The final results show stronger coupling between LFP recorded from the centromedian-paraficicular complex of the thalamus and the tic marks, in comparison to electrocorticogram (ECoG) recordings from the hand area of the primary motor cortex (M1) in terms of the area under the curve (AUC) of the receiver operating characteristic (ROC) curve.
Entropy minimization algorithm for multilayer perceptrons

We (2000) have previously proposed the use of quadratic Renyi's error entropy with a Parzen density estimator with Gaussian kernels as an alternative optimality criterion for supervised neural network training, and showed that it produces better performance on the test data compared to the mean squares error (MSE). The error entropy criterion imposes the minimization of average information content in the error signal rather than simply minimizing the energy as MSE does. We have also developed a nonparametric entropy estimator for Renyi's definition that makes possible the use of any entropy order and any suitable kernel function in Parzen density estimation. The new estimator reduces to the previously used estimator for the special choice of Gaussian kernels and quadratic entropy. In this paper, we briefly present the new criterion and show how to apply it to MLP training. We also address the issue of global optimization by the control of the kernel size in the Parzen window estimation.
The Fast Correntropy Mace Filter

In this paper, we implement the newly introduced correntropy MACE filter using the fast Gauss transform (FGT). The correntropy MACE filter is a nonlinear extension to the MACE filter using the correntropy function in a feature space nonlinearly related to the input. The correntropy MACE outperforms the traditional linear MACE in both generalization and rejection abilities. However, in practice, the drawback of the correntropy MACE filter is its computation complexity. This paper present a fast version of the correntropy MACE by using the FGT idea and validates the approximation with results in synthetic aperture radar (SAR) image recognition.
Modeling the relation from motor cortical neuronal firing to hand movements using competitive linear filters and a MLP

Recent research has demonstrated that linear model are able to estimate hand positions using populations of action potentials collected in the pre-motor and motor cortical areas of a primate's brain. One of the applications of this result is to restore movement in patients suffering from paralysis. To implement this technology in real-time, reliable and accurate signal processing models that produce sufficient small error in the estimated hand positions are required. In this paper, we propose the hybrid model approach that combines competitive linear filters with a neural network. The mapping performance of our approach is compared with a single Wiener filter during reaching movements. Our approach demonstrates more accurate estimations.
Online efficient learning with quantized KLMS and L1 regularization

In a recent work, we have proposed the quantized kernel least mean square (QKLMS) algorithm, which is quite effective in online learning sequentially a nonlinear mapping with a slowly growing radial basis function (RBF) structure. In this paper, in order to further reduce the network size, we propose a sparse QKLMS algorithm, which is derived by adding a sparsity inducing l1 norm penalty of the coefficients to the squared error cost. Simulation examples show that the new algorithm works efficiently, and results in a much sparser network while preserving a desirable performance.