Cosine Kernel Research Articles

Dynamic event-triggered neuroadaptive fault-tolerant control of quadrotor UAV with a novel cosine kernel

The fault-tolerant control (FTC) for trajectory tracking of a quadrotor unmanned aerial vehicle (UAV) has attracted researchers. The non-linear model of the UAV, coupled with model uncertainties, external disturbances, and actuator failures, requires the function approximation of the lumped non-linearity for controller design. One of the most efficient ways to approximate non-linearity is using radial basis function neural networks (RBFNNs). To date, RBFNNs have been formulated, trained, and used directly for function approximation, which requires considerable computation to derive the control laws. The proposed control and parameter estimation laws approximate the non-linearity by using RBFNNs indirectly. The proposed laws with virtual parameter estimation do not require the actual formulation of RBFNNs and their weights, thus saving on computational resources. For kernel optimization, the Gaussian kernels with exponential terms in RBFNNs are replaced by cosine kernels with algebraic terms, which shows faster convergence as per simulation results. To save on communication bandwidth, static event-triggering communication mechanisms (SECM) and dynamic event-triggering mechanisms (DECM) have been proposed. As DECM works on dynamically changing variables, it saves more communication bandwidth, as tested in simulation. Lyapunov stability analysis proves that errors are uniformly ultimately bounded (UUB). The performance of the proposed algorithm has been tested through numerical simulations, which show superior performance when compared with similar studies. The proposed algorithm has been validated in a real-time Gazebo simulator.

Cosine convolutional neural network and its application for seizure detection

Traditional convolutional neural networks (CNNs) often suffer from high memory consumption and redundancy in their kernel representations, leading to overfitting problems and limiting their application in real-time, low-power scenarios such as seizure detection systems. In this work, a novel cosine convolutional neural network (CosCNN), which replaces traditional kernels with the robust cosine kernel modulated by only two learnable factors, is presented, and its effectiveness is validated on the tasks of seizure detection. Meanwhile, based on the cosine lookup table and KL-divergence, an effective post-training quantization algorithm is proposed for CosCNN hardware implementation. With quantization, CosCNN can achieve a nearly 75% reduction in the memory cost with almost no accuracy loss. Moreover, we design a configurable cosine convolution accelerator on Field Programmable Gate Array (FPGA) and deploy the quantized CosCNN on Zedboard, proving the proposed seizure detection system can operate in real-time and low-power scenarios. Extensive experiments and comparisons were conducted using two publicly available epileptic EEG databases, the Bonn database and the CHB-MIT database. The results highlight the performance superiority of the CosCNN over traditional CNNs as well as other seizure detection methods.

POINT CLOUD SIMPLIFICATION METHOD BASED ON IMPROVED FUZZY C-MEANS WITH AUTOMATIC NUMBER OF CLUSTERS

The essence of the point cloud is to express geometric information about objects by getting discrete coordinates on their surfaces. However, with a million points, this data may record redundant details in which it is needless to be kept for the model’s analysis. In addition, there is also a limitation where the processors cannot process the large-size datasets. The point cloud simplification algorithm was developed to solve the stated obstacles in data processing. Numerous algorithms have been published to produce the best methods for data reduction process. Since the simplification process might eliminate essential features of the data, this study introduces the features preservation process to keep the important points before the simplification. This study employed the Fuzzy C-Means (FCM) algorithms for the simplification stage due to their simplicity and ability to generate an accurate result. Regardless, the FCM still suffers from drawbacks, where their initial cluster centres are prone to fall into local optima. This study improved the FCM by employing the Score and Minimum Distance (SMD) to determine the number of clusters and cluster centres. The SMD is enhanced by changing the Gaussian to Cosine kernel function to increase the accuracy. This new technique is named SMD(C)-IFCM. The method was then applied to the 3D point cloud of a box, cup, and Stanford bunny. The performance of the developed method was compared with the original SMD-FCM and SMD-IFCM for the percentage of the simplified data, error evaluation, and processing time. The result and analysis showed that the developed method had the best score, which was six (6) out of nine (9) measurements, compared to the other two methods with scores of one (1) and two (2) respectively. This score suggests that the developed algorithm successfully reduced the error evaluation and the processing time to generate the output.

Comparative of machine learning classification strategies for electron energy loss spectroscopy: Support vector machines and artificial neural networks

Machine Learning (ML) strategies applied to Scanning and conventional Transmission Electron Microscopy have become a valuable tool for analyzing the large volumes of data generated by various S/TEM techniques. In this work, we focus on Electron Energy Loss Spectroscopy (EELS) and study two ML techniques for classifying spectra in detail: Support Vector Machines (SVM) and Artificial Neural Networks (ANN). Firstly, we systematically analyze the optimal configurations and architectures for ANN classifiers using random search and the tree-structured Parzen estimator methods. Secondly, a new kernel strategy is introduced for the soft-margin SVMs, the cosine kernel, which offers a significant advantage over the previously studied kernels and other ML classification strategies. This kernel allows us to bypass the normalization of EEL spectra, achieving accurate classification. This result is highly relevant for the EELS community since we also assess the impact of common normalization techniques on our spectra using Uniform Manifold Approximation and Projection (UMAP), revealing a strong bias introduced in the spectra once normalized. In order to evaluate and study both classification strategies, we focus on determining the oxidation state of transition metals through their EEL spectra, examining which feature is more suitable for oxidation state classification: the oxygen K peak or the transition metal white lines. Subsequently, we compare the resistance to energy loss shifts for both classifiers and present a strategy to improve their resistance. The results of this study suggest the use of soft-margin SVMs for simpler EELS classification tasks with a limited number of spectra, as they provide performance comparable to ANNs while requiring lower computational resources and reduced training times. Conversely, ANNs are better suited for handling complex classification problems with extensive training data.

Incorporating kernelized multi-omics data improves the accuracy of genomic prediction

BackgroundGenomic selection (GS) has revolutionized animal and plant breeding after the first implementation via early selection before measuring phenotypes. Besides genome, transcriptome and metabolome information are increasingly considered new sources for GS. Difficulties in building the model with multi-omics data for GS and the limit of specimen availability have both delayed the progress of investigating multi-omics.ResultsWe utilized the Cosine kernel to map genomic and transcriptomic data as {n}times {n} symmetric matrix (G matrix and T matrix), combined with the best linear unbiased prediction (BLUP) for GS. Here, we defined five kernel-based prediction models: genomic BLUP (GBLUP), transcriptome-BLUP (TBLUP), multi-omics BLUP (MBLUP, boldsymbol M=mathrm{ratio}timesboldsymbol G+(1-mathrm{ratio})timesboldsymbol T), multi-omics single-step BLUP (mssBLUP), and weighted multi-omics single-step BLUP (wmssBLUP) to integrate transcribed individuals and genotyped resource population. The predictive accuracy evaluations in four traits of the Chinese Simmental beef cattle population showed that (1) MBLUP was far preferred to GBLUP (ratio = 1.0), (2) the prediction accuracy of wmssBLUP and mssBLUP had 4.18% and 3.37% average improvement over GBLUP, (3) We also found the accuracy of wmssBLUP increased with the growing proportion of transcribed cattle in the whole resource population.ConclusionsWe concluded that the inclusion of transcriptome data in GS had the potential to improve accuracy. Moreover, wmssBLUP is accepted to be a promising alternative for the present situation in which plenty of individuals are genotyped when fewer are transcribed.

Seeking patterns in rms voltage variations at the sub-10-minute scale from multiple locations via unsupervised learning and patterns' post-processing

This paper addresses the issue of seeking sub-10-min patterns in fast rms voltage variations from time-limited measurement data at multiple locations worldwide. This is a rarely considered time scale in studies that could be important for the incorrect operation of end-user equipment. Moreover, measurements from multiple locations could be significant from the view of seeking pattern methods. To learn more about this time scale, we propose an unsupervised learning method that employs a Kernel Principal Component Analysis (KPCA) with a Cosine kernel to extract principal features from 10-min time series of voltage variations with a 1-s resolution followed by a k-means clustering to group the features. The scheme is applied to measurements from 57 low-voltage locations in 19 countries from 2009 to 2018. Fifteen initial clusters/patterns are then extracted and converted to ten new (general) patterns using a clusters' merging strategy with highly similar patterns employed in a new post-processing approach useful for multiple locations. Utilizing data from multiple locations in multiple countries ensures a level of generality of the patterns. It also allows comparing the locations. Next to the ten general patterns, some typical patterns are extracted separately for every location. A statistical indices analysis confirms that a complete picture of sub-10-min oscillations needs both statistical indices (quantifying level and variations) and the proposed framework (quantifying patterns). The extracted patterns could be used as a reference for testing/putting requirements on the grid-connected equipment and quantifying the grid's hosting capacity for different types of new distributed generations connected to the grid. The framework is scalable and computationally cheap, making it appropriate for seeking typical patterns in the big data domain. Applying the framework to the much less understood phenomenon will result in providing general knowledge in the field of power quality.

Leader-Follower Formation of Second-Order Nonlinear Multi-Agent Systems by Adaptive Neural Networks with Novel Kernel

In this research work, a novel kernel is conceptualized with the cosine of the distances for radial basis function neural networks (RBFNNs’) for leader-follower formation control problem of second-order nonlinear systems. The adaptive RBFNNs’ acts as a function approximator and also generates the control signal. A weight tuning rule gives the estimated weights. The desired formation for a nonlinear second-order system is achieved. Switching topology is applied between the leader and followers. The results are compared with a purely Gaussian kernel based on Euclidean distances and a mixture of cosine and Gaussian kernels. The overall stability of the system is proved by the Lyapunov function. Numerical simulations show the superior performance of the novel cosine kernel.

Numerical Simulation of the Solitary Wave Collision Process in Time Fractional Orders Based on the Coupled Pure Meshless Method

In this paper, a coupled pure meshless finite pointset method (CFPM) is developed for the first time to numerically predict the inelastic collision process of solitary wave described by the time fractional coupled nonlinear Schrödinger (TF-CNLS) equation. Its construction process is as follows: 1) a high-precision difference scheme is used for the Caputo time fractional derivative; 2) FPM discrete scheme based on Taylor expansion and weighted least square method is adopted for spatial derivatives; 3) The region is locally refined and the double cosine kernel function with good stability is used to improve the numerical accuracy. In the numerical study, the one-dimensional TF-CNLS equations with analytical solutions are solved by CFPM, and the error and convergence rate are analyzed when the nodes are uniformly distributed or locally refined, showing that the proposed method has the approximate second-order accuracy and the flexibility of easy local refinement. Secondly, the inelastic collision process of solitary waves, which is described by the one-dimensional TF-CNLS equation without analytical solution, is numerically predicted by CFPM, and the wave collapse phenomenon depicted above is completely different from the multi-wave phenomenon under the integer order. Meanwhile, by comparing the result with that obtained by finite difference method, it suggests that the CFPM is reliable to predict the complex propagation of the inelastic collision process of the solitary waves under the time fractional order.

KCRR: a nonlinear machine learning with a modified genomic similarity matrix improved the genomic prediction efficiency.

Nowadays, advances in high-throughput sequencing benefit the increasing application of genomic prediction (GP) in breeding programs. In this research, we designed a Cosine kernel-based KRR named KCRR to perform GP. This paper assessed the prediction accuracies of 12 traits with various heritability and genetic architectures from four populations using the genomic best linear unbiased prediction (GBLUP), BayesB, support vector regression (SVR), and KCRR. On the whole, KCRR performed stably for all traits of multiple species, indicating that the hypothesis of KCRR had the potential to be adapted to a wide range of genetic architectures. Moreover, we defined a modified genomic similarity matrix named Cosine similarity matrix (CS matrix). The results indicated that the accuracies between GBLUP_kinship and GBLUP_CS almost unanimously for all traits, but the computing efficiency has increased by an average of 20 times. Our research will be a significant promising strategy in future GP.

Online disease risk monitoring using DEWMA control chart

Early detection of a disease risk plays a vital role in successful treatment of the disease. Many chronic diseases, e.g., stroke, can be treated satisfactorily if they can be detected early. Traditionally, people evaluate their health conditions by comparing the current readings of their medical risk factors with some threshold values, and if irregular readings are triggered out, further medical tests are conducted to find the causes of the disease. A limitation of the traditional disease detection methods is the usage of only current time point data while ignoring the historical data. To use the history of the process for early detection of the disease using statistical process control, we suggest the use of a double exponential weighted moving average control chart to monitor risk factors sequentially. For the estimation of disease risk factors, different kernel functions are used. In particular, we use Epanechnikov, triangular, tricube, biweight, Gaussian, triweight, and cosine kernels. To evaluate the performance of different kernel functions, we conducted simulations as well as a real data set is used. The real data set is about 1055 stroke patients, out of which 27 individuals have suffered from a stroke attack at least once during the study time and the remaining 1028 people did not experience stroke. Numerical results show that the suggested method performs well in detection of early disease risk. Furthermore, it is observed that the biweight kernel function performs better than the other kernel functions for online disease risk monitoring. It is also noticed that for small smoothing parameters of the DEWMA chart, the Epanechinkov and cosine kernels perform better whereas tricube and biweight for the large smoothing parameters.

An Amalgamation of Decision Tree and Cosine Kernel SYM for the Fire Detection in Forest Cover

An Amalgamation of Decision Tree and Cosine Kernel SYM for the Fire Detection in Forest Cover

Logistic Regression Based on Statistical Learning Model with Linearized Kernel for Classification

In this paper, we propose a logistic regression classification method based on the integration of a statistical learning model with linearized kernel pre-processing. The single Gaussian kernel and fusion of Gaussian and cosine kernels are adopted for linearized kernel pre-processing respectively. The adopted statistical learning models are the generalized linear model and the generalized additive model. Using a generalized linear model, the elastic net regularization is adopted to explore the grouping effect of the linearized kernel feature space. Using a generalized additive model, an overlap group-lasso penalty is used to fit the sparse generalized additive functions within the linearized kernel feature space. Experiment results on the Extended Yale-B face database and AR face database demonstrate the effectiveness of the proposed method. The improved solution is also efficiently obtained using our method on the classification of spectra data.

Auto-correlation functions of astrophysical processes, and their relation to Gaussian processes

Context. Accounting for the effects of stellar magnetic phenomena is indispensable to fully exploit radial velocities (RVs) obtained using modern exoplanet-hunting spectrometers. Correlated time variations are often mitigated by non-trivial noise models in the framework of Gaussian processes. These models rely on fitting kernel functions that are motivated on mathematical grounds, and whose physical interpretation is often elusive. Aims. We aim to establish a clear connection between stellar magnetic activity affecting RVs and their corresponding correlations with physical parameters, and compare this connection with kernels used in the literature. Methods. We use simple activity models to investigate the relationship between the physical processes generating the signals and the covariances typically found in data, and to demonstrate the qualitative behaviour of this relationship. We use the StarSim code to calculate RVs of an M dwarf with different realistic evolving spot configurations. The auto-correlation function (ACF) of a synthetic data set shows a very specific behaviour and is explicitly related to the kernel. Gaussian process regression is performed using the quasi-periodic (QP) and simple harmonic oscillator kernels of the george and celerite codes, respectively. Comparison of the resulting kernels with the exact ACFs allows us to cross-match the kernel hyper-parameters with the introduced physical values, study the overall capabilities of the kernels, and improve their definition. Results. We find that the QP kernel provides a more straightforward interpretation of the physics. It is able to consistently recover both the introduced rotation period Prot and the spot lifetime. Our study indicates that the performance can be enhanced by fixing the form factor w and adding a physically motivated cosine term with period Prot∕2, where the contribution to the ACF for the different spot configurations differs significantly. The newly proposed quasi-periodic with cosine (QPC) kernel leads to significantly better model likelihoods, can potentially distinguish between different spot configurations, and can thereby improve the sensitivity of RV exoplanet searches.

Semi-resolved CFD-DEM modeling of gas-particle two-phase flow in the micro-abrasive air jet machining

Abrasive air jet (AAJ) machining is attractive for micromachining hard and brittle materials, while it is usually a big challenge to numerically investigate the particle velocity and concentration distribution in the particle erosion process in the AAJ. In this work, a recently developed semi-resolved CFD-DEM approach which bridges the simulation gap between the resolved and unresolved CFD-DEM, is further improved to reconstruct the background information with a double cosine kernel function. The semi-resolved CFD-DEM is then employed to numerically investigate the gas-particle two-phase flow in the AAJ and numerical results show that this semi-resolved CFD-DEM is more accurate in modeling particulate flow in the fine AAJ nozzle than the conventional unresolved CFD-DEM. We further conduct mechanism investigations on the AAJ micromachining process including particle flow characteristics inside the cylindrical nozzle, velocity, and concentration distribution over the nozzle exit, which are essential jet characteristic features. We identified the particle flow patterns, analyzed the particle distribution, and its correlation with air pressure, abrasive mass flow rate, and turbulence effects. The present simulation results and analyses can be great helpful in understanding the erosion mechanism and optimizing the setting parameters to improve the cutting performance of AAJ.

Cosine kernel based density peaks clustering algorithm

Density peaks clustering (DPC) determines the density peaks according to density-distance, and local density computation significantly impacts the clustering performance of the DPC algorithm. Following this lead, a revised DPC algorithm based on cosine kernel is proposed and examined in this paper. The cosine kernel function uses local information of datasets to define the local density, which not only finds the position difference of different samples within the cutoff distance, but also balances the influence of centre points and boundary points of clusters on local density of samples. Theoretical analysis and experimental verification are included to demonstrate the proposed algorithm's improvement in clustering performance and computational time over the DPC algorithm.

Cosine kernel based density peaks clustering algorithm

Cosine kernel based density peaks clustering algorithm

On Wiener’s Tauberian theorems and convolution for oscillatory integral operators

The main aim of this work is to obtain Paley--Wiener and Wiener's Tauberian results associated with an oscillatory integral operator, which depends on cosine and sine kernels, as well as to introduce a consequent new convolution. Additionally, a new Young-type inequality for the obtained convolution is proven, and a new Wiener-type algebra is also associated with this convolution.

Block sparse multi‐lead ECG compression exploiting between‐lead collaboration

Multilead ECG compression (MlEC) has attracted tremendous attention in long-term monitoring of the patients heart behavior. This paper proposes a method denoted by block sparse MlEC (BlS MlEC) in order to exploit between-lead correlations to compress the signals in a more efficient way. This is due to the fact that multi-lead ECG signals are multiple observations of the same source (heart) from different locations. Consequently, they have high correlation in terms of the support set of their sparse models which leads them to share dominant common structure. In order to obtain the block sparse model, the collaborative version of lasso estimator is applied. In addition, we have shown that raised cosine kernel has advantages over conventional Gaussian and wavelet (Daubechies family) due to its specific properties. It is demonstrated that using raised cosine kernel in constructing the sparsifying basis matrix gives a sparser model which results in higher compression ratio and lower reconstruction error. The simulation results show the average improvement of 37%, 88% and 90-97% for BlS M-lEC compared to the non-collaborative case with raised cosine kernel, Gaussian kernel and collaborative case with Daubechies wavelet kernels, respectively, in terms of reconstruction error while the compression ratio is considered fixed.

Convolutional kernel networks based on a convex combination of cosine kernels

Convolutional Kernel Networks (CKNs) are efficient multilayer kernel machines, which are constructed by approximating a convolution kernel with a mapping based on Gaussian functions. In this paper, we introduce a new approximation of the same convolution kernel based on a convex combination of cosine kernels. CKNs are structurally similar to Convolutional Neural Networks (CNNs), but the convolution operation in CKNs is based on the Euclidean distance, which is not common in convolutional networks. We show that the CKN model obtained by the proposed approximation leads to the ordinary convolution operation, which is based on the inner product. From this point of view, the proposed model is a step forward towards bridging the gap between kernel methods and deep learning. In this paper, we use two methods for learning filters of the proposed CKN: Random Fourier Features, which is a randomized data-independent method for approximating shift-invariant kernels, and a novel method based on the minimization of the sum of squared errors of approximating shift-invariant kernels. Although the RFF method is much faster than ordinary CKN, it requires a high number of random features in order to obtain an acceptable accuracy. To overcome this problem, we proposed the second method, in which the filters are learned in a data-dependent fashion. We evaluate the proposed model on visual recognition datasets MNIST, CIFAR-10, C-Cube, and FERET. Our experiments show that the proposed model surpasses ordinary CKNs in terms of accuracy. Specifically, on CIFAR-10, the accuracy of the proposed method is 1.7% higher than ordinary CKN.

ECG signal compression and denoising via optimum sparsity order selection in compressed sensing framework

Advanced signal processing is widely used in healthcare systems and equipment. Compressing ECG signals is beneficial in long-term monitoring of patients’ behavior. Compressed Sensing (CS) based ECG compression has shown superiority over the existing ECG compression approaches. In current CS ECG compression methods, sparsity order (number of basis vectors involved in the compression) is determined either empirically or by thresholding approaches. Here, we propose a new method denoted by Optimum Sparsity Order Selection (OSOS) that calculates the sparsity order by minimizing reconstruction error. In addition, we have shown that basis matrix based on raised Cosine kernel has more efficiency in compression over the Gaussian basis matrices. The fundamentals of OSOS algorithm is such that the method is robust to observation noise. Simulation results confirm efficiency of our method in terms of compression ratio.