Kernel Matrix Research Articles

An Efficient Implementation for Regularized Frequency Response Function and Transient Estimation

In this paper, we propose an efficient implementation for the kernel-based regularized frequency response function (FRF) and transient estimation. In particular, we show that when the diagonal correlated (DC) kernel is used, the output kernel matrix in the frequency domain has a hierarchically of-diagonal low-rank (HODLR) structure, and by exploring this structure, the FRF and transient estimates can be computed very efficiently The overall computational complexity is O(y2Nb) log2Nb), where Nb is the number of data in the interested frequency band and 7 is the HODLR rank of the output kernel matrix that is often much smaller than N&. The efficacy of the proposed implementation is demonstrated by numerical simulations.

Efficient Approximations for Matrix-Based Rényi's Entropy on Sequential Data.

The matrix-based Rényi's entropy (MBRE) has recently been introduced as a substitute for the original Rényi's entropy that could be directly obtained from data samples, avoiding the expensive intermediate step of density estimation. Despite its remarkable success in a broad of information-related tasks, the computational cost of MBRE, however, becomes a bottleneck for large-scale applications. The challenge, when facing sequential data, is further amplified due to the requirement of large-scale eigenvalue decomposition on multiple dense kernel matrices constructed by sliding windows in the region of interest, resulting in O(mn3) overall time complexity, where m and n denote the number and the size of windows, respectively. To overcome this issue, we adopt the static MBRE estimator together with a variance reduction criterion to develop randomized approximations for the target entropy, leading to high accuracy with substantially lower query complexity by utilizing the historical estimation results. Specifically, assuming that the changes of adjacent sliding windows are bounded by β << 1 , which is a trivial case in domains, e.g., time-series analysis, we lower the complexity by a factor of √{β} . Polynomial approximation techniques are further adopted to support arbitrary α orders. In general, our algorithms achieve O(mn2√{β}st) total computational complexity, where s, t << n denote the number of vector queries and the polynomial degrees, respectively. Theoretical upper and lower bounds are established in terms of the convergence rate for both s and t , and large-scale experiments on both simulation and real-world data are conducted to validate the effectiveness of our algorithms. The results show that our methods achieve promising speedup with only a trivial loss in performance.

Iterated discrete Hardy-type inequalities with three weights for a class of matrix operators

Iterated Hardy-type inequalities are one of the main objects of current research on the theory of Hardy inequalities. These inequalities have become well-known after study boundedness properties of the multidimensional Hardy operator acting from the weighted Lebesgue space to the local Morrie-type space. In addition, the results of quasilinear inequalities can be applied to study bilinear Hardy inequalities. In the paper, we discussed weighted discrete Hardy-type inequalities containing some quasilinear operators with a matrix kernel where matrix entries satisfy discrete Oinarov condition. The research of weighted Hardy-type inequalities depends on the relations between parameters p, q and θ, so we considered the cases 1 &lt; p ≤ q &lt; θ &lt; ∞ and p ≤ q &lt; θ &lt; ∞, 0 &lt; p ≤1, criteria for the fulfillment of iterated discrete Hardy-type inequalities are obtained. Moreover, an alternative method of proof was shown in the work.

MNCLCDA: predicting circRNA-drug sensitivity associations by using mixed neighbourhood information and contrastive learning

BackgroundcircRNAs play an important role in drug resistance and cancer development. Recently, many studies have shown that the expressions of circRNAs in human cells can affect the sensitivity of cells to therapeutic drugs, thus significantly influencing the therapeutic effects of these drugs. Traditional biomedical experiments required to verify this sensitivity relationship are not only time-consuming but also expensive. Hence, the development of an efficient computational approach that can accurately predict the novel associations between drug sensitivities and circRNAs is a crucial and pressing need.MethodsIn this research, we present a novel computational framework called MNCLCDA, which aims to predict the potential associations between drug sensitivities and circRNAs to assist with medical research. First, MNCLCDA quantifies the similarity between the given drug and circRNA using drug structure information, circRNA gene sequence information, and GIP kernel information. Due to the existence of noise in similarity information, we employ a preprocessing approach based on random walk with restart for similarity networks to efficiently capture the useful features of circRNAs and drugs. Second, we use a mixed neighbourhood graph convolutional network to obtain the neighbourhood information of nodes. Then, a graph-based contrastive learning method is used to enhance the robustness of the model, and finally, a double Laplace-regularized least-squares method is used to predict potential circRNA-drug associations through the kernel matrices in the circRNA and drug spaces.ResultsNumerous experimental results show that MNCLCDA outperforms six other advanced methods. In addition, the excellent performance of our proposed model in case studies illustrates that MNCLCDA also has the ability to predict the associations between drug sensitivity and circRNA in practical situations.ConclusionsAfter a large number of experiments, it is illustrated that MNCLCDA is an efficient tool for predicting the potential associations between drug sensitivities and circRNAs, thereby can provide some guidance for clinical trials.

On Solutions of a System of Nonlinear Integral Equations of Convolution Type on the Entire Real Line

We consider a special system of integral equations of convolution type with a monotone convex nonlinearity naturally arising when searching for stationary or limit states in various dynamic models of applied nature, for example, in models of the spread of epidemics, and prove theorems stating the existence or absence of a nontrivial bounded solution with limits at +@ depending on the values of these limits and on the structure of the matrix kernel of the system. We also study the uniqueness of such a solution assuming that it exists. Specific examples of systems whose parameters satisfy the conditions stated in our theorems are given.

Improved biological neural network approach for path planning of differential drive agricultural robots with arbitrary shape

To improve the path planning ability of a differential drive agricultural robot with arbitrary shape, a novel path planning method based on improved biological neural dynamics approach is proposed. Taking a T-shaped robot as an example, its shape features at different orientations are described through kernel matrix rotation. The coordinates and orientation of the robot are used as neuron position parameters to construct a 3-D neural network, and the neuron state is determined by convolutional calculation. Neural connections are defined based on the translational and rotational motion properties of the robot. By subdividing the workspace network, more flexible rotation options for the robot are obtained. Then, biological neural dynamics is established to determine a stable neural activity landscape, and a collision-free path can be obtained by consecutively selecting the adjacent neuron with maximum activity. The two key factors to improve the path planning ability are the flexible rotation options of the robot in a grid workspace and the consideration of the interaction between the robot body and the surrounding obstacles. It is proved that the proposed approach can find a feasible path within the range of rational numbers. Finally, its strong path planning ability is demonstrated by several experiments in narrow and complex environments.

Pure kernel graph fusion tensor subspace clustering under non-negative matrix factorization framework

Currently, graph-based multi-kernel subspace clustering methods have achieved rich research results in dealing with nonlinear data structures. However, most of the methods still have the following two limitations: (1) the model optimization goal is finding the optimal consensus kernel rather than the optimal affinity graph, which leads to kernel noise always interfering with the learning of the target affinity graph in the optimization process; (2) in the process of finding the optimal affinity graph, only the correlation between different kernel views is exploited, ignoring the higher-order correlation between multiple kernel views. In light of this, we propose a pure kernel graph fusion tensor (PKGT) subspace clustering under non-negative matrix factorization (NMF) framework. Specifically, we first use NMF to construct local affinity feature graphs with standard block diagonal structure for each base kernel matrix, and then achieve adaptive weight assignment by optimizing the inconsistencies among multiple local affinity feature graphs. Finally, we use tensor to capture the higher-order correlation between multiple local affinity feature graphs to provide more feature information for the learning of optimal target affinity graph, which enhances the model clustering performance. Extensive experiments on nine real datasets demonstrate that PKGT has superior clustering performance. The code is available at https://github.com/ZS0124/PKGT.

Evaluation of MAX-DOAS Profile Retrievals under Different Vertical Resolutions of Aerosol and NO2 Profiles and Elevation Angles

In the Multi-Axis Differential Absorption Spectroscopy (MAX-DOAS) trace gas and aerosol profile inversion algorithm, the vertical resolution and the observation information obtained through a series of continuous observations with multiple elevation angles (EAs) can affect the accuracy of an aerosol profile, thus further affecting the results of the gas profile. Therefore, this study examined the effect of the vertical resolution of an aerosol profile and EAs on the NO2 profile retrieval by combining simulations and measurements. Aerosol profiles were retrieved from MAX-DOAS observations and co-observed using light detection and ranging (Lidar). Three aerosol profile shapes (Boltzmann, Gaussian, and exponential) with vertical resolutions of 100 and 200 m were used in the atmospheric radiative transfer model. Firstly, the effect of the vertical resolution of the input aerosol profile on the retrieved aerosol profile with a resolution of 200 m was studied. The retrieved aerosol profiles from the two vertical resolution aerosol profiles as input were similar. The aerosol profile retrieved from a 100 m resolution profile as input was slightly overestimated compared to the input value, whereas that from a 200 m resolution input was slightly underestimated. The relative deviation of the aerosol profile retrieved from the 100 m resolution as input was higher than that of the 200 m. MAX-DOAS observations in Hefei city on 4 September 2020 were selected to verify the simulation results. The aerosol profiles retrieved from the oxygen collision complex (O4) differential slant column density derived from MAX-DOAS observations and Lidar simulation were compared with the input Lidar aerosol profiles. The correlation between the retrieved and input aerosol profiles was high, with a correlation coefficient R &gt; 0.99. The aerosol profiles retrieved from the Lidar profile at 100 and 200 m resolutions as input closely matched the Lidar aerosol profiles, consistent with the simulation result. However, aerosol profiles retrieved from MAX-DOAS measurements differed from the Lidar profiles due to the influence of the averaging kernel matrix smoothing, the different location and viewing geometry, and uncertainties associated with the Lidar profiles. Next, NO2 profiles of different vertical resolutions were used as input profiles to retrieve the NO2 profiles under a single aerosol profile scenario. The effect of the vertical resolution on the retrieval of NO2 profiles was found to be less significant compared to aerosol retrievals. Using the Lidar aerosol profile as the a priori aerosol information had little effect on NO2 profile retrieval. Additionally, the retrieved aerosol profiles and aerosol optical depths varied under different EAs. Ten EAs (i.e., 1, 2, 3, 4, 5, 6, 8, 15, 30, and 90°) were found to obtain more information from observations.

Quantum Alphatron: quantum advantage for learning with kernels and noise

At the interface of machine learning and quantum computing, an important question is what distributions can be learned provably with optimal sample complexities and with quantum-accelerated time complexities. In the classical case, Klivans and Goel discussed the Alphatron, an algorithm to learn distributions related to kernelized regression, which they also applied to the learning of two-layer neural networks. In this work, we provide quantum versions of the Alphatron in the fault-tolerant setting. In a well-defined learning model, this quantum algorithm is able to provide a polynomial speedup for a large range of parameters of the underlying concept class. We discuss two types of speedups, one for evaluating the kernel matrix and one for evaluating the gradient in the stochastic gradient descent procedure. We also discuss the quantum advantage in the context of learning of two-layer neural networks. Our work contributes to the study of quantum learning with kernels and from samples.

Multiple kernel graph clustering with shifted Laplacian reconstruction

Multiple kernel graph clustering methods have gained favor among researchers for their ability to combine the strengths of graph learning and multiple kernel methods. We propose a novel method named multiple kernel graph clustering with shifted Laplacian reconstruction (SLR-MKGC). Specifically, the kernel matrix is regarded as an affinity graph, and then the graph is transformed to a shifted Laplacian matrix. By decomposing the shifted Laplacian matrix, the latent data representation is obtained, simultaneously preserving the main energy and clustering information. As a result, the effects of noise and redundancy are reduced and the quality of the raw data are improved. Then, the obtained representation is used to reconstruct a final affinity graph with a desired block diagonal structure. Further, we conduct extensive experiments on seven benchmark datasets and compare nine state-of-the-art clustering methods. Experimental results show that SLR-MKGC exhibits excellent performance on most datasets. For example, compared to other state-of-the-art methods, SLR-MKGC achieves a performance improvement of 5.13% on the clustering accuracy term on the BBCSport2 dataset, demonstrating the promise of SLR-MKGC. The source code is available at https://github.com/dililidida/SLR-MKGC.

Kernel Geometric Mean Metric Learning

Geometric mean metric learning (GMML) algorithm is a novel metric learning approach proposed recently. It has many advantages such as unconstrained convex objective function, closed form solution, faster computational speed, and interpretability over other existing metric learning technologies. However, addressing the nonlinear problem is not effective enough. The kernel method is an effective method to solve nonlinear problems. Therefore, a kernel geometric mean metric learning (KGMML) algorithm is proposed. The basic idea is to transform the input space into a high-dimensional feature space through nonlinear transformation, and use the integral representation of the weighted geometric mean and the Woodbury matrix identity in new feature space to generalize the analytical solution obtained in the GMML algorithm as a form represented by a kernel matrix, and then the KGMML algorithm is obtained through operations. Experimental results on 15 datasets show that the proposed algorithm can effectively improve the accuracy of the GMML algorithm and other metric algorithms.

Improving ISOMAP Efficiency with RKS: A Comparative Study with t-Distributed Stochastic Neighbor Embedding on Protein Sequences

Data visualization plays a crucial role in gaining insights from high-dimensional datasets. ISOMAP is a popular algorithm that maps high-dimensional data into a lower-dimensional space while preserving the underlying geometric structure. However, ISOMAP can be computationally expensive, especially for large datasets, due to the computation of the pairwise distances between data points. The motivation behind this study is to improve efficiency by leveraging an approximate method, which is based on random kitchen sinks (RKS). This approach provides a faster way to compute the kernel matrix. Using RKS significantly reduces the computational complexity of ISOMAP while still obtaining a meaningful low-dimensional representation of the data. We compare the performance of the approximate ISOMAP approach using RKS with the traditional t-SNE algorithm. The comparison involves computing the distance matrix using the original high-dimensional data and the low-dimensional data computed from both t-SNE and ISOMAP. The quality of the low-dimensional embeddings is measured using several metrics, including mean squared error (MSE), mean absolute error (MAE), and explained variance score (EVS). Additionally, the runtime of each algorithm is recorded to assess its computational efficiency. The comparison is conducted on a set of protein sequences, used in many bioinformatics tasks. We use three different embedding methods based on k-mers, minimizers, and position weight matrix (PWM) to capture various aspects of the underlying structure and the relationships between the protein sequences. By comparing different embeddings and by evaluating the effectiveness of the approximate ISOMAP approach using RKS and comparing it against t-SNE, we provide insights on the efficacy of our proposed approach. Our goal is to retain the quality of the low-dimensional embeddings while improving the computational performance.

ANEW ARCHITECTURE OF KEY GENERATION USING DWT FOR IMAGE ENCRYPTION WITH THREE LEVELS ARNOLD TRANSFORM PERMUTATION

The security of image transmission is an important issue in digital communication. As well as it is necessary to preserve and protect important information for several applications like military, medical and other services related to high confidentiality over the Internet or other unprotected networks. In this paper a proposed encryption scheme was introduced that using Lorenz system with a circular convolution and discreet cosine transform (DCT). The diffusion process was achieved using three levels of Arnold transform permutation: - namely, block level, inside each block and pixel level. The image was divided into blocks of sizes 8x8 pixels and shuffle by applying Fisher-Yates permutation image pixels. The DCT was applied to each block and multiplied by the H kernel matrix to achieve the circular convolution. Next the logistic map is used for diffusion to get the cipher image. A new key generation method is applied in order to produce the key values for generating the chaos numbers sequence. Finally applying the discreet wavelet transform (DWT) to the image will produced four quarters (LL, LH, HL and HH). The cosine of each pixel in the LL and HH quarters were computed. The sine of each pixel in the LH and HL quarters were also computed in order to generate the keys for the chaos sequence. By using this way of keys generation in every image, the differential attack possibility will be negligible

MJAR: A novel joint generalization-based diagnosis method for industrial robots with compound faults

Compound faults inevitably occur in multi-joint industrial robots resulting in excessive vibration. Intelligent diagnosis for the occurrence and position of fault joints can efficiently reduce the maintenance cost. Compared with laboratory disassembly parts, joint diagnosis of in-situ industrial robots is more challenging due to coupling of multiple subsystems and the industrial noise interference. This paper proposes a novel joint generalization-based fault diagnosis method for industrial robots via the multi-joint attention residual network (MJAR) model. Each joint signals are independently input to parallel residual convolution with unidirectional matrix kernel (ResCUM) in multi-joint decoupling attention (MJDA) module, which is exclusively designed combining residual and attention mechanism to provide decoupling capability of compound faults. And the multi-spatial reconstruction (MSR) module based on sparse sampling is design to provide multi-scale feature extraction adapted to real industrial signals. MJAR can diagnose unseen compound fault combinations without using any transfer strategy as the robot joint generalization-based fault diagnosis (RJGFD) framework. Integrated experiment results show that the MJAR is superior to some advanced congener DL methods.

Wind Power Curve Modeling With Large-Scale Generalized Kernel-Based Regression Model

Accurate wind power curves (WPCs) are crucial for wind energy development and utilization, e.g., wind power forecasting and wind turbine condition monitoring. In the era of big data, large-scale datasets make the training of power curve models inefficient, especially for kernel-based models. Furthermore, most models do not take into account the error characteristics of WPC modeling. In this study, a large-scale generalized kernel-based regression model is proposed to solve the above problem. First, a generalized loss function, which can model both symmetric and asymmetric error distributions, is designed for model training. Then, the Nyström technique is employed to get the approximate kernel matrix, based on which an eigenvalue-based kernel regression framework is constructed. Next, a large-scale generalized kernel-based regression model is developed with model parameters tuned using the alternating direction method of multipliers. Before WPC modeling, a three-step data processing method based on isolation forest is designed to process missing data, irrational data, and outliers in the collected data. The WPC modeling results on four large-scale wind datasets demonstrate that the proposed model generates accurate WPCs with high efficiency. Furthermore, the effect of turbulence intensity on WPC modeling and the effectiveness of LSGKRM with multivariate inputs are also verified.

Kernel properties related to carotenoid release during in vitro gastrointestinal digestion in commercial dent maize hybrids

The objective of study was to investigate the relationships between maize kernel properties and carotenoid release during simulated gastrointestinal digestion of 103 hybrids of dent type. Commercial maize hybrids significantly differed in kernel hardness, chemical composition and carotenoid profile. Across all hybrids, the amount of digestible individual carotenoids increased as follows: β-carotene < α-cryptoxanthin < β-cryptoxanthin < lutein < zeaxanthin. The amount of digested carotenoids correlated negatively with amylose content and amylose-to-amylopectin ratio, while it correlated positively with the content of neutral detergent fibres and amylopectin as well as the Stenvert index. However, the content of endosperm lipids could not be related to carotenoid digestibility. Findings clearly indicate that the carotenoid release from the kernel during digestion is related to specific physical and chemical properties, leading to a better understanding of the effects of kernel matrix structure on carotenoid digestibility in dent-type maize hybrids.

Improved deep mixed kernel randomized network for wind speed prediction

Abstract Forecasting wind speed is an extremely complicated and challenging problem due to its chaotic nature and its dependence on several atmospheric conditions. Although there are several intelligent techniques in the literature for wind speed prediction, their accuracies are not yet very reliable. Therefore, in this paper, a new hybrid intelligent technique named the deep mixed kernel random vector functional-link network auto-encoder (AE) is proposed for wind speed prediction. The proposed method eliminates manual tuning of hidden nodes with random weights and biases, providing prediction model generalization and representation learning. This reduces reconstruction error due to the exact inversion of the kernel matrix, unlike the pseudo-inverse in a random vector functional-link network, and shortens the execution time. Furthermore, the presence of a direct link from the input to the output reduces the complexity of the prediction model and improves the prediction accuracy. The kernel parameters and coefficients of the mixed kernel system are optimized using a new chaotic sine–cosine Levy flight optimization technique. The lowest errors in terms of mean absolute error (0.4139), mean absolute percentage error (4.0081), root mean square error (0.4843), standard deviation error (1.1431) and index of agreement (0.9733) prove the efficiency of the proposed model in comparison with other deep learning models such as deep AEs, deep kernel extreme learning machine AEs, deep kernel random vector functional-link network AEs, benchmark models such as least square support vector machine, autoregressive integrated moving average, extreme learning machines and their hybrid models along with different state-of-the-art methods.

A hybrid stochastic interpolation and compression method for kernel matrices

Kernel functions play a pivotal role in a wide range of scientific computing and machine learning problems, but they ofter result in dense kernel matrices that impose great challenges in computational costs at large scale. To address this issue, we develop a set of fast kernel matrix compressing algorithms, which can reduce computation cost of matrix operations in the related applications. The foundation of these algorithms is the polyharmonic spline interpolation, which encompass a set of radial basis functions that allow flexible choices of interpolating nodes, and a set of polynomial basis functions that guarantee the solvability and convergence of the interpolation. With these properties, original data points in the interacting kernel function can be randomly sampled with great flexibility, so the proposed method is suitable for complicated data structures, such as high-dimensionality, random distribution, or manifold. To further boost the algorithm accuracy and efficiency, our scheme incorporates a QR sampling strategy, and combined with a recently developed fast stochastic SVD to form a hybrid method. If the overall number of degree of freedom is N, then the compressing algorithm has complexity of O(N) for low-rank matrices, and O(Nlog⁡N) for general matrices with a hierarchical structure. Numerical results for data on various domains and different kernel functions validate the accuracy and efficiency of the proposed method.

A Novel Method Based on GPU for Real-Time Anomaly Detection in Airborne Push-Broom Hyperspectral Sensors

The airborne hyperspectral remote sensing systems (AHRSSs) acquire images with high spectral resolution, high spatial resolution, and high temporal dimension. While the AHRSS captures more detailed information from the terrain objects, the computational complexity of data processing is greatly increased. As an important application technology in the hyperspectral domain, anomaly detection (AD) processing must be real-time and high-precision in many cases, such as post-disaster rescue, military battlefield search, and natural disaster detection. In this paper, the real-time AD technology for the push-broom AHRSS is studied, the mathematical model is established, and a novel implementation framework is proposed. Firstly, the optimized kernel minimum noise fraction (OP-KMNF) transformation is employed to extract informative and discriminative features between the background and anomalies. Secondly, the Nyström method is introduced to reduce the computational complexity of OP-KMNF transformation by decomposing and extrapolating the sub-kernel matrix to estimate the eigenvector of the entire kernel matrix. Thirdly, the extracted features are transferred to hard disks for data storage. Then, taking the extracted features as input data, the background separation model-based CEM anomaly detector (BSM-CEMAD) is imported to detect anomalies. Finally, graphics processing unit (GPU) parallel computing is utilized in the Nyström-based OP-KMNF (NOP-KMNF) transformation and the BSM-CEMAD to improve the execution efficiency, and the real-time AD for the push-broom AHRSS could be realized. To test the feasibility of the implementation framework proposed in this paper, the experiment is carried out with the Airborne Multi-Modular Imaging Spectrometer (AMMIS) developed by the Shanghai Institute of Technical Physics as the data acquisition platform. The experimental results show that the proposed method outperforms many other state-of-the-art AD methods in anomalies detection and background suppression. Moreover, under the condition that the downlink data could retain most of the hyperspectral data information, the proposed method achieves real-time detection of pixel-level anomalies, with the initial delay not exceeding 1 s, the false alarm rate (FAR) less than 5%, and the true positive rate (TPR) close to 98%.

Vigilance estimation using truncated l1 distance kernel-based sparse representation regression with physiological signals

BackgroundWith a large number of accidents caused by the decline in the vigilance of operators, finding effective automatic vigilance monitoring methods is a work of great significance in recent years. Based on physiological signals and machine learning algorithms, researchers have opened up a path for objective vigilance estimation. MethodsSparse representation (SR)-based recognition algorithms with excellent performance and simple models are very promising approaches in this field. This paper aims to study the adaptability and performance improvement of truncated l1 distance (TL1) kernel on SR-based algorithm in the context of physiological signal vigilance estimation. Compared with the traditional radial basis function (RBF), the TL1 kernel has good adaptiveness to nonlinearity and is suitable for the discrimination of complex physiological signals. A recognition framework based on TL1 and SR theory is proposed. Firstly, the inseparable physiological features are mapped to the reproducing kernel Kreĭn space through the infinite-dimensional projection of the TL1 kernel. Then the obtained kernel matrix is converted into the symmetric positive definite matrix according to the eigenspectrum approaches. Finally, the final prediction result is obtained through the sparse representation regression process. ResultsWe verified the performance of the proposed framework on the popular SEED-VIG dataset containing physiological signals (electroencephalogram and electrooculogram) associated with vigilance. In the experimental results, the TL1 kernel is superior to the RBF kernel in both performance and kernel parameter stability. ConclusionsThis demonstrates the effectiveness of the TL1 kernel in distinguishing physiological signals and the excellent vigilance estimation capability of the proposed framework. Moreover, the contribution of our research motivates the development of physiological signal recognition based on kernel methods.