Spatial transcriptomics (ST), known as an expensive medical examination, plays an important role in analyzing the spatial heterogeneity of tumors. When considering the correlation between tissue morphological patterns and gene profiles, predicting corresponding gene expression from pathology images obtained from affordable biopsies is regarded as an instantaneous and cost-effective alternative. However, accurately modeling the complex and nonlinear relationship between histological features and gene expression remains challenging. Existing deep learning models often struggle to generalize on limited ST datasets due to their large and overparameterized architectures. The primary advantage of kernel adaptive filtering (KAF) lies in its ability to transform a challenging nonlinear problem arising in the original space into a linear regression problem in the higher-dimensional feature space via kernel methods. Therefore, this paper proposes a framework called KAFSTExp, which utilizes the state-of-the-art pathology foundation model UNI to extract image feature vectors, and then introduces the kernel least mean square algorithm with Nyström approximation to predict the normalized transcript counts of specific genes. Extensive experiments show that KAFSTExp significantly improves prediction accuracy while reducing computational cost and training time. KAFSTExp demonstrates consistent performance gains across multiple ST datasets, achieving relative improvements in Pearson correlation coefficient ranging from 1.24% to 94.23%, with an average increase of 19.80% over the best-performing non-KAF methods. External validation and further clinical analysis confirm the generalization performance and clinical application value of the proposed KAFSTExp.

Indoor positioning within the Internet of Things (IoT) has become critically important, with accuracy and robustness being essential for its practical applications. However, the complexity of real-world disturbances, including both Gaussian and non-Gaussian noise, poses significant challenges to existing methods. Kernel adaptive filtering (KAF) has proven effective in addressing these challenges, yet traditional KAF approaches face issues with growing structural complexity and increasing memory demands. To address these drawbacks, this study introduces an enhanced sparsification technique within the random Fourier features (RFFs) framework. The improvement lies in adopting the generalized Gaussian distribution (GGD) to be better suited for real-world noise, leading to the development of the ESCGKAF algorithm—a robust solution for high-precision indoor positioning in online scenarios. The algorithm leverages the half-quadratic (HQ) optimization on the kernel risk-sensitive loss (KRSL) cost function, which is further refined through the conjugate gradient (CG) method, to achieve a superior performance in noisy environments. The proposed approach permits a more generalized representation of random features, surpassing traditional Gaussian-based RFF methods in terms of adaptability and robustness. To further enhance performance in complex scenarios, MESCGKAF algorithm is proposed by introducing a multikernel strategy. The effectiveness of the proposed algorithms is validated in two real-world scenarios, showing marked performance improvement.

Existing adaptive filtering methods encounter significant challenges in simultaneously ensuring accurate prediction and robust stability when applied to real-time dynamic modeling of fractional-order nonlinear systems. To address these limitations, this paper proposes the fixed-point kernel least mean squares (FPKLMS) algorithm, which extends classical kernel adaptive filtering by introducing a novel fixed-point iteration strategy. Specifically, the proposed algorithm reformulates the weight update mechanism as a fixed-point problem in the reproducing kernel Hilbert space (RKHS), while accommodating structural variations in the weight updating operator. Through rigorous theoretical analysis, we establish the global convergence of the FPKLMS algorithm and derive explicit convergence rate bounds under mild assumptions. Experiments on fractional-order Chua’s and Lorenz circuits demonstrate that the FPKLMS algorithm achieves superior robustness, stability, and real-time prediction performance over existing methods. This approach provides an efficient and reliable framework for real-time modeling of fractional-order nonlinear dynamic systems, effectively addressing the dual requirements of accurate prediction and robust stability.

More and more applications under Internet of Things have strong need for more dedicated localization techniques. As a wireless signal strength measurement standard, received signal strength indicator (RSSI) nowadays is widely utilized as a quantity to build advanced fingerprint indoor localization techniques. However, the mixed noise such as Gaussian noise together with the abrupt noise always causes the deviation of the RSSI value and the mismatched fingerprints in the fingerprint-based method, which results in the deterioration of positioning accuracy. In this paper, we propose an online risk-sensitive localization technique named compositional online kernel indoor localization (COKIL), which further improves the performance and reduces the prediction variance under multi-path effects. Meanwhile, the Student’s t kernel is firstly employed in COKIL to fight against RSSI instability, which leads to the great performance improvement compared with the Gaussian kernel . Moreover, surprise criterion, novelty criterion and kernel orthogonal matching pursuit are embedded into COKIL to reduce the size of the neural networks . Comparing their performances in experiments, surprise criterion is the optimal sparse method in practice. Finally, a new model-based technique, RSSIq, is proposed to deal with the missing fingerprints, which significantly improves the performance in indoor environment compared to traditional path-loss model.

In this article, the multisynchronization issue of coupled memristive neural networks (CMNNs) with unbounded time delays is investigated. To begin with, a class of generalized Gaussian-wavelet-type activation functions is adopted to extend the number of stable equilibrium states. On this basis, a distributed impulsive controller is constructed to realize the multiple synchronization of the delayed CMNNs. Under the concepts of$\mu $-stability, Filippov solution, and differential inclusion, some sufficient conditions are derived such that the addressed system can possess$(2r + 1)^{n}\,\,\mu $-stable synchronization manifolds. The convergence performance of solutions is determined by the time delays. As the time delays increase, the stability of synchronization manifolds will transform from exponential stability to power-stability, log-stability, or log–log-stability as special cases. Moreover, considering the modeling error and external disturbance, we further investigated the multisynchronization of delayed CMNNs with parametric uncertainties and stochastic perturbations, and some robust multisynchronization criteria are obtained. Finally, the effectiveness of the obtained results is verified by numerical simulations.

In this letter, a novel kernel function named$q$-Rényi kernel is proposed. Based on it, a new online adaptive learning algorithm is presented, which is derived based on the recursive adaptive filtering paradigm under the reproducing kernel Hilbert space. The proposed learning algorithm is different from the conventional kernel-based learning paradigm in two senses: first, the reproducing kernel so-called$\boldsymbol {q}$-Rényi kernel is firstly derived and employed; and second, a sparsity constraint is utilized to generate a small size of neural networks while maintaining a high learning performance. The effectiveness of the proposed algorithm is demonstrated via numerical simulations.

In this letter, a novel robust two-dimensional nearfield millimeter-wave (MMW) image reconstruction algorithm is developed based on compressed sensing (CS) in the presence of impulsive measurement noise. To enable the sparse MMW image recovery, the CS algorithm usually employs the popular ℓ2-norm as the data fidelity term and a combination of multiple sparsityinduced functions as the penalty term. The ℓ2-norm is non-robust against impulsive noise since the Gaussian noise distribution assumption is not valid, and the presence of impulsive noise will severely degrade the robustness of the compressive MMW image recovery. To gain more robustness performance, a complex correntropy based data-fitting term, namely complex correntropic loss (CC-loss), is used to replace the ℓ2-norm for the near-field MMW measurement contaminated by impulsive noise. In order to solve the corresponding minimization problem, an additive half quadratic method is used to transform the CC-loss term to its convex form, and then a parallel primal-dual process is used to guarantee the convergence of the proposed algorithm. In total, 150-GHz MMW experimental results show that the proposed algorithm can achieve accurate image reconstruction from compressive measurements under different impulsive noise levels.

This letter proposes a robust formulation for sparse signal reconstruction from compressed measurements corrupted by impulsive noise, which exploits the$\boldsymbol {q}$-Gaussian generalized correntropy$\boldsymbol {(1< q< 3)}$as the loss function for the residual error and utilizes a$\ell _{0}$-norm penalty term for sparsity inducing. To solve this formulation efficiently, we develop a gradient-based adaptive filtering algorithm which incorporates a zero-attracting regularization term into the framework of adaptive filtering. This new proposed algorithm blending the advantages of adaptive filtering and$\boldsymbol {q}$-Gaussian generalized correntropy can obtain accurate reconstruction and satisfactory robustness with a proper shape parameter$\boldsymbol {q}$. Numerical experiments on both synthetic sparse signals and natural images are conducted to illustrate the superior recovery performance of the proposed algorithm to the state-of-the-art robust sparse signal reconstruction algorithms.

In this letter, a novel information theoretic measure, namely q-Gaussian kernel mean p-power error (QKMPE), is proposed by defining the mean p-power error in the q-Gaussian kernel space, which is a generalization of the kernel mean p-power error measure. Furthermore, a recursive kernel adaptive filter algorithm, named as recursive least q-Gaussian kernel mean p-power, is derived under the least QKMPE criterion for robust learning in noisy environment. This new proposed algorithm reveals superior performance against Gaussian-type noise as well as the nonGaussian perturbation, especially when the data contain large outliers. Experimental results in the context of Mackey-Glass time series prediction confirm the effectiveness of the proposed algorithm.

This letter presents a new sparsity basis selection compressed sensing method (SBSCS) for improving signal reconstruction from compressed sensing (CS) measurements. Based on the observation that different classes of transform cause different sparsity expressions and better sparsity expression leads to better signal recovery, the proposed SBSCS method searches the best class of transform and basis in a set of redundant tree-structured dictionaries by nesting sparsity maximization within the CS minimization. The SBSCS method adaptively selects the class of transform and basis with the best sparsity measure at each ℓ1iteration and converges quickly to the final class of transform and basis. Numerical experiments show that the proposed SBSCS method improves the quality of signal recovery over the existing best basis compressed sensing method (BBCS) proposed by Peyré in 2010.

Probability density function (PDF) plays a vital role in many applications involving stochastic process. A good approximation for real-time PDF conditioned on certain performance criterion could help to acquire unknown information about the system. With the help of this kind of information, which was not available earlier, many features of various models that describe the real system can be estimated effectively, especially for non-linear non-Gaussian stochastic system. In this paper, we elucidate some PDFs with only one parameter that have a definite physical meaning based on Tsallis entropy. The PDFs that we calculated here are all Gaussian-like, and Gaussian distribution is attained when the parameter of Tsallis entropy approaches zero. Based on these explicit form of Gaussian-like PDFs we calculated here, an extension of Gaussian particle filter (GPF) called Gaussian-like particle filter (GLPF) is proposed and the simulation results show that the GLPF is a more effective way to estimate the state of non-linear stochastic system compared with the GPF.