Iterative Rule Research Articles

An Improved Adaptive Grid-Based Progressive Triangulated Irregular Network Densification Algorithm for Filtering Airborne LiDAR Data

Ground filtering is crucial for airborne Light Detection and Ranging (LiDAR) data post-processing. The progressive triangulated irregular network densification (PTD) algorithm and its variants outperform others in accuracy, stability, and robustness, using grid-based seed point selection, TIN construction, and iterative rules for ground point identification. However, these methods still face limitations in removing low points and accurately preserving terrain details, primarily due to their sensitivity to grid size. To overcome this issue, a novel PTD filtering algorithm based on an adaptive grid (AGPTD) was proposed. The main contributions of the proposed method include an outlier removal method using a radius outlier removal algorithm and Kd-tree, a method for establishing an adaptive two-level grid based on point cloud density and terrain slope, and an adaptive selection method for angle and distance thresholds in the iterative densification processing. The performance of the AGPTD algorithm was assessed based on widely used benchmark datasets. Results show that the AGPTD algorithm outperforms the classical PTD algorithm in retaining ground feature points, especially in reducing Type I error and average total error significantly. In comparison with other advanced algorithms developed in recent years, the novel algorithm showed the lowest average Type I error, the minimal average total error, and the greatest average Kappa coefficient, which were 1.11%, 2.28%, and 90.86%, respectively. Additionally, the average accuracy, precision, and recall of AGPTD were 97.69%, 97.52%, and 98.98%, respectively.

Diffusion process with structural changes for subspace clustering

Spectral clustering-based methods have gained significant popularity in subspace clustering due to their ability to capture the underlying data structure effectively. Standard spectral clustering focuses on only pairwise relationships between data points, neglecting interactions among high-order neighboring points. Integrating the diffusion process can address this limitation by leveraging a Markov random walk. However, ensuring that diffusion methods capture sufficient information while maintaining stability against noise remains challenging. In this paper, we propose the Diffusion Process with Structural Changes (DPSC) method, a novel affinity learning framework that enhances the robustness of the diffusion process. Our approach broadens the scope of nearest neighbors and leverages the dropout idea to generate random transition matrices. Furthermore, inspired by the structural changes model, we use two transition matrices to optimize the iteration rule. The resulting affinity matrix undergoes self-supervised learning and is subsequently integrated back into the diffusion process for refinement. Notably, the convergence of the proposed DPSC is theoretically proven. Extensive experiments on benchmark datasets demonstrate that the proposed method outperforms existing subspace clustering methods. The code of our proposed DPSC is available at https://github.com/zhudafa/DPSC.

6DoF Object Pose and Focal Length Estimation from Single RGB Images in Uncontrolled Environments.

Accurate 6DoF (degrees of freedom) pose and focal length estimation are important in extended reality (XR) applications, enabling precise object alignment and projection scaling, thereby enhancing user experiences. This study focuses on improving 6DoF pose estimation using single RGB images of unknown camera metadata. Estimating the 6DoF pose and focal length from an uncontrolled RGB image, obtained from the internet, is challenging because it often lacks crucial metadata. Existing methods such as FocalPose and Focalpose++ have made progress in this domain but still face challenges due to the projection scale ambiguity between the translation of an object along the z-axis (tz) and the camera's focal length. To overcome this, we propose a two-stage strategy that decouples the projection scaling ambiguity in the estimation of z-axis translation and focal length. In the first stage, tz is set arbitrarily, and we predict all the other pose parameters and focal length relative to the fixed tz. In the second stage, we predict the true value of tz while scaling the focal length based on the tz update. The proposed two-stage method reduces projection scale ambiguity in RGB images and improves pose estimation accuracy. The iterative update rules constrained to the first stage and tailored loss functions including Huber loss in the second stage enhance the accuracy in both 6DoF pose and focal length estimation. Experimental results using benchmark datasets show significant improvements in terms of median rotation and translation errors, as well as better projection accuracy compared to the existing state-of-the-art methods. In an evaluation across the Pix3D datasets (chair, sofa, table, and bed), the proposed two-stage method improves projection accuracy by approximately 7.19%. Additionally, the incorporation of Huber loss resulted in a significant reduction in translation and focal length errors by 20.27% and 6.65%, respectively, in comparison to the Focalpose++ method.

Iterative outlier detection and refinement rule of compensation for phase aberrations in digital holographic microscopy.

We propose a robust and accurate compensation method for phase aberrations based on the iterative outlier detection and refinement (ODR) rule. This method does not require additional steps to select the known flat region manually or by image segmentation. Based on the proposed method, the phase aberration in regions of a specimen can be detected and refined iteratively. Then, the least squares fitting can be carried out to estimate the coefficients of Zernike polynomials and obtain the accurate phase aberration finally. Computer simulations and real experiments validate the feasibility and effectiveness, and the results show that the proposed method is robust to noise and has superior accuracy even when the specimen occupies half of the field of view.

Iterative Tomographic Image Reconstruction Algorithm Based on Extended Power Divergence by Dynamic Parameter Tuning.

Computed tomography (CT) imaging plays a crucial role in various medical applications, but noise in projection data can significantly degrade image quality and hinder diagnosis accuracy. Iterative algorithms for tomographic image reconstruction outperform transform methods, especially in scenarios with severe noise in projections. In this paper, we propose a method to dynamically adjust two parameters included in the iterative rules during the reconstruction process. The algorithm, named the parameter-extended expectation-maximization based on power divergence (PXEM), aims to minimize the weighted extended power divergence between the measured and forward projections at each iteration. Our numerical and physical experiments showed that PXEM surpassed conventional methods such as maximum-likelihood expectation-maximization (MLEM), particularly in noisy scenarios. PXEM combines the noise suppression capabilities of power divergence-based expectation-maximization with static parameters at every iteration and the edge preservation properties of MLEM. The experimental results demonstrated significant improvements in image quality in metrics such as the structural similarity index measure and peak signal-to-noise ratio. PXEM improves CT image reconstruction quality under high noise conditions through enhanced optimization techniques.

GWO+RuleFit: rule-based explainable machine-learning combined with heuristics to predict mid-treatment FDG PET response to chemoradiation for locally advanced non-small cell lung cancer.

Objective.Vital rules learned from fluorodeoxyglucose positron emission tomography (FDG-PET) radiomics of tumor subregional response can provide clinical decision support for precise treatment adaptation. We combined a rule-based machine learning (ML) model (RuleFit) with a heuristic algorithm (gray wolf optimizer, GWO) for mid-chemoradiation FDG-PET response prediction in patients with locally advanced non-small cell lung cancer.Approach.Tumors subregions were identified using K-means clustering. GWO+RuleFit consists of three main parts: (i) a random forest is constructed based on conventional features or radiomic features extracted from tumor regions or subregions in FDG-PET images, from which the initial rules are generated; (ii) GWO is used for iterative rule selection; (iii) the selected rules are fit to a linear model to make predictions about the target variable. Two target variables were considered: a binary response measure (ΔSUVmean ⩾ 20% decline) for classification and a continuous response measure (ΔSUVmean) for regression. GWO+RuleFit was benchmarked against common ML algorithms and RuleFit, with leave-one-out cross-validated performance evaluated by the area under the receiver operating characteristic curve (AUC) in classification and root-mean-square error (RMSE) in regression.Main results.GWO+RuleFit selected 15 rules from the radiomic feature dataset of 23 patients. For treatment response classification, GWO+RuleFit attained numerically better cross-validated performance than RuleFit across tumor regions and sets of features (AUC: 0.58-0.86 vs. 0.52-0.78,p= 0.170-0.925). GWO+Rulefit also had the best or second-best performance numerically compared to all other algorithms for all conditions. For treatment response regression prediction, GWO+RuleFit (RMSE: 0.162-0.192) performed better numerically for low-dimensional models (p= 0.097-0.614) and significantly better for high-dimensional models across all tumor regions except one (RMSE: 0.189-0.219,p< 0.004).Significance. The GWO+RuleFit selected rules were interpretable, highlighting distinct radiomic phenotypes that modulated treatment response. GWO+Rulefit achieved parsimonious models while maintaining utility for treatment response prediction, which can aid clinical decisions for patient risk stratification, treatment selection, and biologically driven adaptation. Clinical trial: NCT02773238.

Development of mathematical methods for diagnosing kidney diseases using fuzzy set tools

An approach based on fuzzy set theory is presented in the scientific article to enhance the efficiency of diagnosing kidney diseases by decreasing the time required for making medical decisions. The suggested approach employs fuzzy models and algorithms that consider the uncertainty and variability of clinical data to optimize the assessment of the functional state of the kidneys, taking into account various risk factors and individual characteristics of patients. The paper suggests a technique to develop a system of fuzzy decision rules. This technique combines E. Shortliff’s iterative rules with functions from the studied classes of kidney diseases. Mathematical modeling and experimental studies have indicated relatively high effectiveness in classifying different forms of kidney diseases. The results can be used to formulate intelligent decision support systems in clinical practice and improve diagnostic and monitoring processes. Moreover, the findings may aid in shaping more targeted and effective health policies at the national and regional levels, enhancing access to healthcare, and promoting the population’s overall health.

Distributed maximum correntropy unscented Kalman filter under hybrid attacks in non‐Gaussian environment

AbstractThis paper addresses a distributed nonlinear filtering issue based on maximum correntropy for dealing with randomly occurring hybrid cyber‐attacks in non‐Gaussian environment. The types of cyber‐attacks include denial of service attacks and deception attacks. First, a modified distributed unscented Kalman filter is proposed, using Cauchy kernel‐based maximum correntropy criterion instead of the traditional mean square error criterion, against cyber‐attacks and non‐Gaussian noise. Then based on fixed‐point iterative rules and information fusion strategy, the update equations of state estimates and covariance matrices of the proposed filter are obtained. Furthermore, the sufficient condition guaranteeing its convergence and computational complexity are also given. Finally, an illustrative example is presented to verify the effectiveness of the proposed filter under hybrid cyber‐attacks in non‐Gaussian environment.

Neural network compensator-based robust iterative learning control scheme for mobile robots nonlinear systems with disturbances and uncertain parameters

Aiming at the problem of trajectory tracking control for mobile robot nonlinear systems with non-repetitive uncertain parameters, we propose a novel neural network compensator-based robust iterative learning control (NNRILC) scheme to achieve excellent tracking performance and uncertainty compensation. The NNRILC scheme consists of a parallel structure that includes a robust iterative learning control (RILC) term and a neural network (NN) compensator. The RILC term is used to ensure robust control performance and promise closed-loop stability. The compensator based on the neural network is employed to handle the uncertainties resulted from the nonlinear dynamics as well as the suppressed disturbances in the mobile robot nonlinear systems. Additionally, the fourth-order Runge-Kutta algorithm is employed to solve the state differential equation of the mobile robot. Consequently, The H∞ robust technique is used to construct an iterative learning control update rule to reduce the impact of disturbances. Meanwhile, the RILC scheme is designed to optimize the neural network initial parameters and weights of the NN compensator at each trial. Then the convergence of the proposed NNRILC scheme is analyzed, and the results are incorporated into the control update for the next process trial. Finally, the effectiveness of the proposed method is verified by mobile robot simulation.

Iterative Rule Extension for Logic Analysis of Data: An MILP-Based Heuristic to Derive Interpretable Binary Classifiers from Large Data Sets

Data-driven decision making is rapidly gaining popularity, fueled by the ever-increasing amounts of available data and encouraged by the development of models that can identify nonlinear input–output relationships. Simultaneously, the need for interpretable prediction and classification methods is increasing as this improves both our trust in these models and the amount of information we can abstract from data. An important aspect of this interpretability is to obtain insight in the sensitivity–specificity trade-off constituted by multiple plausible input–output relationships. These are often shown in a receiver operating characteristic curve. These developments combined lead to the need for a method that can identify complex yet interpretable input–output relationships from large data, that is, data containing large numbers of samples and features. Boolean phrases in disjunctive normal form (DNF) are highly suitable for explaining nonlinear input–output relationships in a comprehensible way. Mixed integer linear programming can be used to obtain these Boolean phrases from binary data though its computational complexity prohibits the analysis of large data sets. This work presents IRELAND, an algorithm that allows for abstracting Boolean phrases in DNF from data with up to 10,000 samples and features. The results show that, for large data sets, IRELAND outperforms the current state of the art in terms of prediction accuracy. Additionally, by construction, IRELAND allows for an efficient computation of the sensitivity–specificity trade-off curve, allowing for further understanding of the underlying input–output relationship. History: Accepted by Andrea Lodi, Area Editor for Design &amp; Analysis of Algorithms–Discrete. Funding: This work was supported by the Netherlands Organization for Scientific Research (Nederlandse Organisatie voor Wetenschappelijk Onderzoek) [Grant VI.VENI.192.043]. Supplemental Material: The online supplement is available at https://doi.org/10.1287/ijoc.2021.0284 .

Inter- and intra-hypergraph regularized nonnegative matrix factorization with hybrid constraints

The accurate low rank representation of high-dimensional data learned by the manifold regularized nonnegative matrix factorization framework is effective in data clustering. In previous work, this work has mainly been solved in the way of similarity matrix induction. To further increase the efficacy of low-rank representations, we propose a novel semi-supervised non-negative matrix factorization (NMF) model in this study called inter- and intra-hypergraph regularized non-negative matrix factorization with hybrid constraints (IGNMFC). IGNMFC constructs intra-hypergraph regularization and intra-hypergraph regularization by hypergraph learning, which can precisely induce high-dimensional data to map toward low-dimensional. Moreover, hybrid constraints are introduced to improve the exclusivity and sparsity of low-dimensional representations, and the result accounts for the benefit of this method in learning distinguishable subspace representations. Finally, IGNMFC is transformed into an optimal problem and an efficient iteration rule is proposed. Experiments on several datasets demonstrate that the proposed method outperforms the state-of-the-art NMF algorithms, and can achieve at least 7.9%∼15% accuracy improvement in most cases.

The average trapping time of non-nearest-neighbor jumps on nested networks

In this paper, we consider the trapping problem on the nearest-neighbor (NN) and non-nearest-neighbor (NNN) jumps on nested networks. Based on the nested construction of the network and the use of probability generating function tool, the iterative rules of two successive generations of the network are found, and the analytical expression of the average trapping time (ATT) is finally obtained. We allow two jump modes in the network at the same time, and the results show that the choice probability of the jump mode is not related to the exponential term of the scaling expression, but to its leading factor term. According to the analytic solution of ATT, we can find that the value of ATT expands superlinearly with the increase of network size. In addition, the numerical simulation results of parameters q (the probability of choosing NNN jump) and n (the generation of the network) show that with fixed n, ATT decreases with the increase of q; while with fixed q, ATT increases with the increase of n. In summary, this work can observe the effect of different hopping modes on random walk efficiency in complex networks.

Jointly Distributed Filtering Based on Generalized Maximum Correntropy Criterion: Memory-Based Event-Triggered Cases

This article addresses jointly distributed entropy filtering issues based on the generalized maximum correntropy criterion (GMCC) for discrete-time stochastic parameter systems with fault and non-Gaussian noise effects. By taking current and historical triggered information, a memory-based event-triggered scheme with a time-varying threshold is put forward to govern the network communication. According to the constructed jointly distributed entropy filter with a two-step form, the upper bounds of the filtering error covariance matrices are derived and an ideal filter gain is obtained to maximize GMCC. Furthermore, an accessible gain is received via fixed-point iterative rules and the corresponding convergence is disclosed in theory. Finally, an application of the proposed distributed filter in ballistic object tracking is provided to show its effectiveness under non-Gaussian environments.

A Derivative-Incorporated Adaptive Gradient Method for Federated Learning

As a new machine learning technique, federated learning has received more attention in recent years, which enables decentralized model training across data silos or edge intelligent devices in the Internet of Things without exchanging local raw data. All kinds of algorithms are proposed to solve the challenges in federated learning. However, most of these methods are based on stochastic gradient descent, which undergoes slow convergence and unstable performance during the training stage. In this paper, we propose a differential adaptive federated optimization method, which incorporates an adaptive learning rate and the gradient difference into the iteration rule of the global model. We further adopt the first-order moment estimation to compute the approximate value of the differential term so as to avoid amplifying the random noise from the input data sample. The theoretical convergence guarantee is established for our proposed method in a stochastic non-convex setting under full client participation and partial client participation cases. Experiments for the image classification task are performed on two standard datasets by training a neural network model, and experiment results on different baselines demonstrate the effectiveness of our proposed method.

A determination of Catalan numbers in 18th century Italy by Giovanni Rizzetti (1675–1751)

We discuss the probabilistic question faced by the Italian scholar Giovanni Rizzetti (1675–1751) and suggest this is a variant of what we refer to today as the “ballot sequences”, variant to which Catalan numbers offer a solution.Rizzetti's search for a solution led him to produce an iterative rule which involved the consideration of Catalan numbers. Although coming up with these were not his final goal, the rule he elaborated allowed him to carry on calculating them as long as he wanted. As such, it is possible this was the first time such numbers were determined.

Research on international logistics supply chain management strategy based on deep reinforcement learning

Abstract The use of deep reinforcement learning algorithms for strategy formulation in supply chain management enables the nodes in the supply chain to better improve their management strategies. In this paper, a supply chain model is constructed as a starting point, and deep reinforcement learning algorithms are introduced on this basis. Firstly, the decision problem of uncertainty is handled by the reinforcement learning method of functions, and the DQN algorithm (deep neural network algorithm) is divided into two parts for iterative rules. Then the target network is established to make the iterative process more stable, to improve the convergence of the algorithm, evaluate the loss function in the training process of the network, and to determine its influence factor. Then the neural network is used to improve the iteration rule, improve the output layer, select the final action, and define the model expectation reward. Finally, the Bellman equation is fitted to the function by a deep neural network to calculate the final result. The experimental results show that by analyzing and constructing the cost of international logistics under supply chain management, the capacity utilization rate of ocean freight link is 57% The unloading link is 74% and the total capacity utilization rate is calculated as 76%. It shows that using deep reinforcement learning algorithms under international logistics supply chain management is feasible and necessary for improving the management strategy research of supply chains.

Reconfiguration of Distributed Power Distribution Networks Based on Gravitational Search Algorithms

Distributed power supply access to the system affects the tidal distribution of the distribution network. The article establishes a mathematical optimization model with network loss minimization and load balance minimization as the objective function. In this paper, the idea of elite strategy is introduced into the gravitational search algorithm and combined with the Sigmoid function, an optimization method of distribution network reconfiguration based on the improved gravitational search algorithm is proposed by improving the particle iteration rule. The mathematical model is solved using the improved algorithm, and the results show that the net loss and load balance of the system is reduced after the distribution network reconfiguration. The simulation results verify the effectiveness and feasibility of the proposed method, which has a strong global optimization capability and fast convergence.

Large-scale non-negative subspace clustering based on Nyström approximation

Large-scale subspace clustering usually drops the requirements of the full similarity matrix and Laplacian matrix but constructs the anchor affinity matrix and uses matrix approximation methods to reduce the clustering complexity. However, the existing anchor affinity matrix calculation methods only consider the global structure of data. Moreover, directly using the anchor affinity matrix to approximate the full Laplacian matrix cannot guarantee the best low-rank approximation, which affects the clustering results. To address these problems, this paper proposes a large-scale non-negative subspace clustering method based on Nyström approximation. Firstly, we modify the objective function of the anchor affinity matrix by adding the local structure term, taking into account both the local and global data characteristics for better affinity learning. Secondly, a matrix iterative update rule is derived to optimize the objective function according to the non-negative Lagrangian relaxation, and its rationality and convergence are proved. Finally, two effective Laplacian matrix decomposition methods based on Nyström approximation are designed to obtain more accurate eigenvectors to improve the clustering quality. The proposed algorithms are tested on various benchmark datasets. The experimental results show that our methods have competitive performance compared with state-of-the-art large-scale clustering algorithms.

Grier: graph repairing based on iterative embedding and rules

Grier: graph repairing based on iterative embedding and rules

Meta-AF: Meta-Learning for Adaptive Filters

Adaptive filtering algorithms are pervasive throughout signal processing and have had a material impact on a wide variety of domains including audio processing, telecommunications, biomedical sensing, astrophysics and cosmology, seismology, and many more. Adaptive filters typically operate via specialized online, iterative optimization methods such as least-mean squares or recursive least squares and aim to process signals in unknown or nonstationary environments. Such algorithms, however, can be slow and laborious to develop, require domain expertise to create, and necessitate mathematical insight for improvement. In this work, we seek to improve upon hand-derived adaptive filter algorithms and present a comprehensive framework for learning online, adaptive signal processing algorithms or update rules directly from data. To do so, we frame the development of adaptive filters as a meta-learning problem in the context of deep learning and use a form of self-supervision to learn online iterative update rules for adaptive filters. To demonstrate our approach, we focus on audio applications and systematically develop meta-learned adaptive filters for five canonical audio problems including system identification, acoustic echo cancellation, blind equalization, multi-channel dereverberation, and beamforming.We compare our approach against common baselines and/or recent state-of-the-art methods. We show we can learn high-performing adaptive filters that operate in real-time and, in most cases, significantly outperform each method we compare against – all using a single general-purpose configuration of our approach.