Splitting Algorithm Research Articles

ApSpGEMM: Accelerating Large-scale SpGEMM with Heterogeneous Collaboration and Adaptive Panel

The Sparse General Matrix-Matrix multiplication (SpGEMM) is a fundamental component for many applications, such as algebraic multigrid methods (AMG), graphic processing, and deep learning. However, the unbearable latency of computing high-dimensional, large-scale sparse matrix multiplication on GPUs hinders the development of these applications. An effective approach is heterogeneous cores collaborative computing, but this method must address three aspects: (1) irregular non-zero elements lead to load imbalance and irregular memory access, (2) different core computing latency differences reduce computational parallelism, and (3) temporary data transfer between different cores introduces additional latency overhead. In this work, we propose an innovative framework for collaborative large-scale sparse matrix multiplication on CPU-GPU heterogeneous cores, named ApSpGEMM. ApSpGEMM is based on sparsity rules and proposes reordering and splitting algorithms to eliminate the impact of non-zero element distribution features on load and memory access. Then adaptive panels allocation with affinity constraints among cores improves computational parallelism. Finally, carefully arranged asynchronous data transmission and computation balance communication overhead. Compared with state-of-the-art SpGEMM methods, our approach provides excellent absolute performance on matrices with different sparse structures. On heterogeneous cores, the GFlops of large-scale sparse matrix multiplication is improved by 2.25 to 7.21 times.

Joint optimization of recyclable inventory routing problem under uncertainties in an incentive-based recycling system

Due to the value of resource recovery and the development of a circular economy, waste recycling has gathered global attention. Recently, many emerging cities designed new systems like an incentive-based recycling system (IBRS). In such systems, recyclables are collected through community recycling nodes by offering incentives, then transported to street recycling stations and sorted before being finally recycled. The increased recycling nodes and the incentives enhance the convenience and residents’ enthusiasm for waste recycling, but also intensify the uncertainty of recycling quantities and the complexity of the recycling operation management. Poor recycling operation management may result in increased recycling costs or greater loss of recyclables, which discourages residents from participating in recycling. Based on an existing IBRS, this study investigates the joint optimization problem of the recyclable inventory management at each community recycling node and the vehicle routing from the recycling nodes to the recycling station. A two-stage dual-objective multi-period stochastic programming model is established to minimize the loss of recyclables and logistics costs, which is further reformulated using the weighting method and transportation cost approximation parameters. To solve the reformulated model, a three-phase iterative algorithm is designed by combining the progressive hedging algorithm and route splitting algorithm based on the Lin-Kernighan heuristic. A case study is conducted using data from Shanghai’s IBRS. The proposed joint decision model is superior to separate decisions and the three-phase iterative algorithm can reduce the average total cost by up to 42.12% compared to the genetic algorithm and the Iteration-Move-Search method in the literature. Additionally, a sensitivity analysis is conducted to provide managerial insights.

Exploring the LULC dynamics and its relation with land surface temperature variation using split window algorithm: A study of Barasat subdivision, West Bengal, India.

Rapid urban growth in an unplanned way, decreased forest cover and consequential changes in land use in urban and rural areas have become pivotal obstacles for policymakers and urban planners to a great extent. Specifically, in a developing country like India, the repercussions of these changes have generated a substantial alteration in climate in the form of increased land surface temperature (LST), heat islands and associated human health risks. This research was initiated to assess the interrelationship between LST and LULC dynamics using spatial techniques over the Barasat Sub-Division in West Bengal (India). This study encompasses the extraction of LST using satellite images, seasonal variations of LST, the relationship of different land indices (i.e. NDVI, NDBI, NDMI and NDWI) with LST, and hotspot analysis of the landscape to get a comprehensive understanding of LST changes from 1988 to 2023, seasonal patterns, and relationships with LULC dynamics in the study area. The results of this research signify a substantial percentage increase in built-up spaces (51%), a decline in fallow areas (- 73%), relatively higher LST changes (3.41°C) in high-density built-up areas (e.g. Madhyamgram), a positive relationship (e.g. r2 = 0.59) between NDBI and LST, a transition from a cold spot to a hot spot share of 20% and a persisting hot spot of 42% throughout the summer season (1988 to 2023) in the selected landscape. The findings of this study will improve our present knowledge of seasonal fluctuations in land surface temperature (LST) and the variables that influence them. These findings will also draw attention to the growing worries about the fast variations in LST and the climatic and health hazards they pose. It is advised to establish planned urban expansion, efficient land use and land cover (LULC) management laws and encourage green areas that support sustainable development in India's urban surroundings in order to reduce these dangers.

Deep self-organizing map neural networks improve the segmentation for inadequate plantar pressure imaging data set

ABSTRACT This study introduces a deep self-organizing map neural network based on level-set (LS-SOM) for the customization of a shoe-last defined from plantar pressure imaging data. To alleviate the over-segmentation problem of images, which refers to segmenting images into more subcomponents, a domain-based segmentation model of plantar pressure images was constructed. The domain growth algorithm was subsequently modified by optimizing its parameters. A SOM with 10, 15, 20, and 30 hidden layers was compared and validated according to domain growth characteristics by using merging and splitting algorithms. Furthermore, we incorporated a level set segmentation method into the plantar pressure image algorithm to enhance its efficiency. Compared to the literature, this proposed method has significantly improved pixel accuracy, average cross-combination ratio, frequency-weighted cross-combination ratio, and boundary F1 index comparison. Using the proposed methods, shoe lasts can be designed optimally, and wearing comfort is enhanced, particularly for people with high blood pressure.

A performant energy-conserving particle reweighting method for Particle-in-Cell simulations

A new particle-based reweighting method is developed and demonstrated in the Aleph Particle-in-Cell with Direct Simulation Monte Carlo (PIC-DSMC) program. Novel splitting and merging algorithms ensure that modified particles maintain physically consistent positions and velocities. This method allows a single reweighting simulation to efficiently model plasma evolution over orders of magnitude variation in density, while accurately preserving energy distribution functions (EDFs). Demonstrations on electrostatic sheath and collisional rate dynamics show that reweighting simulations achieve accuracy comparable to fixed weight simulations with substantial computational time savings. This highly performant reweighting method is recommended for modeling plasma applications that require accurate resolution of EDFs or exhibit significant density variations in time or space.

Convergence of a class of algorithms with the level-set subdifferential error bound

In this paper, we study the convergence of algorithms for a class of nonconvex and nonsmooth optimization problems via an level-set subdifferential error bound. Many algorithms (cf. forward-backward splitting algorithm and alternating proximal minimization algorithm) satisfy sufficient descent and relative error conditions. We also find that these algorithms satisfy a quadratic error condition. Under these conditions and the level-set subdifferential error bound, we study the global convergence and the convergence rates of these algorithms without the Kurdyka-Łojasiewicz property which is stronger than the level-set subdifferential error bound. Two examples are given to illustrate the broader applicability of our findings across these algorithms.

An efficient Newton-type matrix splitting algorithm for solving generalized absolute value equations with application to ridge regression problems

A generalized Newton-based matrix splitting (GNMS) method is proposed for solving the generalized absolute value equations (GAVEs). Under mild conditions, the GNMS method converges to the unique solution of GAVEs. Moreover, we can obtain a few weaker convergence conditions for some existing methods. Numerical results verify the effectiveness of the proposed method.

Bregman Proximal Linearized ADMM for Minimizing Separable Sums Coupled by a Difference of Functions

AbstractIn this paper, we develop a splitting algorithm incorporating Bregman distances to solve a broad class of linearly constrained composite optimization problems, whose objective function is the separable sum of possibly nonconvex nonsmooth functions and a smooth function, coupled by a difference of functions. This structure encapsulates numerous significant nonconvex and nonsmooth optimization problems in the current literature including the linearly constrained difference-of-convex problems. Relying on the successive linearization and alternating direction method of multipliers (ADMM), the proposed algorithm exhibits the global subsequential convergence to a stationary point of the underlying problem. We also establish the convergence of the full sequence generated by our algorithm under the Kurdyka–Łojasiewicz property and some mild assumptions. The efficiency of the proposed algorithm is tested on a robust principal component analysis problem and a nonconvex optimal power flow problem.

Screening osteoporosis in elderly using a new two inertial‎ ‎projective forward-backward splitting algorithm

Screening osteoporosis in elderly using a new two inertial‎ ‎projective forward-backward splitting algorithm

Interpretable Machine Learning-Based Influence Factor Identification for 3D Printing Process-Structure Linkages.

Three-dimensional printing technology is a rapid prototyping technology that has been widely used in manufacturing. However, the printing parameters in the 3D printing process have an important impact on the printing effect, so these parameters need to be optimized to obtain the best printing effect. In order to further understand the impact of 3D printing parameters on the printing effect, make theoretical explanations from the dimensions of mathematical models, and clarify the rationality of certain important parameters in previous experience, the purpose of this study is to predict the impact of 3D printing parameters on the printing effect by using machine learning methods. Specifically, we used four machine learning algorithms: SVR (support vector regression): A regression method that uses the principle of structural risk minimization to find a hyperplane in a high-dimensional space that best fits the data, with the goal of minimizing the generalization error bound. Random forest: An ensemble learning method that constructs a multitude of decision trees and outputs the class that is the mode of the classes (classification) or mean prediction (regression) of the individual trees. GBDT (gradient boosting decision tree): An iterative ensemble technique that combines multiple weak prediction models (decision trees) into a strong one by sequentially minimizing the loss function. Each subsequent tree is built to correct the errors of the previous tree. XGB (extreme gradient boosting): An optimized and efficient implementation of gradient boosting that incorporates various techniques to improve the performance of gradient boosting frameworks, such as regularization and sparsity-aware splitting algorithms. The influence of the print parameters on the results under the feature importance and SHAP (Shapley additive explanation) values is compared to determine which parameters have the greatest impact on the print effect. We also used feature importance and SHAP values to compare the importance impact of print parameters on results. In the experiment, we used a dataset with multiple parameters and divided it into a training set and a test set. Through Bayesian optimization and grid search, we determined the best hyperparameters for each algorithm and used the best model to make predictions for the test set. We compare the predictive performance of each model and confirm that the extrusion expansion ratio, elastic modulus, and elongation at break have the greatest influence on the printing effect, which is consistent with the experience. In future, we will continue to delve into methods for optimizing 3D printing parameters and explore how interpretive machine learning can be applied to the 3D printing process to achieve more efficient and reliable printing results.

Conformal Multi‐Target Hyperrectangles

ABSTRACTWe propose conformal hyperrectangular prediction regions for multi‐target regression. We propose split conformal prediction algorithms for both point and quantile regression to form hyperrectangular prediction regions, which allow for easy marginal interpretation and do not require covariance estimation. In practice, it is preferable that a prediction region is balanced, that is, having identical marginal prediction coverage, since prediction accuracy is generally equally important across components of the response vector. The proposed algorithms possess two desirable properties, namely, tight asymptotic overall nominal coverage as well as asymptotic balance, that is, identical asymptotic marginal coverage, under mild conditions. We then compare our methods to some existing methods on both simulated and real data sets. Our simulation results and real data analysis show that our methods outperform existing methods while achieving the desired nominal coverage and good balance between dimensions.

Parallel inertial forward–backward splitting methods for solving variational inequality problems with variational inclusion constraints

The inertial forward–backward splitting algorithm can be considered as a modified form of the forward–backward algorithm for variational inequality problems with monotone and Lipschitz continuous cost mappings. By using parallel and inertial techniques and the forward–backward splitting algorithm, in this paper, we propose a new parallel inertial forward–backward splitting algorithm for solving variational inequality problems, where the constraints are the intersection of common solution sets of a finite family of variational inclusion problems. Then, strong convergence of proposed iteration sequences is showed under standard assumptions imposed on cost mappings in a real Hilbert space. Finally, some numerical experiments demonstrate the reliability and benefits of the proposed algorithm.

A Kinetic-magnetohydrodynamic Model with Adaptive Mesh Refinement for Modeling Heliosphere Neutral-plasma Interaction

The charge exchange between the interstellar medium and the solar wind plasma is crucial for determining the structures of the heliosphere. Since both the neutral-ion and neutral–neutral collision mean free paths are either comparable to or larger than the size of the heliosphere, the neutral phase space distribution can deviate far away from the Maxwellian distribution. A kinetic description for the neutrals is crucial for accurately modeling the heliosphere. It is computationally challenging to run three-dimensional time-dependent kinetic simulations due to the large number of macroparticles. In this paper, we present the new highly efficient Solar Wind with Hydrogen Ion Exchange and Large-scale Dynamics-2 model with a kinetic model of neutrals and a magnetohydrodynamic model for the ions and electrons. To improve the simulation efficiency, we implement adaptive mesh refinement and particle splitting and merging algorithms for the neutral particles to reduce the particle number that is required for an accurate simulation. We present several tests to verify and demonstrate the capabilities of the model.

Hierarchical Heuristic Species Delimitation under the Multispecies Coalescent Model with Migration.

The multispecies coalescent (MSC) model accommodates genealogical fluctuations across the genome and provides a natural framework for comparative analysis of genomic sequence data from closely related species to infer the history of species divergence and gene flow. Given a set of populations, hypotheses of species delimitation (and species phylogeny) may be formulated as instances of MSC models (e.g., MSC for one species versus MSC for two species) and compared using Bayesian model selection. This approach, implemented in the program bpp, has been found to be prone to over-splitting. Alternatively heuristic criteria based on population parameters (such as popula- tion split times, population sizes, and migration rates) estimated from genomic data may be used to delimit species. Here we develop hierarchical merge and split algorithms for heuristic species delimitation based on the genealogical divergence index (𝑔𝑑𝑖) and implement them in a python pipeline called hhsd. We characterize the behavior of the 𝑔𝑑𝑖 under a few simple scenarios of gene flow. We apply the new approaches to a dataset simulated under a model of isolation by distance as well as three empirical datasets. Our tests suggest that the new approaches produced sensible results and were less prone to over-splitting. We discuss possible strategies for accommodating paraphyletic species in the hierarchical algorithm, as well as the challenges of species delimitation based on heuristic criteria.

Research on multi-source sparse optimization method and its application on gearbox compound fault detection

In general, gearbox is prone to occur compound fault frequently because of its harsh working environment, its fault vibration signal often contains polymorphic-oscillatory components and is corrupted by heavy background noise, which brings great difficulty to diagnose fault. Sparse decomposition is often utilized to extract weak fault feature among heavy background noise. In order to solve the problems of traditional sparse decomposition method, such as lacking signal fidelity, causing local optimal solution by using the non-convex objective function, and presenting poor universality, a multi-source sparse optimization objective function with convexity is constructed based on the generalized mini-max concave penalty function. By using forward–backward splitting algorithm combination with Laplace wavelet dictionary, Morlet wavelet dictionary and DFT dictionary, the sparse coefficients corresponding to polymorphic-oscillatory components can be computed efficiently and each oscillatory component can be extracted accurately. Finally, simulation and experimental signal validate that the proposed method can decompose fault signal according to oscillatory property and diagnose gearbox compound fault without the prior knowledge of specific fault numbers.

Outer reflected forward–backward splitting algorithm with inertial extrapolation step

ABSTRACT This paper studies an outer reflected forward–backward splitting algorithm with an inertial step to find a zero of the sum of three monotone operators composing the maximal monotone operator, Lipschitz monotone operator, and a cocoercive operator in real Hilbert spaces. One of the interesting features of the proposed method is that both the Lipschitz monotone operator and the cocoercive operator are computed explicitly each with one evaluation per iteration. We obtain weak and strong convergence results under some easy-to-verify assumptions. We also obtain a non-asymptotic O ( 1 / n ) convergence rate of our proposed algorithm in a non-ergodic sense. We finally give some numerical illustrations arising from compressed sensing and image processing and show that our proposed method is effective and competitive with other related methods in the literature.

Novel algorithms based on forward-backward splitting technique: effective methods for regression and classification

In this paper, we introduce two novel forward-backward splitting algorithms (FBSAs) for nonsmooth convex minimization. We provide a thorough convergence analysis, emphasizing the new algorithms and contrasting them with existing ones. Our findings are validated through a numerical example. The practical utility of these algorithms in real-world applications, including machine learning for tasks such as classification, regression, and image deblurring reveal that these algorithms consistently approach optimal solutions with fewer iterations, highlighting their efficiency in real-world scenarios.

Enhancing Groundwater Quality Evaluation Using Associative Rule Mining Technique with Random Forest Split Gini Indexing Algorithm for Nitrate Concentration Analysis

Human actions and changing weather patterns are contributing to the growing demand for groundwater resources. Nevertheless, evaluating the quality of groundwater is crucial. Nitrate is a significant water contaminant that can lead to blue-baby syndrome or methemoglobinemia. Therefore, it is necessary to assess the level of nitrate in groundwater. Current methods involve evaluating the quality of groundwater and integrating it into the models. The inappropriate datasets, lack of performance, and other constraints are limitations of current methods. Ground water dataset is used and pre-processed the data’s. Selected data’s are feature extracted and associated with the rule ranking. In the suggested model, the use of associative rule mining technique has been implemented to address these challenges and assess nitrate levels in groundwater. The method of rule ranking is carried out using association rule mining technique to divide the datasets. The split gini indexing algorithm is introduced in the proposed model for data classification. The Split Gini Indexing algorithm is a decision tree induction algorithm that is used to build decision trees for classification tasks. It is based on the Gini impurity measure, which measures the heterogeneity of a dataset. The quality of groundwater has been classified using Naïve Bayes, SVM, and KNN algorithms. The proposed approach's efficiency is evaluated by calculating performance metrics such as precision, accuracy, F1-score, and recall values. The suggested method in the current research attains an improved accuracy of 0.99, demonstrating enhanced performance.

Assessing the Impact of Land Use and Land Cover Changes on Surface Temperature Dynamics Using Google Earth Engine: A Case Study of Tlemcen Municipality, Northwestern Algeria (1989–2019)

Changes in land use and land cover (LULC) have a significant impact on urban planning and environmental dynamics, especially in regions experiencing rapid urbanization. In this context, by leveraging the Google Earth Engine (GEE), this study evaluates the effects of land use and land cover modifications on surface temperature in a semi-arid zone of northwestern Algeria between 1989 and 2019. Through the analysis of Landsat images on GEE, indices such as normalized difference vegetation index (NDVI), normalized difference built-up index (NDBI), and normalized difference latent heat index (NDLI) were extracted, and the random forest and split window algorithms were used for supervised classification and surface temperature estimation. The multi-index approach combining the Normalized Difference Tillage Index (NDTI), NDBI, and NDVI resulted in kappa coefficients ranging from 0.96 to 0.98. The spatial and temporal analysis of surface temperature revealed an increase of 4 to 6 degrees across the four classes (urban, barren land, vegetation, and forest). The Google Earth Engine approach facilitated detailed spatial and temporal analysis, aiding in understanding surface temperature evolution at various scales. This ability to conduct large-scale and long-term analysis is essential for understanding trends and impacts of land use changes at regional and global levels.

Modified splitting algorithms for approximating solutions of split variational inclusions in Hilbert spaces

Modified splitting algorithms for approximating solutions of split variational inclusions in Hilbert spaces