Hierarchical Partitioning Strategy Research Articles

A hierarchical data partitioning strategy for irregular applications: a case study in digital pathology

A hierarchical data partitioning strategy for irregular applications: a case study in digital pathology

Fuzzy machine learning predictions of settling velocity based on fractal aggregate physical features in water treatment

The dynamics of gravitational sedimentation in water treatment are crucial for optimising particulate matter removal. This study addresses the effect of fractal aggregate features on settling velocity and explores fuzzy machine learning (ML) for predicting this phenomenon. Particle image velocimetry determined aggregate velocities within a sedimentation column, with features identified concurrently. Using a comprehensive methodological framework, significant predictors were selected through various statistical analyses. The fuzzy ML model, developed with the ‘FisPro’ package in R, incorporated a hierarchical partitioning scheme using Lukasiewicz and Sum operators for conjunction and disjunction processes, respectively. The Wang-Mendel method extracted fuzzy rules, with defuzzification achieved using the maximum crisp operator. Hyperparameter optimization was conducted through grid search techniques, and model performance was evaluated using 3-fold cross-validation. The findings reveal that Margination, Radius, and Clumpiness significantly impact settling velocity. The model demonstrates exceptional predictive accuracy (R2 = 0.923) across both training and validation datasets, highlighting its potential for forecasting terminal velocity in water treatment. This research suggests that precise predictions of sedimentation dynamics can improve particulate matter removal efficiency and encourages further investigations into diverse aggregate types and environmental scenarios, advocating for integrating physics-informed ML approaches to enhance the model.

Data-based equations for damage evaluation of reinforced concrete columns with square cross sections

This study aims to develop simple equations for assessing the damage of reinforced concrete (RC) columns subjected to seismic loading. A fiber element model in OpenSees, validated against experimental data, was used to generate a large dataset of 56548 data values for various RC columns. The Monte Carlo Hierarchical Adaptive Random Partitioning (MC-HARP) strategy was then applied to evaluate the sufficiency of the dataset and propose reliable equations for estimating the residual displacement ratio (RDR), damage index (DI), and residual curvature of RC columns under given displacement demands. A relationship between these parameters and the structural performance levels was also established. Residual displacement is a practical measure that can be observed in the field after an earthquake. The proposed equations facilitate the determination of the performance level of the structure after an earthquake event. The findings of this paper can also be used in designing new structures within a performance-based seismic design (PBSD) context.

An enhanced method for improving the accuracy of small failure probability of structures

This paper presents a hierarchical partitioning strategy (HP) for probability space to improve the accuracy of metamodel and avoid the memory problems of computer in dealing with small failure probability events. By the continuous partition of probability space, the construction of adaptive Kriging metamodel is intelligently divided into two steps. Thereafter, the well-trained Kriging via two steps is used to approximate the relationship between the extreme value of response and basic random variables of the system. By combining the probability density evolution method with well-trained Kriging metamodel, the reliability of the investigated stochastic system can be readily obtained with a one-dimensional integration operation. Subsequently, a new reliability analysis method is proposed, called HP-AK-PDEM (Hierarchical Partitioning strategy-based Adaptive Kriging combining Probability Density Evolution Method). To demonstrate the accuracy and efficiency of the proposed method, three analytical performance functions with nonlinear features and a ten-story shear-frame structure are addressed. The comparative study of different reliability methods is carried out as well. Numerical results demonstrate that the presented method has better accuracy and higher efficiency in dealing with the problems of small and rare failure probability issues encountered in engineering structures.

Accelerating Stochastic Gradient Descent Based Matrix Factorization on FPGA

Matrix Factorization (MF) based on Stochastic Gradient Descent (SGD) is a powerful machine learning technique to derive hidden features of objects from observations. In this article, we design a highly parallel architecture based on Field-Programmable Gate Array (FPGA) to accelerate the training process of the SGD-based MF algorithm. We identify the challenges for the acceleration and propose novel algorithmic optimizations to overcome them. By transforming the SGD-based MF algorithm into a bipartite graph processing problem, we propose a 3-level hierarchical partitioning scheme that enables conflict-minimizing scheduling and processing of edges to achieve significant speedup. First, we develop a fast heuristic graph partitioning approach to partition the bipartite graph into induced subgraphs; this enables to efficiently use the on-chip memory resources of FPGA for data reuse and completely hide the data communication between FPGA and external memory. Second, we partition all the edges of each subgraph into non-overlapping matchings to extract the maximum parallelism. Third, we propose a batching algorithm to schedule the execution of the edges inside each matching to reduce the memory access conflicts to the on-chip RAMs of FPGA. Compared with non-optimized FPGA-based baseline designs, the proposed optimizations result in up to 60× data dependency reduction, 4.2× bank conflict reduction, and 15.4× speedup. We evaluate the performance of our design using a state-of-the-art FPGA device. Experimental results show that our FPGA accelerator sustains a high computing throughput of up to 217 billion floating-point operations per second (GFLOPS) for training very large real-life sparse matrices. Compared with highly-optimized GPU-based accelerators, our FPGA accelerator achieves up to 12.7× speedup. Based on our optimization methodology, we also implement a software-based design on a multi-core platform, which demonstrates 1.3× speedup compared with the state-of-the-art multi-core implementation.

A Ternary Parallelization Approach of MLFMA for Solving Electromagnetic Scattering Problems With Over 10 Billion Unknowns

In this paper, we present a flexible and efficient ternary parallelization approach for the multilevel fast multipole algorithm (MLFMA) for the solution of extremely large 3-D scattering problems with over 10 billion unknowns. In the ternary parallelization approach, a binary clustering tree of all the message passing interface (MPI) processes is built first. Then, the MLFMA tree is categorized into plane wave partitioning, hierarchical-structure partitioning, and box partitioning (BP) levels via a top–down approach to match the process clustering tree. Compared with the bottom–up approach, interprocess communications in the far interaction are reduced. An inner-group transition level is designed for switching partitions on the intermediate level between the hierarchical-structure partitioning and BP levels. The ternary strategy can realize as high parallel efficiency as the hierarchical partitioning strategy while maintaining flexibility in selecting the total number of processes. An auxiliary-tree-based parallel mesh refinement technique and a hybrid octree storage strategy are designed to facilitate the realization of fast full-wave simulation on a scale of over 10 billion unknowns with the ternary MLFMA. The accuracy of the solutions is validated by comparing the radar cross sections (RCSs) of a sphere of diameter 3042 wavelengths with 10 773 415 728 unknowns via the MLFMA and the Mie series, which is the largest number of unknowns to be computed via full wave numerical methods to date. Furthermore, the solutions for complicated objects, namely a ship and an aircraft model, both of which have maximum lengths that exceed 10 000 wavelengths and over 10 billion unknowns, are presented.

Adaptive Inter CU Depth Decision for HEVC Using Optimal Selection Model and Encoding Parameters

High efficiency video coding adopts a new hierarchical coding structure, including coding unit (CU), prediction unit (PU), and transform unit to achieve higher coding efficiency than its predecessor H.264/AVC high profile. However, its hierarchical unit partitioning strategy leads to huge computational complexity. In this paper, an adaptive inter CU depth decision algorithm is proposed, which exploits both temporal correlation of CU depth and available encoding parameters. An optimal selection model of CU depth is established to estimate the range of candidate CU depth by exploiting the temporal correlation of CU depth among current CU and temporally co-located CUs. To reduce the accumulated errors in the process of CU depth prediction, the maximum depth of the co-located CUs and the coded block flag (CBF) of the current CU are used. Moreover, PU size and CBF information are also used to decide the maximum depth for the current CU. Experimental results show that the proposed CU depth decision approach reduces 56.3% and 51.5% average encoding time, and the Bjontegaard delta bit rate increases only 1.3% and 1.1% for various test sequences under the random access and the low delay B conditions, respectively.

A multi-level clustering scheme based on cliques and clusters for wireless sensor networks

Wireless sensor networks (WSNs) have a wide range of applications in our lifetime. Indeed, WSNs perform a various missions and tasks in odor localization, firefighting, medical service, surveillance and security. In order to accomplish these tasks, the sensors have to perform partitioning protocols to form an organization into clusters and cliques. The hierarchical clustering is the key solution for WSNs to deal with the scalability problems in a network composed of millions of nodes. In this paper, a new hierarchical partitioning scheme is presented, named MCCC. It is cliques and clusters based hierarchical scheme that takes into account the size of cliques and clusters, it also minimizes the number of hops between the cluster head and its nodes. The proposed scheme is motivated by the need to have minimum and maximum size for cliques and clusters. This hierarchical scheme is proposed to respond to the energy and memory constraints for WSNs.

Exploiting FPGA-Aware Merging of Custom Instructions for Runtime Reconfiguration

Runtime reconfiguration is a promising solution for reducing hardware cost in embedded systems, without compromising on performance. We present a framework that aims to increase the performance benefits of reconfigurable processors that support full or partial runtime reconfiguration. The proposed framework achieves this by: (1) providing a means for choosing suitable custom instruction selection heuristics, (2) leveraging FPGA-aware merging of custom instructions to maximize the reconfigurable logic block utilization in each configuration, and (3) incorporating a hierarchical loop partitioning strategy to reduce runtime reconfiguration overhead. We show that the performance gain can be improved by employing suitable custom instruction selection heuristics that, in turn, depend on the reconfigurable resource constraints and the merging factor (extent to which the selected custom instructions can be merged). The hierarchical loop partitioning strategy leads to an average performance gain of over 31% and 46% for full and partial runtime reconfiguration, respectively. Performance gain can be further increased to over 52% and 70% for full and partial runtime reconfiguration, respectively, by exploiting FPGA-aware merging of custom instructions.

Hierarchical parallelization of the multilevel fast multipole algorithm (MLFMA)

Due to its O(N log N) complexity, the multilevel fast multipole algorithm (MLFMA) is one of the most prized algorithms of computational electromagnetics and certain other disciplines. Various implementations of this algorithm have been used for rigorous solutions of large-scale scattering, radiation, and miscellaneous other electromagnetics problems involving 3-D objects with arbitrary geometries. Parallelization of MLFMA is crucial for solving real-life problems discretized with hundreds of millions of unknowns. This paper presents the hierarchical partitioning strategy, which provides a very efficient parallelization of MLFMA on distributed-memory architectures. We discuss the advantages of the hierarchical strategy over previous approaches and demonstrate the improved efficiency on scattering problems discretized with millions of unknowns.

Solutions of large-scale electromagnetics problems involving dielectric objects with the parallel multilevel fast multipole algorithm

Fast and accurate solutions of large-scale electromagnetics problems involving homogeneous dielectric objects are considered. Problems are formulated with the electric and magnetic current combined-field integral equation and discretized with the Rao-Wilton-Glisson functions. Solutions are performed iteratively by using the multilevel fast multipole algorithm (MLFMA). For the solution of large-scale problems discretized with millions of unknowns, MLFMA is parallelized on distributed-memory architectures using a rigorous technique, namely, the hierarchical partitioning strategy. Efficiency and accuracy of the developed implementation are demonstrated on very large problems involving as many as 100 million unknowns.

PARALLEL IMPLEMENTATION OF MLFMA FOR HOMOGENEOUS OBJECTS WITH VARIOUS MATERIAL PROPERTIES

We present a parallel implementation of the multilevel fast multipole algorithm (MLFMA) for fast and accurate solutions of electromagnetics problems involving homogeneous objects with diverse material properties. Problems are formulated rigorously with the electric and magnetic current combined-field integral equation (JMCFIE) and solved iteratively using MLFMA parallelized with the hierarchical partitioning strategy. Accuracy and efficiency of the resulting implementation are demonstrated on canonical problems involving perfectly conducting, lossless dielectric, lossy dielectric, and double-negative spheres.

A Hierarchical Partitioning Strategy for an Efficient Parallelization of the Multilevel Fast Multipole Algorithm

We present a novel hierarchical partitioning strategy for the efficient parallelization of the multilevel fast multipole algorithm (MLFMA) on distributed-memory architectures to solve large-scale problems in electromagnetics. Unlike previous parallelization techniques, the tree structure of MLFMA is distributed among processors by partitioning both clusters and samples of fields at each level. Due to the improved load-balancing, the hierarchical strategy offers a higher parallelization efficiency than previous approaches, especially when the number of processors is large. We demonstrate the improved efficiency on scattering problems discretized with millions of unknowns. In addition, we present the effectiveness of our algorithm by solving very large scattering problems involving a conducting sphere of radius 210 wavelengths and a complicated real-life target with a maximum dimension of 880 wavelengths. Both of the objects are discretized with more than 200 million unknowns.

Provably scalable parallel multilevel fast multipole algorithm

In the parallel multilevel fast multipole algorithm (MLFMA), there exist two fundamental partitioning schemes for the distribution of the workload across processors: the spatial distribution of boxes and the spectral distribution of field samples. These two schemes can be combined in various manners. It is analytically and numerically shown that, in two dimensions, the recently introduced hierarchical approach yields a scalable parallel MLFMA. For the three-dimensional case, it is proved that only the combination of the hierarchical partitioning scheme and a two‐dimensional partitioning of the field samples leads to a scalable algorithm.

Modular construction of model partitioning processes for parallel logic simulation

Logic simulation of complex VLSI models is very time consuming. Simulation speed can be increased by model partitioning and assigning the resulting parts to simulator instances which cooperate over a loosely coupled system. We have developed a distributed framework, parallelMAP, that implements a hierarchical model partitioning strategy. It can serve both as production environment in VLSI design and as an experimental test bed for algorithm development. In this paper, we describe the possibilities that parallelMAP offers for the modular construction of partitioning processes, starting from basic sequential and parallel modules. Experimental experiences refer to IBM processor models comprising from 1.5 x 105 to 2.5 x 106 elements at gate level.

Greedy mixture learning for multiple motif discovery in biological sequences

This paper studies the problem of discovering subsequences, known as motifs, that are common to a given collection of related biosequences, by proposing a greedy algorithm for learning a mixture of motifs model through likelihood maximization. The approach adds sequentially a new motif to a mixture model by performing a combined scheme of global and local search for appropriately initializing its parameters. In addition, a hierarchical partitioning scheme based on kd-trees is presented for partitioning the input dataset in order to speed-up the global searching procedure. The proposed method compares favorably over the well-known MEME approach and treats successfully several drawbacks of MEME. Experimental results indicate that the algorithm is advantageous in identifying larger groups of motifs characteristic of biological families with significant conservation. In addition, it offers better diagnostic capabilities by building more powerful statistical motif-models with improved classification accuracy.

Hierarchical strategy of model partitioning for VLSI-design using an improved mixture of experts approach

The partitioning of complex processor models on the gate and register-transfer level for parallel functional simulation based on the clock-cycle algorithm is considered. We introduce a hierarchical partitioning scheme combining various partitioning algorithms in the frame of a competing strategy. Melting together different partitioning results within one level using superpositions we crossover to a mixture of experts one. This approach is improved applying genetic algorithms. In addition we present two new partitioning algorithms both of them taking cones as fundamental units for building partitions.

A partitioning strategy for efficient nonlinear finite element dynamic analysis on multiprocessor computers

A computational procedure is presented for the nonlinear dynamic analysis of unsymmetric structures on vector multiprocessor systems. The procedure is based on a novel hierarchical partitioning strategy in which the response of the unsymmetric structure at any time instant is approximated by a linear combination of symmetric and antisymmetric response vectors (or modes), each obtained by using only a fraction of the degrees of freedom of the original finite element model. The three key elements of the procedure which result in high degree of concurrency throughout the solution process are: (a) mixed (or primitive variable) formulation with independent shape functions for the different fields; (b) operator splitting or restructuring of the discrete equations at each time step to delineate the symmetric and antisymmetric vectors constituting the response, and (c) two-level iterative process for generating the response of the structure. An assessment is made of the effectiveness of the procedure on the CRAY X-MP/4 computers.