Quality Of Partitions Research Articles

Data-Driven Dynamic Security Partition Assessment of Power Systems Based on Symmetric Electrical Distance Matrix and Chebyshev Distance

A rapid dynamic security assessment (DSA) is crucial for online preventive and restoration decision-making. The deep learning-based DSA models have high efficiency and accuracy. However, the complex model structure and high training cost make them hard to update quickly. This paper proposes a dynamic security partition assessment method, aiming to develop accurate and incrementally updated DSA models with simple structures. Firstly, the power grid is self-adaptively partitioned into several local regions based on the mean shift algorithm. The input of the mean shift algorithm is a symmetric electrical distance matrix, and the distance metric is the Chebyshev distance. Secondly, high-level features of operating conditions are extracted based on the stacked denoising autoencoder. The symmetric electrical distance matrix is modified to represent fault locations in local regions. Finally, DSA models are constructed for fault locations in each region based on the radial basis function neural network (RBFNN) and Chebyshev distance. An online incremental updating strategy is designed to enhance the model adaptability. With the simulation software PSS/E 33.4.0, the proposed dynamic security partition assessment method is verified in a simplified provincial system and a large-scale practical system in China. Test results demonstrate that the Chebyshev distance can improve the partition quality of the mean shift algorithm by approximately 50%. The RBFNN-based partition assessment model achieves an accuracy of 98.96%, which is higher than the unified assessment with complex models. The proposed incremental updating strategy achieves an accuracy of over 98% and shortens the updating time to 30 s, which can meet the efficiency of online application.

Solving the Problem of Fuzzy Partition-Distribution with Determination of the Location of Subset Centers

A large number of real-world problems from various fields of human activity can be reduced to optimal partitioning-allocation problems with the purpose of minimizing the partitioning quality criterion. A typical representative of such problem is an infinite-dimensional transportation problem and more generalized problems—infinite-dimensional problems of production centers placement along with the partitioning of the area of continuously distributed consumers with the purpose of minimizing transportation and production costs. The relevant problems are characterized by some kind of uncertainty level of a not-probabilistic nature. A method is proposed to solve an optimal fuzzy partitioning-allocation problem with the subsets centers placement for sets of n-dimensional Euclidean space. The method is based on the synthesis of the methods of fuzzy theory and optimal partitioning-allocation theory, which is a new science field in infinite-dimensional mathematical programming with Boolean variables. A theorem was proved that determines the form of the optimal solution of the corresponding optimal fuzzy partitioning-allocation problem with the subsets centers placement for sets of n-dimensional Euclidean space. An algorithm for solving fuzzy partitioning-allocation problems is proposed, which is based on the proved theorem and on a variant of Shor’s r-algorithm—a non-differential optimization method. The application of the proposed method is demonstrated on model tasks, where the coefficient of mistrust is integrated to interpret the obtained result—the minimum value of the membership function, which allows each point of the set partition to be assigned to a specific fuzzy subset.

An end-to-end bi-objective approach to deep graph partitioning

Graphs are ubiquitous in real-world applications, such as computation graphs and social networks. Partitioning large graphs into smaller, balanced partitions is often essential, with the bi-objective graph partitioning problem aiming to minimize both the “cut” across partitions and the imbalance in partition sizes. However, existing heuristic methods face scalability challenges or overlook partition balance, leading to suboptimal results. Recent deep learning approaches, while promising, typically focus only on node-level features and lack a truly end-to-end framework, resulting in limited performance. In this paper, we introduce a novel method based on graph neural networks (GNNs) that leverages multilevel graph features and addresses the problem end-to-end through a bi-objective formulation. Our approach explores node-, local-, and global-level features, and introduces a well-bounded bi-objective function that minimizes the cut while ensuring partition-wise balance across all partitions. Additionally, we propose a GNN-based deep model incorporating a Hardmax operator, allowing the model to optimize partitions in a fully end-to-end manner. Experimental results on 12 datasets across various applications and scales demonstrate that our method significantly improves both partitioning quality and scalability compared to existing bi-objective and deep graph partitioning baselines.

Overlapping Structure Detection in Protein-Protein Interaction Networks Using a Modified Version of Particle Swarm Optimization

In today's world, the science of bioinformatics is developing rapidly, especially with regard to the analysis and study of biological networks. Scientists have used various nature-inspired algorithms to find protein complexes in protein-protein interaction (PPI) networks. These networks help scientists guess the molecular function of unknown proteins and show how cells work regularly. It is very common in PPI networks for a protein to participate in multiple functions and belong to many complexes, and as a result, complexes may overlap in the PPI networks. However, developing an efficient and reliable method to address the problem of detecting overlapping protein complexes remains a challenge since it is considered a complex and hard optimization problem. One of the main difficulties in identifying overlapping protein complexes is the accuracy of the partitioning results. In order to accurately identify the overlapping structure of protein complexes, this paper has proposed an overlapping complex detection algorithm termed OCDPSO-Net, which is based on PSO-Net (a well-known modified version of the particle swarm optimization algorithm). The framework of the OCDPSO-Net method consists of three main steps, including an initialization strategy, a movement strategy for each particle, and enhancing search ability in order to expand the solution space. The proposed algorithm has employed the partition density concept for measuring the partitioning quality in PPI network complexes and tried to optimize the value of this quantity by applying the line graph concept of the original graph representing the protein interaction network. The OCDPSO-Net algorithm is applied to a Collins PPI network and the obtained results are compared with different state-of-the-art algorithms in terms of precision ( ), recall ( ), and F-measure ( ). Experimental results confirm that the proposed algorithm has good clustering performance and has outperformed most of the existing recent overlapping algorithms. .

FSM: A Fine-Grained Splitting and Merging Framework for Dual-Balanced Graph Partition

Partitioning a large graph into smaller subgraphs by minimizing the number of cutting vertices and edges, namely cut size or replication factor, plays a crucial role in distributed graph processing tasks. However, many prior works have primarily focused on optimizing the cut size by considering only vertex balance or edge balance, leading to significant workload imbalance and consequently hindering the performance of downstream tasks. Therefore, in this paper, we address the dual-balanced graph partition problem that minimizes the cut size while simultaneously guaranteeing both vertex and edge balance. We propose a lightweight effective two-phase framework, namely fine-grained splitting and merging (FSM), which decomposes the graph into more and smaller partitions and then merges them. FSM offers the flexibility of integrating with various state-of-the-art single-balanced techniques. We develop two efficient algorithms Fast Merging and Precise Merging to enable trade-offs between computational efficiency and partitioning quality. Experimental results on large real-world graphs demonstrate that FSM achieves state-of-the-art cut size while maintaining dual balance. The runtime for downstream tasks PageRank, connected component, and diameter estimation, can be reduced by a large proportion, up to 9.43%, 11.35%, and 17.94%, respectively.

Social Media WebApp “TweetSphere”

The paper presents a novel approach to addressing the challenges of multiuser operations in Twitter by focusing on the expense of queries and the existing solutions for data partitioning. It introduces a method for reducing server interaction by partitioning data based on user interactions and implementing selective replication for frequently requested user data. This approach significantly improves partition quality, especially with low replication ratios. Additionally, the paper delves into the issue of Twitter spammers and their evolving tactics, proposing new detection features to combat spam accounts. It also explores the detection of duplicate fake accounts on Twitter using feature based analysis and machine learning techniques, with SVM demonstrating the best performance at 93.3% accuracy

LocalTGEP: A Lightweight Edge Partitioner for Time-Varying Graph

Graph edge partitioning (GEP), the allocation of edges into different parts through cut vertices, is essential for the analytics of large-scale graphs. Most GEP models cannot be directly applied to a time-varying graph unless repartitioning the entire graph, which leads to a large consumption of resources. Although a few studies have focused on time-varying graph edge partitioning, they have ignored the memory consumption during the partitioning process. Therefore, a lightweight edge partitioner, referred to as LocalTGEP, broadening the application to time-varying graphs, is proposed herein. Three superiorities of LocalTGEP are highlighted as follows: 1) A satisfactory partitioning quality for a time-varying graph can be achieved without requiring global information owing to the local edge partitioning. 2) Memory consumption of the partitioner is significantly reduced using a novel storage framework of graph data in LocalTGEP. 3) The quality and efficiency of time-varying graph edge partitioning are optimized by designing the push and pop stages in LocalTGEP. Extensive experimental results obtained on 12 real-world graphs demonstrate that LocalTGEP outperforms rival algorithms in terms of memory consumption, partitioning quality, and efficiency.

Group Dynamics in Memory-Enhanced Ant Colonies: The Influence of Colony Division on a Maze Navigation Problem

This paper introduces an agent-based model grounded in the ACO algorithm to investigate the impact of partitioning ant colonies on algorithmic performance. The exploration focuses on understanding the roles of group size and number within a multi-objective optimization context. The model consists of a colony of memory-enhanced ants (ME-ANTS) which, starting from a given position, must collaboratively discover the optimal path to the exit point within a grid network. The colony can be divided into groups of different sizes and its objectives are maximizing the number of ants that exit the grid while minimizing path costs. Three distinct analyses were conducted: an overall analysis assessing colony performance across different-sized groups, a group analysis examining the performance of each partitioned group, and a pheromone distribution analysis discerning correlations between temporal pheromone distribution and ant navigation. From the results, a dynamic correlation emerged between the degree of colony partitioning and solution quality within the ACO algorithm framework.

DEGENERATION ESTIMATION OF A TETRAHEDRAL IN A TETRAHEDRAL PARTITION OF THE THREE-DIMENSIONAL SPACE

Based on the geometric characteristics of the tetrahedron, quantitative estimates of its degeneracy are proposed and their relationship with the condition number of local bases generated by the edges emerging from the same vertex is established. The concept of the tetrahedron degeneracy index is introduced in several versions and their practical equivalence to each other is established. To assess the quality of a particular tetrahedral partition, it is proposed to calculate the empirical distribution function of the degeneracy index on its tetrahedral elements. A model irregular triangulation (tetrahedralization or tetrahedral partition) of three-dimensional space is proposed, depending on the control parameter that determines the quality of its elements. The coordinates of the tetrahedra vertices of the model triangulation tetrahedrons are the sums of the corresponding coordinates of the nodes of some given regular grid and random increments to them. For various values of the control parameter, the empirical distribution function of the tetrahedron degeneration index is calculated, which is considered as a quantitative characteristic of the quality of tetrahedra in the triangulation of a three-dimensional region.

Generalized Ordered Intuitionistic Fuzzy C-Means Clustering Algorithm Based on PROMETHEE and Intuitionistic Fuzzy C-Means

The problem of ordered clustering in the context of decision-making with multiple criteria has garnered significant interest from researchers in the field of management science and operational research. In real-world scenarios, the datasets often exhibit imprecision or uncertainty, which can lead to suboptimal ordered-clustering outcomes. However, the intuitionistic fuzzy c-means (IFCM) clustering algorithm enhances the accuracy and effectiveness of decision-making processes by effectively handling uncertain dataset information for clustering. Therefore, we propose a new clustering algorithm, called the generalized ordered intuitionistic fuzzy c-means (G-OIFCM), based on PROMETHEE and the IFCM clustering algorithm. Different from the classical IFCM clustering algorithm, we use positive flow ( φ + s i ∈ 0 , 1 ) and negative flow ( φ − s i ∈ 0 , 1 ) of PROMETHEE to generate ordered clusters within the intuitionistic environment. We define a new objective function based on the positive and negative flow of the PROMETHEE and IFCM clustering algorithm, whose properties are mathematically justified in terms of convergence and optimization. The performance of the proposed algorithm is evaluated using two different real-world datasets to assess both the ordered clustering and the quality of partitioning. To demonstrate the effectiveness of G-OIFCM, a comparison is conducted with three other algorithms: fuzzy c-means (FCM), ordered fuzzy c-means (OFCM), and an adaptive generalized intuitionistic fuzzy c-means (G-IFCM). The results demonstrate the effectiveness of G-OIFCM in enhancing optimal ordered clustering and utility when dealing with uncertainty in datasets.

Uncertainty clustering internal validity assessment using Fréchet distance for unsupervised learning

Knowing the number of clusters a priori is one of the most challenging aspects of unsupervised learning. Clustering Internal Validity Indices (CIVIs) evaluate partitions in unsupervised algorithms based on metrics like compactness, separation, and density. However, specialized CIVIs for specific applications have been designed, and there is no general CIVI that works in all scenarios. The absence of CIVIs based on crisp uncertainty metrics is especially critical in decision-making processes that involve ambiguity, non-convex distributions, outliers, and overlapping data. To address this problem, we propose a novel Uncertainty Fréchet (UF) CIVI that assesses the certainty of a well-defined partition. UF leverages uncertainty fingerprints based on Type-2 fuzzy Gaussian Mixture Models (T2FGMM) and the Fréchet distance between clusters to introduce a metric that evaluates partition quality. We integrate UF into a merging methodology that combines similar clusters within a partition, allowing us to determine the number of clusters without the need to run the clustering algorithms iteratively as other CIVIs require. We undertake a comprehensive evaluation of our proposal on 5,250 convex, 36 non-convex synthetic datasets, and five benchmark real datasets. In addition, we apply UF in a real-world scenario that involves high uncertainty: Passive Acoustic Monitoring (PAM) of ecosystems, which aims to study ecological transformations through acoustic recordings. The results show that UF exhibits notable performance in synthetic and real-world scenarios, obtaining an Adjusted Mutual Information (AMI) score higher than 0.88 for normal, uniform, gamma, and triangular distribution datasets. In the PAM application, UF identifies the transformation of ecosystems through sound using clustering algorithms and UF, achieving an F1 score of 0.84. Therefore, results show that the UF index is a suitable tool for researchers and practitioners working with highly uncertain data.

Tinba: Incremental partitioning for efficient trajectory analytics

Applications with mobile and sensing devices have already become ubiquitous. In most of these applications, trajectory data is continuously growing to huge volumes. Existing systems for big trajectory data organize trajectories at distributed block storage systems. Systems like DITA that use block storage (e.g., 128 MB each) are more efficient for analytical queries, but they cannot incrementally maintain the partitioned data and do not support delete operations, resulting in difficulties in trajectory analytics. In this paper, we propose an incremental trajectory partitioning framework Tinba that enables distributed block storage systems to efficiently maintain optimized partitions under incremental updates of trajectories. We employ a data flushing technique to bulk ingest trajectory data for random writing in distributed file system (DFS). We recast the incremental partitioning problem as an optimal partitioning problem and prove its NP-hardness. A cost–benefit model is proposed to address the optimal partitioning problem. Moreover, Tinba supports most of the existing similarity measures to quantify the similarity between trajectories. A heuristic is developed to instantiate the Tinba framework. Comprehensive experiments on real-world and synthetic datasets demonstrate the advancements in ingestion performance and partition quality, as opposed to other trajectory partition methods.

Clustering Graphs for GPU Processing

This article discusses the multilevel clustering of graphs used for data processing in the GPU. The quality of graph partitioning can have a significant impact on the overall performance of the software. Therefore, it is very important to quickly find the correct partition of the graph into subgraphs. The article describes the application areas of clustering, features and types of clustering, and also draws conclusions about the relevance of using graph clustering in modern spheres of human activity.

Affective Neural Responses Sonified through Labeled Correlation Alignment

Sound synthesis refers to the creation of original acoustic signals with broad applications in artistic innovation, such as music creation for games and videos. Nonetheless, machine learning architectures face numerous challenges when learning musical structures from arbitrary corpora. This issue involves adapting patterns borrowed from other contexts to a concrete composition objective. Using Labeled Correlation Alignment (LCA), we propose an approach to sonify neural responses to affective music-listening data, identifying the brain features that are most congruent with the simultaneously extracted auditory features. For dealing with inter/intra-subject variability, a combination of Phase Locking Value and Gaussian Functional Connectivity is employed. The proposed two-step LCA approach embraces a separate coupling stage of input features to a set of emotion label sets using Centered Kernel Alignment. This step is followed by canonical correlation analysis to select multimodal representations with higher relationships. LCA enables physiological explanation by adding a backward transformation to estimate the matching contribution of each extracted brain neural feature set. Correlation estimates and partition quality represent performance measures. The evaluation uses a Vector Quantized Variational AutoEncoder to create an acoustic envelope from the tested Affective Music-Listening database. Validation results demonstrate the ability of the developed LCA approach to generate low-level music based on neural activity elicited by emotions while maintaining the ability to distinguish between the acoustic outputs.

Influence of cutting time interval and season on productivity, nutrient partitioning, and forage quality of blue panicgrass (Panicum antidotale Retz.) under saline irrigation in Southern region of Morocco.

Salinity has become a major issue in various parts of the world negatively impacting agricultural activities and leading to diminished crop potential and lower yields. Such situation calls for urgent interventions such as adopting salt-tolerant crops to fill the gap in food and feed availability. Blue panicgrass (Panicum antidotale Retz.) is a promising salt-tolerant forage crop that has shown an appropriate adaptation and performance in the saline, arid, and desertic environments of southern Morocco. However, for obtaining a highest forage productivity with nutritional quality, optimization of the cutting interval is required. Thus, the objective of this study was to determine the optimal cutting time interval allowing high forage production and quality under high salinity conditions. This experiment was conducted over one entire year covering the summer and winter seasons. The effect of five cutting time intervals on selected agro-morphological traits, crop productivity, mineral nutrient accumulation, and forage quality of blue panicgrass in the region of Laayoune, southern Morocco. The finding of this study recommend that cutting blue panicgrass every 40 days maximized the annual fresh and dry forage yield as well as the protein yield, which reached 74, 22, and 2.9 t/ha, respectively. This study also revealed a significant effect of the season on both productivity and quality. However, forage yield declined during the winter and increased during the summer, while protein content increased during winter compared to summer. The mineral nutrient partitioning between shoots and roots, especially the K+/Na+ ratio, indicated that blue panicgrass has salt tolerance mechanism as it excluded sodium from the roots and compartmentalized it in the leaves. In conclusion, there is a potential of blue panicgrass on sustaining forage production under salt-affected drylands, as demonstrated by the response to two key questions: (a) a technical question to farmers for its adoption such as at which interval should blue panicgrass be harvested maximizing both forage yield and quality? And (b) a scientific question on how does blue panicgrass maintain high K+/Na+ ratio to cope with salinity stress?

The construction of blockchain platform for engineering museums based on vectorized image processing technology

Abstract The characteristics of blockchain such as tamper-evident and distributed can effectively solve the increasingly prominent security and privacy issues in engineering pavilions, however, the current throughput of mainstream blockchain platforms is far from meeting the demand for rapid chain-up of massive data in engineering pavilions, and the high redundancy storage mechanism adopted by traditional blockchain cannot be applied to engineering pavilion scenarios. To address the above problems, based on vectorized image processing technology, a hierarchical blockchain architecture is first proposed to store block data in multiple distributed cloud servers and edge servers in a hierarchical manner to cope with the growing data volume in the industrial Internet. Then based on the topology between edge servers, a blockchain network slicing algorithm is designed based on an improved complex network association partitioning algorithm, which improves the blockchain network throughput while shortening the slicing time. Finally, the impact of block broadcast time on throughput is demonstrated by formalizing the block broadcast process as a spanning tree, based on which a spanning tree-based intra-slice master node selection algorithm is proposed to further improve the throughput of the blockchain network. The analysis and experimental results show that the proposed scheme effectively reduces the partitioning time of the blockchain network and the broadcast time of the blocks within each partition. Compared with the classical association partitioning algorithm, this paper's partitioning algorithm can reduce the partitioning time by about 36% without sacrificing the quality of partitioning when partitioning a large-scale network.

A novel hierarchical aggregation algorithm for optimal repartitioning of statistical regions

Data regionalisation allows spatial inference over a population. The statistical regions must be updated to account for population changes, but this update process is more restrictive and iterative than ab initio regionalisation. This creates a need for an algorithmic solution that minimises human-in-the-loop involvement in population-driven regionalisation. The new method must address the basic regionalisation criteria – contiguity, compactness, homogeneity, equinumeriosity, and temporal consistency. We present a novel validation metric to assess the quality of partition based on these criteria. We have developed a novel hybrid aggregation algorithm (HeLP), combining elements of hierarchical and graph-theoretic approaches, for the primary purpose of repartitioning. This algorithm operates in average computational time complexity. HeLP was tested on simulated data and the Australian Statistical Geography Standard. The method can emulate the human operator successfully, providing statistically significant results in repartitioning parcel-based systems, such as the Cadastre.

Distributed Graph Embedding with Information-Oriented Random Walks

Graph embedding maps graph nodes to low-dimensional vectors, and is widely adopted in machine learning tasks. The increasing availability of billion-edge graphs underscores the importance of learning efficient and effective embeddings on large graphs, such as link prediction on Twitter with over one billion edges. Most existing graph embedding methods fall short of reaching high data scalability. In this paper, we present a general-purpose, distributed, information-centric random walk-based graph embedding framework, DistGER, which can scale to embed billion-edge graphs. DistGER incrementally computes information-centric random walks. It further leverages a multi-proximity-aware, streaming, parallel graph partitioning strategy, simultaneously achieving high local partition quality and excellent workload balancing across machines. DistGER also improves the distributed Skip-Gram learning model to generate node embeddings by optimizing the access locality, CPU throughput, and synchronization efficiency. Experiments on real-world graphs demonstrate that compared to state-of-the-art distributed graph embedding frameworks, including KnightKing, DistDGL, and Pytorch-BigGraph, DistGER exhibits 2.33×--129× acceleration, 45% reduction in cross-machines communication, and >10% effectiveness improvement in downstream tasks.

VSCT algorithm for graph partitioning based on volume, size, cuts and time

Dealing with large-scale graphs requires an efficient graph partitioner that produces balanced partitions with fewer cut edges/vertices in a reasonable amount of time. Despite several algorithms that have been proposed, it is still insufficient. Even with the continuous growth of graph volume, they do not consider the graph volume during graph partitioning. Therefore, these algorithms generate an imbalanced workload. We propose a graph partitioner algorithm VSCT based essentially on four key metrics: Volume, Size, Cuts, and Time to maintain high-quality graph partitioning. Using real-world datasets, we show that VSCT performs an efficient partitioning quality against the existing graph partitioning algorithms.

Big data cluster tendency techniques with spectral features for efficient data partitions assessment

Cluster tendency assessment in big data poses a challenge, particularly for non-compact separated (non-CS) datasets with irregular boundaries. This paper introduces a novel Spectral-Based Visual Technique (SVT) to address this limitation. Determining the similarity features for the data objects is a crucial computation in data clustering. Distance measures such as Euclidean and cosine are widely employed in clustering applications. By pre-determining cluster tendency, the quality of clusters is obtained using the algorithms of Visual Assessment of Cluster Tendency (VAT) and cosine-based VAT (cVAT). Both VAT and cVAT utilize Euclidean and cosine distance measures to identify the similarity features of objects. For extensive data cluster tendency assessment, an extended concept of VAT, Clustering using Improved Visual Assessment of Tendency (ClusiVAT), is employed to derive clusters with scalable amounts of time and memory loads. However, it operates efficiently for Compactly Separated (CS) datasets. The research gap lies in the need to deliver the quality of big data partitions (or clusters) for non-compact separated (non-CS) datasets. Thus, this paper proposes a spectral-based visual cluster tendency technique to address the challenge of significant data clustering for non-CS datasets. Experimental analysis employs benchmarked datasets to illustrate the performance of the proposed work compared to other techniques.