Cluster Centers Research Articles

Takagi–Sugeno Fuzzy Parallel Distributed Compensation Control for Low-Frequency Oscillation Suppression in Wind Energy-Penetrated Power Systems

In this paper, a Takagi–Sugeno fuzzy parallel distributed compensation control (TS-PDCC) is proposed for low-frequency oscillation (LFO) suppression in wind energy-penetrated power systems. Firstly, the fuzzy C-mean algorithm (FCMA) is applied to cluster the daily average wind speed of the wind farm, and the obtained wind speed clustering center is used as the premise variable of TS-PDCC, which increases the freedom of parameter setting of the TS fuzzy model and is closer to the actual working environment. Secondly, based on the TS fuzzy model, the TS-PDCC is designed to adjust the active power output of the wind turbine for LFO suppression. To facilitate the computation of controller parameters, the stability conditions are transformed into a set of Linear Matrix Inequalities (LMIs) via the Schur complement. Subsequently, a Lyapunov function is designed to verify the stability of the wind energy-penetrated power system and obtain the parameter ranges. Simulation cases are conducted to verify the validity and superior performance of the proposed TS-PDCC under different operating conditions.

INSPIRE: INvestigating Stellar Population In RElics – VII. The local environment of ultra-compact massive galaxies

ABSTRACT Relic galaxies, the oldest ultra-compact massive galaxies (UCMGs), contain almost exclusively ‘pristine’ stars formed during an intense star formation (SF) burst at high redshift. As such, they allow us to study in detail the early mechanism of galaxy assembly in the Universe. Using the largest catalogue of spectroscopically confirmed UCMGs for which a degree of relicness (DoR) had been estimated, the INSPIRE catalogue, we investigate whether or not relics prefer dense environments. The objective of this study is to determine if the DoR, which measures how extreme the SF history was, and the surrounding environment are correlated. In order to achieve this goal, we employ the AMICO galaxy cluster catalogue to compute the probability for a galaxy to be a member of a cluster, and measure the local density around each UCMG using machine learning-based photometric redshifts. We find that UCMGs can reside both in clusters and in the field, but objects with very low DoR ($\lt 0.3$, i.e. a relatively extended SF history) prefer underdense environments. We additionally report a correlation between the DoR and the distance from the cluster centre: more extreme relics, when located in clusters, tend to occupy the more central regions of them. We finally outline potential evolution scenarios for UCMGs at different DoR to reconcile their presence in both clusters and field environments.

NsDCC: dual-level contrastive clustering with nonuniform sampling for scRNA-seq data analysis.

Dimensionality reduction and clustering are crucial tasks in single-cell RNA sequencing (scRNA-seq) data analysis, treated independently in the current process, hindering their mutual benefits. The latest methods jointly optimize these tasks through deep clustering. However, contrastive learning, with powerful representation capability, can bridge the gap that common deep clustering methods face, which requires pre-defined cluster centers. Therefore, a dual-level contrastive clustering method with nonuniform sampling (nsDCC) is proposed for scRNA-seq data analysis. Dual-level contrastive clustering, which combines instance-level contrast and cluster-level contrast, jointly optimizes dimensionality reduction and clustering. Multi-positive contrastive learning and unit matrix constraint are introduced in instance- and cluster-level contrast, respectively. Furthermore, the attention mechanism is introduced to capture inter-cellular information, which is beneficial for clustering. The nsDCC focuses on important samples at category boundaries and in minority categories by the proposed nearest boundary sparsest density weight assignment algorithm, making it capable of capturing comprehensive characteristics against imbalanced datasets. Experimental results show that nsDCC outperforms the six other state-of-the-art methods on both real and simulated scRNA-seq data, validating its performance on dimensionality reduction and clustering of scRNA-seq data, especially for imbalanced data. Simulation experiments demonstrate that nsDCC is insensitive to "dropout events" in scRNA-seq. Finally, cluster differential expressed gene analysis confirms the meaningfulness of results from nsDCC. In summary, nsDCC is a new way of analyzing and understanding scRNA-seq data.

Distributed PV carrying capacity prediction and assessment for differentiated scenarios based on CNN-GRU deep learning

The increasing penetration of distributed photovoltaic (PV) brings challenges to the safe and reliable operation of distribution networks, distributed PV access to the grid changes the characteristics of the traditional distribution grid. Therefore, the assessment of distributed PV carrying capacity is of great significance for distribution network planning. To this end, a differentiated scenario-based distributed PV carrying capacity assessment method based on a combination of Convolutional Neural Networks (CNN) and Gated Recurrent Unit (GRU) is proposed. Firstly, the meteorological characteristics affecting PV power are quantitatively analyzed using Pearson’s correlation coefficient, and the influence of external factors on PV power characteristics is assessed by integrating the measured data. Then, for the problem of high blindness of clustering parameters and initial clustering centers in the K-means clustering algorithm, the optimal number of clusters is determined by combining the cluster Density Based Index (DBI) and hierarchical clustering. The improved K-means clustering method reduces the complexity of massive scenarios to obtain distributed PV power under differentiated scenarios. On this basis, a distributed PV power prediction method based on the CNN-GRU model is proposed, which employs the CNN model for feature extraction of high-dimensional data, and then the temporal feature data are optimally trained by the GRU model. Based on the clustering results, the solution efficiency is effectively improved and the accurate prediction of distributed PV power is realized. Finally, taking into account the PV access demand of the distribution network, combined with the power flow calculation of distribution network, the bearing capacity of distribution network considering node voltage in differentiated scenarios is evaluated. In addition, verified by source-grid-load measured data in IEEE 33-bus distribution system. The simulation results show that the proposed CNN-GRU fusion deep learning model can accurately and efficiently assess the distributed PV carrying capacity of the distribution network and provide theoretical guidance for realizing distributed PV access on a large scale.

VoiceStyle: Voice-Based Face Generation via Cross-Modal Prototype Contrastive Learning

Can we predict a person’s appearance solely based on their voice? This article explores this question by focusing on generating a face from an unheard voice segment. Our proposed method, VoiceStyle, combines cross-modal representation learning with generation modeling, enabling us to incorporate voice semantic cues into the generated face. In the first stage, we introduce cross-modal prototype contrastive (CMPC) learning to establish the association between voice and face. Recognizing the presence of false negative and deviate positive instances in real-world unlabeled data, we not only use voice–face pairs in the same video but also construct additional semantic positive pairs through unsupervised clustering, enhancing the learning process. Moreover, we recalibrate instances based on their similarity to cluster centers in the other modality. In the second stage, we harness the powerful generative capabilities of StyleGAN to produce faces. We optimize the latent code in StyleGAN’s latent space, guided by the learned voice–face alignment. To address the importance of selecting an appropriate starting point for optimization, we aim to automatically find an optimal starting point by utilizing the face prototype derived from the voice input. The entire pipeline can be implemented in a self-supervised manner, eliminating the need for manually labeled annotations. Through extensive experiments, we demonstrate the effectiveness and performance of our VoiceStyle method in both cross-modal representation learning and voice-based face generation.

Parameterization before Meta-Analysis: Cross-Modal Embedding Clustering for Forest Ecology Question-Answering

In the field of forestry ecology, image data capture factual information, while literature is rich with expert knowledge. The corpus within the literature can provide expert-level annotations for images, and the visual information within images naturally serves as a clustering center for the textual corpus. However, both image data and literature represent large and rapidly growing, unstructured datasets of heterogeneous modalities. To address this challenge, we propose cross-modal embedding clustering, a method that parameterizes these datasets using a deep learning model with relatively few annotated samples. This approach offers a means to retrieve relevant factual information and expert knowledge from the database of images and literature through a question-answering mechanism. Specifically, we align images and literature across modalities using a pair of encoders, followed by cross-modal information fusion, and feed these data into an autoregressive generative language model for question-answering with user feedback. Experiments demonstrate that this cross-modal clustering method enhances the performance of image recognition, cross-modal retrieval, and cross-modal question-answering models. Our method achieves superior performance on standardized tasks in public datasets for image recognition, cross-modal retrieval, and cross-modal question-answering, notably achieving a 21.94% improvement in performance on the cross-modal question-answering task of the ScienceQA dataset, thereby validating the efficacy of our approach. Essentially, our method targets cross-modal information fusion, combining perspectives from multiple tasks and utilizing cross-modal representation clustering of images and text. This approach effectively addresses the interdisciplinary complexity of forestry ecology literature and the parameterization of unstructured heterogeneous data encapsulating species diversity in conservation images. Building on this foundation, intelligent methods are employed to leverage large-scale data, providing an intelligent research assistant tool for conducting forestry ecological studies on larger temporal and spatial scales.

Suppressed possibilistic fuzzy c-means clustering based on shadow sets for noisy data with imbalanced sizes

Possibilistic fuzzy c-means clustering (PFCM) algorithm generates fewer overlapping clustering centers than the possibilistic c-means clustering (PCM) algorithm and possesses better noise immunity than fuzzy c-means clustering (FCM) algorithm. However, with the increasing noise intensity and number of clusters, PFCM still faces the problem of getting partially overlapping clustering centers or mislocated centers in noise regions. Moreover, the sample-size imbalance increasingly intensifies the difficulty of positioning centers of small clusters. To solve the above problems, a suppressed possibilistic fuzzy c-means clustering algorithm based on shadow sets (S-SPFCM) is proposed by introducing the shadow set theory and the "suppressed competitive learning" strategy. Firstly, KL divergence is introduced in the objective function of PFCM to increase the anti-noise robustness of fuzzy memberships against long-range noise and outliers. Secondly, to reduce the number of overlapping centers caused by possibilistic memberships, the shadow set theory is introduced to divide each class adaptively into three regions (core, shadow, and exclusion regions) by an uncertainty balance method. The suppressed competitive learning method is extended by modifying the memberships of points within the three regions, thus artificially guiding the iterative track of clustering centers. Meanwhile, to further reduce the influence of imbalanced sizes, a scheme to reset mislocated centers in the core and shadow regions is also designed. In addition, to improve the segmentation performance of S-SPFCM for noisy images, a suppressed possibilistic fuzzy c-means clustering algorithm based on shadow sets and local information (SL-SPFCM) is also proposed. The SL-SPFCM first improves the Euclidean distance by a distance filtering scheme. Then SL-SPFCM introduces the local median membership of each pixel into the KL divergence of the objective function. Finally, experiments on synthetic datasets and color images which are characteristic of imbalanced sizes and noise injection demonstrate the proposed S-SPFCM and SL-SPFCM algorithms achieve smaller center deviations and higher clustering accuracy compared with several state-of-the-art clustering algorithms.

The geography of healthcare: Mapping patient flow and medical resource allocation in China

The misallocation of medical resources leads to interregional patient flow in search of better healthcare. Using out-of-pocket medical expenditure data and a delineating method, this paper identifies spatial clusters of medical services in China based on patient flow across cities. Our findings indicate that healthcare resources are more concentrated in northern China, while southern China is divided into several large healthcare clusters at the same threshold. The provincial capital and economically significant cities are more likely to serve as medical cluster centers. We further apply the gravity model to examine the effects of healthcare disparity on cross-city medical expenditure. The results reveal that geographic disparities in high-quality medical resources encourage remote healthcare-seeking behavior, and the shorter the distance between locations, the higher the level of medical consumption. Patients are inclined to seek medical services within their own province and within specific medical clusters identified through delineation methods. This effect is more pronounced among patients from non-central cities. This study highlights healthcare inequality by examining cross-regional medical expenditure, providing valuable insights for future healthcare policy.

Center-enhanced video captioning model with multimodal semantic alignment

Video captioning aims at automatically generating descriptive sentences based on the given video, establishing an association between the visual contents and textual languages, has attracted great attention and plays a significant role in many practical applications. Previous researches focus more on the aspect of caption generation, ignoring the alignment of multimodal feature and just simply concatenating them. Besides, video feature extraction is usually done in an off-line manner, which leads to the fact that the extracted feature may not adapted to the subsequent caption generation task. To improve the applicability of extracted features for downstream caption generation and to address the issue of multimodal semantic alignment fusion, we propose an end-to-end center-enhanced video captioning model with multimodal semantic alignment, which integrates feature extraction and caption generation task into a unified framework. In order to enhance the completeness of semantic features, we design a center enhancement strategy where the visual–textual deep joint semantic feature can be captured via incremental clustering, then the cluster centers can serve as the guidance for better caption generation. Moreover, we propose to promote the visual–textual multimodal alignment fusion by learning the visual and textual representation in a shared latent semantic space, so as to alleviate the multimodal misalignment problem. Experimental results on two popular datasets MSVD and MSR-VTT demonstrate that the proposed model could outperform the state-of-the-art methods, obtaining higher-quality caption results.

A mean shift algorithm incorporating reachable distance for spatial clustering

Spatial clustering is a widely used technique in spatial analysis that groups similar objects together based on their proximity in space. However, traditional clustering algorithms often fail to ensure the accessibility of cluster centers, which limits their validity in practical applications such as facility location problems. To address this issue, this article introduces a novel Mean Shift algorithm that incorporates reachable distance and an iterative mechanism to accurately locate cluster centers. The proposed algorithm initially labels clustering elements with road network coordinates to facilitate the calculation of reachable distance and the cluster center iterative mechanism. Subsequently, the mean shift vector function is modified to employ reachable distance as the measure of geographic reachable similarity. Unlike existing algorithms, our approach allows for cluster centers to be positioned independently of the clustering elements, guaranteeing geographical accessibility. Through simulation experiments, we demonstrate that our proposed algorithm not only outperforms existing methods in terms of solution quality, but also effectively addresses the limitations of disregarding geographical obstacles and unreachable cluster centers.

A Clustering Pruning Method Based on Multidimensional Channel Information

Pruning convolutional neural networks offers a promising solution to mitigate the computational complexity challenges encountered during application deployment. However, prevalent pruning techniques primarily concentrate on model parameters or feature mapping analysis to devise static pruning strategies, often overlooking the underlying feature extraction capacity of convolutional kernels. To address this, the study first quantitatively expresses the feature extraction capability of convolutional channels from three aspects: global features, distribution metrics, and directional metrics. It explores the multi-dimensional information of the channels, calculates the overall expectation, variance, and cosine distance from the unit vector as the quantitative results of the channels. Subsequently, a clustering algorithm is employed to categorize the multidimensional information. This approach ensures that convolutional channels grouped within each cluster possess similar feature extraction capabilities. An enhanced differential evolutionary algorithm is utilized to optimize the number of clustering centers across all convolutional layers, ensuring optimal grouping. The final step involves achieving channel sparsification through the calculation of crowding distances for each sample within its designated cluster. This preserves a diverse subset of channels that are critical for maintaining model accuracy. Extensive empirical evaluations conducted on three benchmark image classification datasets demonstrate the efficacy of this method. For instance, on the ImageNet dataset, the ResNet-50 model experiences a substantial reduction in FLOPs by 58.43% while incurring a minimal decrease in TOP-1 accuracy of only 1.15%.

A hybrid genetic-fuzzy ant colony optimization algorithm for automatic K-means clustering in urban global positioning system

This paper introduces an innovative automatic K-means clustering algorithm, namely HGA-FACO, which seamlessly integrates the noise algorithm, Genetic Algorithm (GA), Ant Colony Optimization (ACO), and Adaptive Fuzzy System (AFS). The rationale behind the HGA-FACO algorithm is to mitigate the shortcomings of traditional K-means, particularly the reliance on pre-determined cluster centers and the need for specifying the number of clusters in advance. By optimizing the search strategy, HGA-FACO efficiently circumvents local optima and effectively explores the global optimal solution, resulting in more accurate and stable clustering outcomes. To validate the superiority of the HGA-FACO over conventional K-Means Clustering (KMeans) and other intelligent clustering approaches such as ACO-KMeans, GA-KMeans (GAK), particle swarm optimization KMeans (PSOK), and ACO-GAK, we conducted comprehensive experiments on taxi Global Positioning System (GPS) datasets sourced from four distinct cities. Employing rigorous evaluation metrics including Silhouette Coefficient (SC), Partition Coefficient (PBM), Davies-Bouldin Index (DBI), and Sum of Squared Errors (SSE), the experimental results convincingly demonstrate that the HGA-FACO significantly outperforms its counterparts across all metrics, highlighting its exceptional performance in clustering effectiveness and compactness. While the HGA-FACO faces challenges related to computational complexity and the necessity for initial parameter tuning, its performance limitations on small-sized or unevenly distributed datasets are acknowledged. Nevertheless, the algorithm's advancements in the field of clustering algorithms are undeniable and hold immense potential for practical applications, notably in city hotspot identification.

Trends and Collaborations in Livestock Extension Research: A Bibliometric Analysis (2015-2024)

This study employs bibliometric analysis to investigate trends in livestock extension research from January 2015 to June 2024, utilizing data sourced from the dimension.ai database. The analysis encompasses a comprehensive review of publication trends, research categories, influential journals, collaborative networks among authors, and the impact of seminal studies. The findings reveal a notable increase of 51.55 per cent in scholarly interest and publications over the years, indicating growing attention towards enhancing livestock productivity, sustainability, and socio-economic outcomes. Key research domains such as agricultural, veterinary, and food sciences emerge as predominant areas of focus, with significant contributions observed in interdisciplinary fields like environmental sciences and human geography. Network analyses using tools like VOSviewer highlight robust collaborative relationships among researchers, identifying central figures and clusters that drive collaborative research efforts in livestock extension. The study also identified “Climate change vulnerability, adaptation and risk perceptions at farm level in Punjab, Pakistan” published in 2016, with nearly 294 citations as top-cited article and other affiliations, emphasizing their pivotal roles in advancing knowledge and practices within the field. Overall, this bibliometric analysis provides valuable insights into the evolving landscape of livestock extension research, demonstrating how such analytical approaches contribute to understanding research trends, fostering interdisciplinary collaborations, and guiding future research directions in agricultural sciences.

Sectoral electricity micro-spatial load forecasting based on partitional clustering technique

<p>Load demand forecasting is crucial in energy supply planning due to economic progress and territorial expansion, where land utilization transforms dynamically. An accurate sectoral load prediction can preclude the loss of beneficial opportunities arising from excessive load demand or excessive investment at a low-growth juncture. However, the particular area in this sectoral approach is still relatively large, rendering it incapable of precisely projecting load at minor points (micro-spatial). This study has proposed a micro-spatial load prediction strategy that categorizes identified areas into smaller grids or districts. This procedure includes clustering similar sites together for improved accuracy. K-Means is one of the partitional clustering approaches, a clustering algorithm utilizing object-based centroid-based partitioning approaches. The algorithm determines a cluster's centroid or centre as the average point for the cluster. This technique is advantageous as it can process extensive data efficiently and is appropriate for circular data. This technique can divide the data into multiple partitions, ensuring that each object belongs to precisely one cluster. Subsequently, mathematical modelling is used to predict the load of each cluster, which can then be utilized to more accurately evaluate the positions and sizes of prospective substations, transmission, and distribution facilities.</p>

The Improvement of Density Peaks Clustering Algorithm and Its Application to Point Cloud Segmentation of LiDAR.

This work focuses on the improvement of the density peaks clustering (DPC) algorithm and its application to point cloud segmentation in LiDAR. The improvement of DPC focuses on avoiding the manual determination of the cut-off distance and the manual selection of cluster centers. And the clustering process of the improved DPC is automatic without manual intervention. The cut-off distance is avoided by forming a voxel structure and using the number of points in the voxel as the local density of the voxel. The automatic selection of cluster centers is realized by selecting the voxels whose gamma values are greater than the gamma value of the inflection point of the fitted γ curve as cluster centers. Finally, a new merging strategy is introduced to overcome the over-segmentation problem and obtain the final clustering result. To verify the effectiveness of the improved DPC, experiments on point cloud segmentation of LiDAR under different scenes were conducted. The basic DPC, K-means, and DBSCAN were introduced for comparison. The experimental results showed that the improved DPC is effective and its application to point cloud segmentation of LiDAR is successful. Compared with the basic DPC, K-means, the improved DPC has better clustering accuracy. And, compared with DBSCAN, the improved DPC has comparable or slightly better clustering accuracy without nontrivial parameters.

An investigation of anisotropy in the bubbly turbulent flow via direct numerical simulations

We investigated the effects of bubble count, flow direction, and Eötvös number on deformable bubbles in turbulent channel flow. For a given shear Reynolds number Re = 180 and fixed bubble volume fractions (1.263% and 2.525%), we conducted a series of direct numerical simulations using a coupled level-set and volume-of-fluid solver to evaluate their impact on bubble volume fraction distribution, velocity fields, and turbulence characteristics. Each aspect was studied based on the microscopic equations of two-phase flow, and the accuracy of the modeling terms used in current Reynolds-averaged Navier–Stokes equation (RANS) models was assessed. The influence on the anisotropic state was analyzed using the Lumley triangle, and the anisotropy of Reynolds stresses was captured through the exact balance equations. The results indicate that in upward flow, bubbles tend to accumulate near the wall, with smaller Eötvös numbers leading to closer proximity to the wall and greater attenuation of the liquid-phase velocity. This distribution enhances energy dissipation and turbulence isotropy. In downward flow, bubbles cluster in the channel center, generating additional pseudo-turbulence and attenuating energy in the buffer layer. Moreover, the interfacial transfer of turbulent energy, as currently modeled in RANS, is found to be inadequate for upward flows.

A Novel Classification Model Based on Hybrid K-Means and Neural Network for Classification Problems

We propose a new classification model—a new classification model for clustering overlapping problems based on K-Means and neural networks. K-means clustering algorithm belongs to unsupervised learning. It is a classic algorithm for solving clustering problems. Since this algorithm calculates its categories based on distance, the results tend to converge to the local optimal solution and have poor boundary clustering properties. The K-Means classification algorithm defines clusters by the distance between the cluster center value and the target object, and the optimal result is obtained through continuous iteration. Therefore, clustering results are overlapped, and there are often outliers that do not belong to the current cluster, resulting in unsatisfactory clustering results. Our model offers a new method to segment non-ideal data in overlapping regions. Since clustering algorithms cannot effectively identify and classify this part of the data, we split this part of the data and train it using a neural network. The results are then integrated into the clustered data. In the experiment, the k-fold cross-validation method ensures the model stability of the results. We used the accuracy to evaluate the quality of the model, and we used standard deviation and mean deviation to detect clustering results. Five sets of experimental data from the cross-experiment show that compared with the K-Means classification model, the accuracy of our model is effectively improved. Doi: 10.28991/HIJ-2024-05-03-012 Full Text: PDF

An Examination and Analysis of the Clustering of Healthcare Centers and their Spatial Accessibility in Tehran Metropolis: Insights from Google POI Data

Metropolises, as centers of diverse activities, encounter numerous challenges, including equitable access to healthcare services. This study examines the inequality in healthcare center accessibility in Tehran, a critical factor for sustainable urban development. Utilizing Google Point of Interest data, healthcare center clusters in Tehran were identified, and various clustering algorithms were tested. The Mean Shift Cluster algorithm was selected as the most effective. The study also mapped accessibility by analyzing the radius of neighborhoods around urban blocks. The findings reveal a significant imbalance in the distribution of healthcare centers, with a concentration in the city center that does not align with population density—a key indicator of demand. Notably, District 7, despite being centrally located, relatively has a higher clusters’ concentration of lower-quality healthcare centers, highlighting disparities. Overall, 6 percent of Tehran's sub-districts experience spatial inequality in access to healthcare centers, while a separate 6 percent face inequality in accessing high-quality healthcare facilities, predominantly situated in the northeastern, southwestern, and western parts of the city. These results underscore the need for targeted urban planning to address the uneven distribution of healthcare resources and promote equitable access across Tehran.

Optical polarimetry study of the Lambda-Orionis star-forming region

We present an optical polarimetry study of the nearby star-forming region Lambda-Orionis to map the plane-of-the-sky magnetic field geometry to understand the magnetized evolution of the HII region and the associated small molecular clouds. We made multiwavelength polarization observations of 34 bright stars distributed across the region. We also present the R-band polarization measurements that focused on the small molecular clouds, bright-rimmed clouds (BRC), BRC 17, and BRC 18, which are located at the periphery of the HII region. The magnetic field lines exhibit a large-scale ordered orientation consistent with the Planck submillimeter polarization measurements. The magnetic field lines in the two BRCs are found to be roughly in north-south directions. However, a larger dispersion is noted in the orientation for BRC 17 compared to BRC 18. Using a structure-function analysis, we estimate the strength of the plane-of-the-sky component of the magnetic field as ∼28 μG for BRC 17 and ∼40 μG for BRC 18. The average dust grain size and the mean value of the total-to-selective extinction ratio (RV) in the HII region are found to be ∼0.51 ± 0.05 μm and ∼2.9 ± 0.3, respectively. The distance of the whole HII region is estimated as ∼392 ± 8 pc by combining astrometry information from Global Astrometric Interferometer for Astrophysics (Gaia) early data release 3 (EDR3) for young stellar objects associated with BRCs and confirmed members of the central cluster Collinder 69.

A fuzzy K-Means algorithm based on Fisher distribution for the identification of rock discontinuity sets

Rock discontinuities significantly impact the mechanical and hydraulic behavior of rock masses. A crucial aspect of rock engineering involves classifying discontinuities with similar orientations into groups. For this purpose, clustering algorithms, such as K-Means and Fuzzy K-Means (FKM), have been employed. However, the outcomes of these algorithms are influenced by the selection of initial cluster centers. This paper proposes an improved FKM algorithm to automatically identify rock discontinuity sets based on the Fisher distribution (FFKM). The algorithm uses the Fisher distribution to generate and select appropriate initial cluster centers. The performance of FFKM was initially validated using a published data set, and its results were compared with other clustering methods commonly used for grouping discontinuities. Results demonstrated the superior performance of FFKM over the FKM algorithm, comparable to other methods. Subsequently, the proposed algorithm was employed to analyze a fracture data set sampled at an open-pit iron mine. The FFKM facilitated identifying the correct number of sets and produced results consistent with the fracture sets observed in the field. Finally, the algorithm was verified using an artificial discontinuity data set, and the results demonstrated that the method correctly identified the number of sets and provided discontinuity sets similar to the original data set. The FFKM algorithm offers significant advantages: it maintains the essential characteristics of the FKM algorithm, effectively addresses the challenge of selecting suitable initial cluster centers, requires only the expected number of discontinuity sets as an input parameter, processes data within an acceptable computation time, serves as a tool for defining the number of discontinuity sets, and mitigates the drawbacks of the stereographic projection method.