Initial Centroids Research Articles

A New Particle Swarm Optimization Algorithm for Outlier Detection: Industrial Data Clustering in Wire Arc Additive Manufacturing

In this paper, a novel outlier detection method is proposed for industrial data analysis based on the fuzzy C-means (FCM) algorithm. An adaptive switching randomly perturbed particle swarm optimization algorithm (ASRPPSO) is put forward to optimize the initial cluster centroids of the FCM algorithm. The superiority of the proposed ASRPPSO is demonstrated over five existing PSO algorithms on a series of benchmark functions. To illustrate its application potential, the proposed ASRPPSO-based FCM algorithm is exploited in the outlier detection problem for analyzing the real-world industrial data collected from a wire arc additive manufacturing pilot line in Sweden. Experimental results demonstrate that the proposed ASRPPSO-based FCM algorithm outperforms the standard FCM algorithm in detecting outliers of real-world industrial data. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Electric arc (which is governed by the current and arc voltage) plays a significant role in monitoring the operating status of the wire arc additive manufacturing (WAAM) process. The nominal periodic current and voltage may occasionally change abruptly due to anomalies (such as arc instability, unstable metal transfer, geometrical deviations, and surface contaminations), which would affect the quality of the fabricated component. This paper focuses on detecting possible anomalies by analyzing the current and voltage during the WAAM process. A novel clustering-based outlier detection method is proposed for anomaly detection where abnormal and normal instances are categorized into two separate clusters. A new particle swarm optimization algorithm is put forward to optimize the initial cluster centroid so as to improve the detection accuracy. The proposed outlier detection method is applied to real-world data collected from a WAAM pilot line for detecting abnormal instances. Experimental results demonstrate the effectiveness of the proposed outlier detection method. The proposed outlier detection method can be applied to other industrial applications including electrical engineering, mechanical engineering and medical engineering. In the future, we aim to develop an online outlier detection system based on the proposed method for real-time for anomaly detection and defect prediction.

High-density cluster core-based [formula omitted]-means clustering with an unknown number of clusters

The k-means algorithm, known for its simplicity and adaptability, faces challenges related to manual cluster number selection and sensitivity to initial centroid placement. This paper introduces an innovative framework aimed at overcoming these challenges. By proposing a data-driven cluster number estimation method and a robust initialization strategy based on high-density cluster cores, our approach revolutionizes k-means, unlocking its full unsupervised potential and ensuring superior performance, even in scenarios involving overlapping clusters. The method employs a novel density-based technique to accurately identify cluster cores, resulting in substantial improvements over existing methods. Rigorous experimentation on synthetic and real-world datasets demonstrates an average performance enhancement of 15% in terms of the Adjusted Rand Index for datasets with overlapping clusters, surpassing the capabilities of state-of-the-art density-based clustering methods and traditional k-means. Moreover, our method autonomously determines the optimal number of clusters, facilitating true unsupervised learning and eliminating the impact of initial centroid placement on clustering outcomes. This leads to stable and consistent results, addressing key limitations of the conventional k-means algorithm. The practical applicability of our approach is exemplified in image segmentation tasks, showcasing its versatility and reliability in real-world scenarios.

Optimasi Centroid Awal Algoritma K-Medoids Menggunakan Particle Swarm Optimization Untuk Segmentasi Customer

Customer segmentation is an important strategy in a company, it affects good customer relationships which will result in increased profits. Grouping customers in data mining can use several algorithms, but K-Medoids is the right choice because it can reduce noise and outlier sensitivity. However, the selection of cluster centers is still random and has an effect on the results of clustering, so it is necessary to improve the k-medoids algorithm so that the resulting cluster value can be optimal. Particle Swarm Optimization is an optimization algorithm that is often used and has been proven to improve the results of a clustering. In this case, optimization using Particle Swarm Optimization (PSO) in the selection of the initial cluster center needs to be applied to the k-medoids algorithm so that the results of the cluster can be optimal. The results of the study showed the Davies-Bouldin Index (DBI) value for K-Medoids K 2 = 0.379, K 3 = 0.283, and K 4 = 0.593, while the DBI value PSO + K-Medoids K 2 = 0.088, K 3 = 0.226, and K4 = 0.363. The DBI value shows that PSO optimization on K-Medoids to determine the initial centroid is proven to improve the results of clustering than standard K-Medoids.

Study and methodology exploration of high-potassium glass and lead-barium glass classification patterns based on cluster analysis and decision tree

This study aims to analyze the classification patterns of high-potassium glass and lead-barium glass. It involves preprocessing the data through cluster analysis and employing machine learning decision trees and K-means clustering models for in-depth analysis. In the clustering analysis model, we start by performing a cluster difference analysis on the feature attributes of high-potassium glass and lead-barium glass to obtain initial classification results. Subsequently, we use machine learning decision tree models to partition the data into training and testing sets to explore the classification patterns. Construct a K-means clustering model by iteratively determining the initial cluster centroids' positions using an algorithm and calculating the silhouette coefficient for different numbers of clusters.This process aids in determining the appropriate number of clusters and the initial cluster centroids' positions. The results indicate significant differences in various features between high-potassium glass and lead-barium glass, and the employment of decision trees and K-means models successfully classifies artifacts. In conclusion, this study provides a robust method for the classification of high-potassium glass and lead-barium glass, offering valuable insights for research and application in related fields.

DBGSA: A novel data adaptive bregman clustering algorithm

Traditional clustering algorithms such as K-means are highly sensitive to the initial centroid selection and perform poorly on non-convex dataset. To address these problems, a novel data adaptive Bregman clustering algorithm (DBGSA) is proposed in this paper, which combines the universal gravitational algorithm to bring similar points closer in the dataset. In addition, we introduce the Bregman divergence generalized power mean information loss minimization to identify cluster centers and build a hyperparameter identification optimization model, which effectively solves the problems of manual adjustment and uncertainty in the improved dataset. Extensive experiments are conducted on four simulated datasets and six real datasets. The results demonstrate that DBGSA significantly improves the accuracy of various clustering algorithms by an average of 63.8% compared to the contrasted algorithms, making it applicable to diverse datasets.

Hamiltonian Monte Carlo to Characterize Induced Earthquakes: Application to a ML 3.4 Event in the Groningen Gas Field and the Role of Prior

AbstractThe Hamiltonian Monte Carlo algorithm is known to be highly efficient when sampling high‐dimensional model spaces due to Hamilton's equations guiding the sampling process. For weakly non‐linear problems, linearizing the forward problem enhances this efficiency. This study integrates this linearization with geological prior knowledge for optimal results. We test this approach to estimate the source parameters of a 3.4 magnitude induced event that originated in the Groningen gas field in 2019. The source parameters are the event's centroid (three components), its moment tensor (six components), and its origin time. In terms of prior knowledge, we tested two sets of centroid priors. The first set exploits the known fault geometry of the Groningen gas field, whereas the second set is generated by placing initial centroid priors on a uniform horizontal grid at a depth of 3 km (the approximate depth of the gas reservoir). As for the forward problem linearization, we use an approach in which the linearization is run iteratively in tandem with updates of the centroid prior. We demonstrate that, in the absence of a sufficiently accurate initial centroid prior, the linearization of the forward model necessitates multiple initial centroid priors. Eventually, both prior sets yield similar posteriors. Most importantly, however, they agree with the geological knowledge of the area: the posterior peaks for model vectors containing a centroid near a major fault and a moment tensor that corresponds to normal faulting along a plane with a strike almost aligning with that of the major fault.

ImpKmeans: An Improved Version of the K-Means Algorithm, by Determining Optimum Initial Centroids, based on Multivariate Kernel Density Estimation and Kd-Tree

ImpKmeans: An Improved Version of the K-Means Algorithm, by Determining Optimum Initial Centroids, based on Multivariate Kernel Density Estimation and Kd-Tree

GAPBAS: Genetic algorithm-based privacy budget allocation strategy in differential privacy K-means clustering algorithm

The differential privacy k-means (DP k-means) clustering algorithm emerged to address the privacy protection challenges in the field of data mining. However, the algorithm encounters difficulties in achieving clustering usability and convergence. Privacy budget (ε), a critical parameter determining the noise addition in differential privacy algorithms, garners significant attention. Consequently, researchers have shifted their focus to studying privacy budget allocation strategies within the DP k-means clustering algorithm. However, the selection of a privacy budget allocation strategy in the DP k-means algorithm is an NP-hard problem. Our initial intuition is that genetic algorithms can efficiently discover relatively optimal privacy budget sequences. In this context, we propose a genetic algorithm-based privacy budget allocation strategy (GAPBAS) to ensure the convergence and usability of the DP k-means algorithm. Firstly, convergence is ensured by selecting improved initial centroids and rigorously controlling the minimum privacy budget for the DP k-means algorithm. Additionally, the privacy budget allocation strategy of the DP k-means algorithm is reformulated as a combinatorial optimization problem. This entails merging privacy budgets from multiple iterative rounds into a sequential sequence and utilizing a genetic algorithm to select the optimal privacy budget allocation strategy, thereby significantly enhancing the usability of the DP k-means algorithm. Comparative experiments against the other four privacy budget allocation strategies in the DP k-means algorithm demonstrate the superior performance of the genetic algorithm-based privacy budget allocation strategy at the same level of privacy protection.

Random centroid initialization for improving centroid-based clustering

A method for improving centroid-based clustering is suggested. The improvement is built on diversification of the k-means++ initialization. The k-means++ algorithm claimed to be a better version of k-means is tested by a computational set-up, where the dataset size, the number of features, and the number of clusters are varied. The statistics obtained on the testing have shown that, in roughly 50 % of instances to cluster, k-means++ outputs worse results than k-means with random centroid initialization. The impact of the random centroid initialization solidifies as both the dataset size and the number of features increase. In order to reduce the possible underperformance of k-means++, the k-means algorithm is run on a separate processor core in parallel to running the k-means++ algorithm, whereupon the better result is selected. The number of k-means++ algorithm runs is set not less than that of k-means. By incorporating the seeding method of random centroid initialization, the k-means++ algorithm gains about 0.05 % accuracy in every second instance to cluster.

Analysis of the Influence Path of Confucianism in the Civic Education of Contemporary College Students in the Context of Big Data

Abstract Under the background of big data, college students’ Civic Education has realized the adjustment of teaching technology and educational paradigm, and the value of big data technology for college students’ Civic Education has become increasingly intuitive. In this paper, firstly, the data points designated for clustering are selected in the dataset as the initial clustering centroids. In response to the Euclidean distance treating variables equally, the coefficient of variation method is proposed for subjective weighting. The support vector machine for solving the two-class classification problem is obtained as a real-valued function to test the parallel efficiency of different clustering mining algorithms in the same experimental setting. Finally, for the training sample input data, it is concluded that the algorithm has a better clustering effect and improves the speed and accuracy of clustering. The feasibility of the proposed influence path is demonstrated by comparing it with the data application of the subjective empirical weighting method. The results show that 8% of students before the experiment thought that integrating Confucianism into Civic Education was valuable and meaningful, and after the experiment, the number of students who thought it was valuable and meaningful increased from 8% to 58%. It indicates that the integration of excellent traditional Confucianism into the ideological and political education of college students is very important to strengthen the ideological and political education of college students.

Clustering approximation via a fusion of multiple random samples

In big data clustering exploration, the situation is paradoxical because there is no prior or insufficient domain knowledge. Moreover, clustering a big dataset is a challenging task in distributed computing framework. To address this, we propose a new distributed clustering approximation framework for big data with quality guarantees. This innovative framework uses multiple disjoint random samples instead of a single random sample to compute an ensemble result as the estimation of the true result of the entire big dataset. To begin, we modeled a large dataset as a collection of random sample data blocks stored in a distributed file system. Henceafter, a subset of data blocks is randomly selected, and to generate the component clustering results, the serial clustering algorithm is executed in parallel on the distributed computing framework. In each selected random sample, the number of clusters and initial centroids is identified using a density peak-based I-niceDP clustering algorithm, and then the k-means sweep refines them. Since the random samples are disjoint and traditional consensus functions cannot be used, we propose two new methods, a graph similarity and a naturally inspired firefly-based algorithm, to integrate the component clustering results into the final ensemble result. The entire clustering process is displayed through systematic support, extensive measures of clusterability, and quality evaluation. The methods are verified in a series of experiments using synthetic and real-world datasets. Our comprehensive experimental results demonstrate that the proposed methods vividly (1) recognize the correct number of clusters by analyzing a subset of samples and (2) exhibit better scalability, efficiency, and clustering stability.

Bert-CK: A study of user profile classification based on Bert and CK-means+ fusion

In traditional user portrait construction methods, static word vectors can extract only shallow semantic representations, which cannot manage word polysemy. Moreover, the common clustering algorithm K-means has the problems of initial K values and unstable initial centroid selection. A Bert-CK model based on Bert and CK-means+ is proposed. First, Bert is used to extract semantic and syntactic text features at various levels, and word vectors and sentence vectors are obtained according to the context. Then, the CK-means+ algorithm is improved based on canopy and mean calculation. Next, the K value and initial centroid are determined. The sentence vectors are input to CK-means+ to obtain user classification and topic features. Finally, semantic features and topic features are fused and classified. CK-means+ is evaluated on the Sogou user portrait dataset. The experimental results verify that Bert-CK is better than the baseline model.

Antlion Optimizer Algorithm Modification for Initial Centroid Determination in K-means Algorithm

Clustering is a grouping of data used in data mining processing. K-means is one of the popular clustering algorithms, is easy to use, and is fast in clustering data. The K-means method groups the data based on k distances and randomly determines the initial centroid as a reference for processing. Careless selection of centroids can result in poor clustering processes and local optima. One of the improvements in determining the initial centroid on the k-means method is to use the optimization method to determine the initial centroid. The modified Antlion Optimizer (ALO) method is used to improve poor clustering in the initial centroid determination and as an alternative to determining the initial centroid in the k-means method for better clustering results. The results of the research on the use of the proposed method for determining the initial centroid provide an increase in clustering compared to the usual k-means and k-means++ methods. This is evidenced by the evaluation of the sum of intragroup distance (SICD) with UCI datasets, namely iris, wine, glass, ecoli, and cancer, in each method, the best SICD value was obtained in the proposed method. Then measuring the best SICD value for each method and dataset is measured by providing a ranking proving that the proposed method on the iris, wine, and cancer datasets gets the first rank, and on the ecoli and glass datasets the proposed method and the k-means++ method both get the first rank. From the average ranking value, the proposed method is ranked first, which provides evidence that the proposed method can improve the clustering results and can be an alternative method for determining the initial center of a cluster using the k-means method.&#x0D;

A hybrid MCDM model with Monte Carlo simulation to improve decision-making stability and reliability

Employing an appropriate method to achieve a reliable decision remains a challenge for decision-makers (DMs) in the multiple-criteria decision-making (MCDM) process owing to its inherent model-related complexity, sensitivity, and uncertainty. In this context, this study proposes an innovative hybrid MCDM model that integrates criteria importance through intercriteria correlation (CRITIC), multi-attributive border approximation area comparison (MABAC), and k-means with Monte Carlo simulation (i.e., CRITIC–MABAC–Kmeans with Monte Carlo simulation), aiming to address MCDM problems with substantial stability and reliability. Specifically, MABAC attests to the stability of this method, as it is less affected by normalization and weighting schemes. In addition, the challenge of conflicting k-means clustering outcomes, owing to diverse initial centroid selections, is mitigated by a Monte Carlo simulation, which identifies the most probable type of result and compensates for small-sample size bias. The model performance is tested using a case study of observing transport safety accomplishments in the ASEAN region. Enhanced multiple comparisons of the experimental results verify the quality, efficiency, and adaptability of the proposed model, indicating its feasibility for DMs, policymakers, and practitioners as a practical tool for handling real-life MCDM activities in various domains under compounded sensitivity and uncertainty.

An improved clustering based on K-means for hotspots data

Riau province is one of the provinces in Indonesia where forest fires frequently occur every year. Hotspot data is geothermal points and they can be utilized as an indicator of forest fires. Clustering’s method can be used to analyze potential forest fires from hotspot data’s cluster pattern. In this study, hybrid genetic algorithm polygamy with K-means (GAP K-means) was used for hotspot data clustering. GA polygamy was used to determine the initial centroid of K-means. It was used to solve the sensitivity of K-means to the initial centroid, and to find the optimal solution faster. Experimentally compared the performance of GAP K-means, GA K-means, and K-means on the hotspots data, two artificial datasets, and three real-life datasets. Sum square error (SSE), davies bouldin index (DBI), silhouette coefficient (SC) and F-measure are used to evaluation clustering. Based this experiment, GAP K-means outperforms than K-means but GAP K-means still not fast to achieve convergent than GA K-means.

Modified bee colony optimization with opposition learning algorithm on use of medical data clustering

Clustering has gained popularity in the data mining field as one of the primary approaches for obtaining data distribution and data analysis. The medical data analysis for different diseases is a great challenge in current research. The benefits of opposition based learning such as faster convergence rate and better approximate result in finding global optimum can be helpful in this area. To achieve faster convergence and better clustering results for medical data, in this work, the authors have proposed an approach utilising modified bee colony optimization with opposition based learning and k-medoids technique. The initial centroid plays an important role in the bee colony optimization based clustering. The proposed approach uses k-medoids algorithm for this task. In order to facilitate faster convergence, it adds the opposite bees which are located at exactly the opposite location of the initial bees. The exploration task is performed by both of these kinds of bees to find potential solutions. This increases the algorithm’s capacity for exploration and, consequently, the rate of convergence. Five distinct medical datasets collected from the UCI library are investigated to demonstrate the algorithm’s efficacy. The implementation results demonstrate that the algorithm gives better convergence rate and clustering quality compared to some the existing algorithms.

Fuzzy C-Means Clustering: A Review of Applications in Breast Cancer Detection.

This paper reviews the potential use of fuzzy c-means clustering (FCM) and explores modifications to the distance function and centroid initialization methods to enhance image segmentation. The application of interest in the paper is the segmentation of breast tumours in mammograms. Breast cancer is the second leading cause of cancer deaths in Canadian women. Early detection reduces treatment costs and offers a favourable prognosis for patients. Classical methods, like mammograms, rely on radiologists to detect cancerous tumours, which introduces the potential for human error in cancer detection. Classical methods are labour-intensive, and, hence, expensive in terms of healthcare resources. Recent research supplements classical methods with automated mammogram analysis. The basic FCM method relies upon the Euclidean distance, which is not optimal for measuring non-spherical structures. To address these limitations, we review the implementation of a Mahalanobis-distance-based FCM (FCM-M). The three objectives of the paper are: (1) review FCM, FCM-M, and three centroid initialization algorithms in the literature, (2) illustrate the effectiveness of these algorithms in image segmentation, and (3) develop a Python package with the optimized algorithms to upload onto GitHub. Image analysis of the algorithms shows that using one of the three centroid initialization algorithms enhances the performance of FCM. FCM-M produced higher clustering accuracy and outlined the tumour structure better than basic FCM.

OPTIMIZATION OF K-MEANS CLUSTERING USING PARTICLE SWARM OPTIMIZATION ALGORITHM FOR GROUPING TRAVELER REVIEWS DATA ON TRIPADVISOR SITES

K-Means Algorithm can be used to group tourists based on reviews on tourist destination objects. This algorithm has a weakness that is sensitive to the determination of the initial centroid. The initial centroid that is determined at random will decreasing the level accuracy, often gets stuck at the local optimum, and gets a random solution. Optimization algorithms such as PSO can overcome this by determining the optimal initial centroid. The optimal number of clusters (K) will be determined using the Elbow method by calculating the SSE value of the resulting cluster. The average Silhouette Coefficient (SC) is used to measure the quality of the clusters produced by the K-Means Algorithm with and without the PSO Algorithm. This study uses secondary data obtained from the UCI Machine Learning Repository with the name Travel Reviews Data Set which consists of 980 records and 10 attributes. The test results show that K=2 is the optimal number of clusters. The K-Means and PSO Algorithm gives an average SC value of 0.300358 which is better than without the PSO Algorithm of 0.300076. The optimal PSO hyperparameter generated is the number of particles=30, \varphi_1=2.2, and {\ \varphi}_2=3 at maximum iteration of 100.

Hybrid bidirectional long short term memory with black widow optimization for crop yield prediction using data mining

SummaryCrop yield prediction is highly significant in the agricultural sector. It helps to understand the growth rate of major food crops and identify measures to improve the overall yield. The article proposes a hybrid strategy called bidirectional long short term memory with black widow optimization (Bi‐LSTM‐BWO) for predicting the annual yield produced with improved accuracy. Initially, data augmentation is performed for the collected dataset to increase the size of the dataset and to reduce the data scarcity problem. Then, the dataset is preprocessed to improve the data's quality and remove the noise and irrelevant information. The data is cleaned, transformed, and discretized in the preprocessing stage using various techniques. Then, the preprocessed data is clustered using an enhanced K‐means clustering technique. To enhance the clustering technique, the proposed technique utilized the rain optimization algorithm that automatically computes the initial centroids to improve the clustering outcome. Finally, the prediction process is performed using the proposed Bi‐LSTM‐BWO prediction scheme. The proposed prediction strategy efficiently predicts the annual yield with a high accuracy rate and minimizes loss. The proposed technique achieves a 99.18%, 99.81% and 99.01% accuracy rates for the summer, autumn and winter yield prediction, respectively.

Speedup of the k-Means Algorithm for Partitioning Large Datasets of Flat Points by a Preliminary Partition and Selecting Initial Centroids

Abstract A problem of partitioning large datasets of flat points is considered. Known as the centroid-based clustering problem, it is mainly addressed by the k-means algorithm and its modifications. As the k-means performance becomes poorer on large datasets, including the dataset shape stretching, the goal is to study a possibility of improving the centroid-based clustering for such cases. It is quite noticeable on non-sparse datasets that the resulting clusters produced by k-means resemble beehive honeycomb. It is natural for rectangular-shaped datasets because the hexagonal cells make efficient use of space owing to which the sum of the within-cluster squared Euclidean distances to the centroids is approximated to its minimum. Therefore, the lattices of rectangular and hexagonal clusters, consisting of stretched rectangles and regular hexagons, are suggested to be successively applied. Then the initial centroids are calculated by averaging within respective hexagons. These centroids are used as initial seeds to start the k-means algorithm. This ensures faster and more accurate convergence, where at least the expected speedup is 1.7 to 2.1 times by a 0.7 to 0.9 % accuracy gain. The lattice of rectangular clusters applied first makes rather rough but effective partition allowing to optionally run further clustering on parallel processor cores. The lattice of hexagonal clusters applied to every rectangle allows obtaining initial centroids very quickly. Such centroids are far closer to the solution than the initial centroids in the k-means++ algorithm. Another approach to the k-means update, where initial centroids are selected separately within every rectangle hexagons, can be used as well. It is faster than selecting initial centroids across all hexagons but is less accurate. The speedup is 9 to 11 times by a possible accuracy loss of 0.3 %. However, this approach may outperform the k-means algorithm. The speedup increases as both the lattices become denser and the dataset becomes larger reaching 30 to 50 times.