Initial Centroids Research Articles

Optimized Centroid-Based Clustering of Dense Nearly-square Point Clouds by the Hexagonal Pattern

Abstract An approach to optimize centroid-based clustering of flat objects is suggested, which is practically important for efficiently solving metric facility location problems. In such problems, the task is to find the best warehouse locations to optimally service a given set of consumers. An example is assigning mobiles to base stations of a wireless communication network. We suggest a hexagonal-pattern-based approach to partition flat nodes into clusters quicker than the k-means algorithm and its modifications do. First, a hexagonal cell lattice is applied to nodes to approximately determine centroids of the clusters. Then the centroids are used as initial centroids to start the k-means algorithm. The suggested method is efficient for centroid-based clustering of dense nearly-square point clouds of 0.1 million points and greater by using no fewer than 6 lattice cells along an axis. Compared to k-means, our method is at least 10 % faster and it is about 0.01 to 0.07 % more accurate in regular Euclidean distances. In squared Euclidean distances, the accuracy gain is 0.14 to 0.21 %. Applying a hexagonal cell lattice determines an upper bound of the clustering quality gap.

Cluster-based denoising autoencoders for rate prediction recommender systems

Recommender system (RS) is a suitable tool for filtering out items and providing the most relevant and suitable items to each user, based on their individual preferences. Deep learning algorithms achieve great success in several fields including RS. The issue with deep learning-based RS models is that, they ignore the differences of users’ preferences, and they build a model based on all the users’ rates. This paper proposed an optimized clustering-based denoising autoencoder model (OCB-DAE) which trains multiple models instead of one, based on users’ preferences using k-means algorithm combined with a nature-inspired algorithm (NIA) such as artificial fish swarm algorithm to determine the optimal initial centroids to cluster the users based on their similar preferences, and each cluster trains its own denoising autoencoder (DAE) model. The results proved that combining NIA with k-means gives better clustering results comparing with using k-means alone. OCB-DAE was trained and tested with MovieLens 1M dataset where 80% of it is used for training and 20% for testing. Root mean squared error (RMSE) score was used to evaluate the performance of the proposed model which was 0.618. It outperformed the other models that use autoencoder and denoising autoencoder without clustering with 38.5% and 29.5% respectively.

A novel initialisation based on hospital-resident assignment for the k-modes algorithm

This paper presents a new way of selecting an initialisation for the k-modes algorithm that allows for a notion of game theoretic fairness that classic initialisations, namely those by Huang and Cao, do not. Our new method utilises the hospital-resident assignment problem to find the set of initial cluster centroids which we compare with two classical initialisation methods for k-modes: the original presented by Huang and the next most popular method of Cao and co-authors. To highlight the merits of our proposed method, two stages of analysis are presented. It is demonstrated that the proposed method is often able to offer computational speed-up of the order of 50%. Improved clustering, in terms of a commonly used cost-function, was witnessed in several cases and can be of the order of 10%, particularly for more complex datasets.

Robust reservoir identification by multi-well cluster analysis of wireline logging data

A novel clustering method is applied to well logs for improved rock type identification in hydrocarbon formations. For grouping the objects in the multi-dimensional data space, we propose a Most Frequent Value (MFV) based clustering technique applied to natural gamma ray, bulk density, sonic, photoelectric index, and resistivity logs. The MFV method is a robust estimator, which assists in finding the cluster centers more reliably than a more noise sensitive K-means clustering approach. The result of K-means cluster analysis highly depends on the choose of the initial centroids. To reduce the risk of inappropriately chosen starting values, we apply a histogram-based selection method to give the best position of the initial cluster centers. We assure the robustness of the solution by calculating the centroid as the MFV of the cluster elements and defining the overall deviation of cluster elements from the center by a weighted Euclidean (Steiner-) distance. The proposed workflow relies on a fully automated weighting of the cluster elements, which does not require a constraint on the statistical distribution of the observed variables. The processing of synthetic data shows high noise rejection capability and efficient cluster recognition even beside considerable amount of outlying and missing data; the accuracy is measured by the difference between the estimated and the exactly known distribution of cluster numbers. The clustering tool is first applied to single borehole data, then the procedure is extended to multi-well logging datasets to reconstruct the multi-dimensional spatial distributions of clusters revealing the lithological and petrophysical characteristics of the studied formations. A large in situ dataset acquired from several boreholes traversing Hungarian gas-bearing clastic reservoirs of Miocene age is analyzed. The accuracy of the field results is confirmed by core permeability measurements, independent well log analysis and a gradient metrics characterizing the noise rejection capability of the clustering method.

Implementation of Fuzzy C-Means Algorithm with Optimized Parameter Grid for Clustering Electronic Product Sales

The sales of electronic products have increased rapidly over the past few years. However, grouping products based on certain criteria is still an unresolved issue. Therefore, research is needed to develop more accurate clustering methods. Currently, the problem with electronic product clustering using the k-means method still has limitations, such as sensitivity to initial centroid values and inability to handle overlap between clusters. Therefore, research is needed to optimize the grid parameter of the Fuzzy C-Means algorithm to produce more accurate clustering. The purpose of this study is to implement the Fuzzy C-Means algorithm with optimized grid parameters to cluster electronic product sales more accurately. The method used in this study is an experimental research method. Electronic product sales data were obtained from specific stores, and the Fuzzy C-Means algorithm with optimized grid parameters was applied to cluster electronic products. The results show that implementing the Fuzzy C-Means algorithm with optimized grid parameters can produce more accurate electronic product clustering compared to the k-means method. By using optimized grid parameters, the Fuzzy C-Means algorithm can handle overlap between clusters and produce more stable centroids with a Dbi accuracy value of 0.510 for Numerical Measure and 0.611 for Mixed Measure.

Stratification-based semi-supervised clustering algorithm for arbitrary shaped datasets

Semi-supervised clustering is not only an important branch of semi-supervised learning but also an improvement direction for clustering. Semi-supervised clustering algorithms designed based on Kmeans, such as the classical Seeded-Kmeans and Constrained-Kmeans, where supervision information is used to guide clustering iterations, have the same disadvantages as the original Kmeans algorithm: they are confined to the assumption of isotropic spherical clusters, leading to the narrow adaptability in handling data of various characteristics. To solve the problem, we propose the scattered centroids initialization clustering algorithm based on Stratification (SCICS). First, based on the concept of influence space, a method for modeling the cluster-level location of any object is presented, according to which we can obtain well-defined cluster decision boundaries through stratification. On this basis, by extending the seed thought, we propose a semi-supervised subclustering algorithm that can break through the limitations of partitional clustering methods that rely on strict assumptions on particular cluster distributions. Experiments on artificial and real-world datasets show that the proposed algorithm gains the ability of clustering arbitrary shaped data and surpasses the competitors in terms of performance and adaptability.

Quantum-PSO based unsupervised clustering of users in social networks using attributes.

Unsupervised cluster detection in social network analysis involves grouping social actors into distinct groups, each distinct from the others. Users in the clusters are semantically very similar to those in the same cluster and dissimilar to those in different clusters. Social network clustering reveals a wide range of useful information about users and has many applications in daily life. Various approaches are developed to find social network users' clusters, using only links or attributes and links. This work proposes a method for detecting social network users' clusters based solely on their attributes. In this case, users' attributes are considered categorical values. The most popular clustering algorithm used for categorical data is the K-mode algorithm. However, it may suffer from local optimum due to its random initialization of centroids. To overcome this issue, this manuscript proposes a methodology named the Quantum PSO approach based on user similarity maximization. In the proposed approach, firstly, dimensionality reduction is conducted by performing the relevant attribute set selection followed by redundant attribute removal. Secondly, the QPSO technique is used to maximize the similarity score between users to get clusters. Three different similarity measures are used separately to perform the dimensionality reduction and similarity maximization processes. Experiments are conducted on two popular social network datasets; ego-Twitter, and ego-Facebook. The results show that the proposed approach performs better clustering results in terms of three different performance metrics than K-Mode and K-Mean algorithms.

Novel Hybrid Optimized Clustering Schemes with Genetic Algorithm and PSO for Segmentation and Classification of Articular Cartilage Loss from MR Images

Medical image segmentation plays an indispensable role in the identification of articular cartilage, tibial and femoral bones from magnetic resonance imaging (MRI). There are various image segmentation strategies that can be used to identify the knee structures of interest. Among the most popular are the methods based on non-hierarchical clustering, including the algorithms K-means and fuzzy C-means (FCM). Although these algorithms have been used in many studies for regional image segmentation, they have two essential drawbacks that limit their performance and accuracy of segmentation. Firstly, they rely on a precise selection of initial centroids, which is usually conducted randomly, and secondly, these algorithms are sensitive enough to image noise and artifacts, which may deteriorate the segmentation performance. Based on such limitations, we propose, in this study, two novel alternative metaheuristic hybrid schemes: non-hierarchical clustering, driven by a genetic algorithm, and Particle Swarm Optimization (PSO) with fitness function, which utilizes Kapur’s entropy and statistical variance. The goal of these optimization elements is to find the optimal distribution of centroids for the knee MR image segmentation model. As a part of this study, we provide comprehensive testing of the robustness of these novel segmentation algorithms upon the image noise generators. This includes Gaussian, Speckle, and impulsive Salt and Pepper noise with dynamic noise to objectively report the robustness of the proposed segmentation strategies in contrast with conventional K-means and FCM. This study reveals practical applications of the proposed algorithms for articular cartilage extraction and the consequent classification performance of early osteoarthritis based on segmentation models and convolutional neural networks (CNN). Here, we provide a comparative analysis of GoogLeNet and ResNet 18 with various hyperparameter settings, where we achieved 99.92% accuracy for the best classification configuration for early cartilage loss recognition.

Implementation of K-Means Algorithm with Clustering Method to Data Management of Covid-19 Case in West Bandung Using Orange Application

Covid-19 cases in Indonesia have not disappeared to the until now. Coronavirus has spread to almost all provinces in Indonesia, one of the province is West Java. There are 27 regencies/cities in West Java that have become the spread of the Covid-19 case, one of which is West Bandung Regency. To make it easier for the regional government of West Bandung Regency to take action in an effort to prevent the spread of Covid-19, research is needed to determine the level of distribution of Covid-19 cases which are divided into 3 clusters, namely high, medium and low clusters. Researchers analyzed using the data mining method with the K-Means Clustering algorithm through the Orange Application. Data processing is started from determining amount of the data to be clustered into 3 high, medium and low, then determining the initial centroid cluster center point (iteration 1) that has been determined randomly, then calculating the distance of each data to the center of the cluster between objects to closest centroid. The distribution of cluster 1, cluster 2, and cluster 3 as many as 16 data in the K-Means Clustering process using the Orange Application. The research results show that there are 8 sub-districts for high clusters, 2 sub-districts for medium clusters and 6 sub-districts for low clusters in West Bandung Regency.

Performance analysis of Kmeans with modified initial centroid selection algorithms and developed Kmeans9+ model

Partition the sample space to the user requirement is an easy and efficient cluster method in many applications. Kmeans is one of the simple and efficient partition algorithms used in many cluster solutions. We suggest Multivariant Silhouette method to predict the cluster count value for Kmeans algorithm. The work proposes three new algorithms for initial seed selection. The Kmeans algorithm is modified using statistical measure Mean, Median, Partition centre for the cluster centroid calculation. In conventional Kmeans algorithm, the samples are compared with all the partition centroids to decide the inclusion of a sample in a cluster. In Kmeans9+ algorithm, the samples are compared only with the centroids of current and eight nearest neighbouring cluster partitions. It reduces the needless comparisons of samples with cluster centroids and improve the efficiency of the algorithm. The performance of created algorithms is evaluated using data from UCI and KBPE SSLC. Cluster efficiency analysis is done using the cluster evaluation indices such as Silhouette and Dunn Index. Nine nearest neighbour uniform partition cluster model Kmeans9+ improve the performance of the K means algorithm and obtain the natural cluster results with minimum iterations.

Optimization of Linear Quantization for General and Effective Low Bit-Width Network Compression

Current edge devices for neural networks such as FPGA, CPLD, and ASIC can support low bit-width computing to improve the execution latency and energy efficiency, but traditional linear quantization can only maintain the inference accuracy of neural networks at a bit-width above 6 bits. Different from previous studies that address this problem by clipping the outliers, this paper proposes a two-stage quantization method. Before converting the weights into fixed-point numbers, this paper first prunes the network by unstructured pruning and then uses the K-means algorithm to cluster the weights in advance to protect the distribution of the weights. To solve the instability problem of the K-means results, the PSO (particle swarm optimization) algorithm is exploited to obtain the initial cluster centroids. The experimental results on baseline deep networks such as ResNet-50, Inception-v3, and DenseNet-121 show the proposed optimized quantization method can generate a 5-bit network with an accuracy loss of less than 5% and a 4-bit network with only 10% accuracy loss as compared to 8-bit quantization. By quantization and pruning, this method reduces the model bit-width from 32 to 4 and the number of neurons by 80%. Additionally, it can be easily integrated into frameworks such as TensorRt and TensorFlow-Lite for low bit-width network quantization.

Defect Data Mining of Power Consumption Law Based on Improved K-Means Algorithm Clustering

With the further construction and development of the smart grid, in the process of power development, production, and use, as well as the process of power distribution and use, each link will produce some high-dimensional data on the power grid with huge volume, complex structure, and complex correlation among them. The distribution of high-dimensional data in space is different from that in low-dimensional space, and the computational cost increases dramatically, which increases the complexity of visualization of high-dimensional power consumption data. Clustering analysis is a way to cluster a large number of users and summarize the typical load characteristics of different types of users. How to determine the prior information conditions of data and how to select the clustering criteria become the key to clustering. Aiming at the problems of traditional clustering algorithms in the current feature clustering analysis, this paper first deals with the load through t-SNE dimensional reduction technology, then combines the GSA elbow criterion and dichotomous K-means algorithm to cluster the load, and finally summarizes three typical load features according to the clustering results. Effective data mining technology is used to cluster and divide the massive load characteristics efficiently, which will dynamically respond to and manage the demand side. The error of classification results is less than 4.28% through the example of load characteristics. The classification accuracy of the test is 12.2% higher than that of the traditional method. According to the experimental results, the characteristics of typical load patterns and the corresponding load curve characteristics are analyzed. It overcomes the dependence of the traditional K-means algorithm on the initial centroid, avoids the algorithm falling into local optimum, and plays an important role in the defect data mining of power consumption law in power enterprises.

Clustering of massive datasets using an Adaptive and efficient K-Means approach

In today’s technology-driven and Internet-obsessed society, it can be challenging to go through huge amounts of information and find relevant knowledge for various educational contexts. Simple, fast, and adaptable machine learning algorithms make such tasks easier to complete. K-means is the most effective unsupervised learning technique for classifying data into meaningful groups. K-means groups data by shared characteristics. K-means clusters are determined by k. Unfortunately, standard k-means requires a lot of math. Scholars have suggested strategies to improve k-means grouping. This work recommends computing initial centroids and establishing a distance between data points that are unlikely to change their cluster in subsequent iterations and those that are extremely likely to do so to lessen the load of k-means clustering for very large data sets. This piece will find information digits whose cluster is statistically likely to alter in the following few cycles. After processing several datasets, it is compared to other K-Means methods

Initial centroid selection for K- means clustering algorithm using the statistical method

An iterative process that converges to one of the many local minima is used in practical clustering methods. K-means clustering is one of the most well-liked clustering methods. It is well known that these iterative methods are very susceptible to the initial beginning circumstances. In order to improve K-means clustering's performance, this research suggests a novel method for choosing initial centroids. The suggested approach is evaluated with online access records, and the results demonstrate that better initial starting points and post-processing cluster refinement result in better solutions.

On fly hybrid swarm optimization algorithms for clustering of streaming data

Clustering is an important data analysis technique for extracting knowledge and hidden patterns in the data. Recently hybrid clustering algorithms have been proposed to solve the local optimum and poor robustness problem due to improper selection of initial cluster centroids in the traditional clustering algorithms. In hybrid algorithms, clustering is solved as an optimization problem by invoking optimization algorithms to find the optimal cluster centroid. Many hybrid clustering algorithms integrating different swarm algorithms and traditional clustering algorithms have been proposed. However, these algorithms were not designed for the on-fly clustering of streaming data. This is necessary for real-time streaming requirements in financial domains like stock markets. This work proposes an on-fly hybrid swarm optimization algorithm for the clustering of streaming data.

Analysis of Power Load Characteristics Based on Adaptive Ensemble Clustering Algorithm

With the growing number of power users and more flexible power consumption, how to cluster the power load curves efficiently becomes particularly important. In order to improve the accuracy, effectiveness and rapidity of load clustering, an adaptive integrated fuzzy clustering algorithm was proposed in this paper. Firstly, the initial clustering centroids were obtained by the improved DPC algorithm; then, under the dual guarantee of Euclidean distance and membership, FCM algorithm was used to cluster load curves; finally, the optimal number of clusters was obtained by the improved adaptive method in the iterative process; thus, the autonomous and accurate clustering of power load curve was realized. The proposed algorithm, DPC algorithm and FCM algorithm were applied to the load clustering experiment of power system respectively. The comparative analysis shows that this algorithm is effective and superior for load curve clustering.

Enhanced Firefly-K-Means Clustering with Adaptive Mutation and Central Limit Theorem for Automatic Clustering of High-Dimensional Datasets

Metaheuristic algorithms have been hybridized with the standard K-means to address the latter’s challenges in finding a solution to automatic clustering problems. However, the distance calculations required in the standard K-means phase of the hybrid clustering algorithms increase as the number of clusters increases, and the associated computational cost rises in proportion to the dataset dimensionality. The use of the standard K-means algorithm in the metaheuristic-based K-means hybrid algorithm for the automatic clustering of high-dimensional real-world datasets poses a great challenge to the clustering performance of the resultant hybrid algorithms in terms of computational cost. Reducing the computation time required in the K-means phase of the hybrid algorithm for the automatic clustering of high-dimensional datasets will inevitably reduce the algorithm’s complexity. In this paper, a preprocessing phase is introduced into the K-means phase of an improved firefly-based K-means hybrid algorithm using the concept of the central limit theorem to partition the high-dimensional dataset into subgroups of randomly formed subsets on which the K-means algorithm is applied to obtain representative cluster centers for the final clustering procedure. The enhanced firefly algorithm (FA) is hybridized with the CLT-based K-means algorithm to automatically determine the optimum number of cluster centroids and generate corresponding optimum initial cluster centroids for the K-means algorithm to achieve optimal global convergence. Twenty high-dimensional datasets from the UCI machine learning repository are used to investigate the performance of the proposed algorithm. The empirical results indicate that the hybrid FA-K-means clustering method demonstrates statistically significant superiority in the employed performance measures and reducing computation time cost for clustering high-dimensional dataset problems, compared to other advanced hybrid search variants.

Analysing Kinship in Severe Acute Respiratory Syndrome Coronavirus 2 DNA Sequences Based on Hierarchical and K-Means Clustering Methods Using Multiple Encoding Vector

<em>Based on the World Health Organization data obtained in mid-April 2021, Coronavirus or Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) has already infected more than 134.9 million people worldwide. The virus attacks human breathing, which can cause lung infections and even death. More than 2.9 million people worldwide have died due to coronavirus infection. Meanwhile in Indonesia, more than 1.5 million people has been infected and 42.5 thousand people died because of this coronavirus. Based on this data, it is important to carry out a kinship analysis of the coronavirus to reduce its spread. Identification of the kinship of the COVID-19 virus and its spread can be done by forming a phylogenetic tree and clustering. This study uses the Multiple Encoding Vector method in analysing the sequences and Euclidean distance to determine the distance matrix. This research will then use the Hierarchical clustering method to determine the number of initial centroids, which will be used later by the K-Means clustering method kinship in the SARS-CoV-2 DNA sequence. This study took samples of DNA sequences of SARS-CoV-2 from several infected countries. From the simulation results, the ancestors of SARS-CoV-2 came from China. The results of the analysis also show that the closest ancestors of COVID-19 to Indonesia came from India. The SARS-CoV-2 DNA sequence also consisted of nine clusters, and the sixth cluster has the most number of members.</em>

Initial curvature and centroid positioning effects on cross-axis flexural pivots accuracy

Cross-axis flexural pivots have been implemented in a variety of applications and many studies have been focused on their accuracy. In this investigation, initial curvature of flexible elements and positioning of their centroids are exploited to improve the rotational performance of the cross-axis pivot. A parametric geometry based on two design variables is developed and proper accuracy criteria are introduced. Rotational performance is evaluated by means of the chained beam constraint model and by nonlinear numerical simulations. Accuracy, stiffness and stress maps are presented. • The design of high-accuracy cross-axis flexural pivots is addressed. • Initial curvature and centroids positioning are exploited to improve accuracy. • A 2-DoF parametric geometry and specific accuracy criteria are introduced. • Accuracy is evaluated by chained beam constraint model and nonlinear FEA. • Accuracy, stiffness and stress design maps are presented.

KNN Algorithm for Identification of Tomato Disease Based on Image Segmentation Using Enhanced K-Means Clustering

Image segmentation is an important process in identifying tomato diseases. The technique that is often used in this segmentation is k-means clustering. One of the main problems in this technique is the case of local minima, where the cluster that is formed is not suitable due to the incorrect selection of the initial centroid. In image data, this case will have an impact on poor segmentation results because it can erase parts that are actually important to be lost or there is still background in the recognition process, which has an impact on decreasing accuracy results. In this research, a method for image segmentation will be proposed using the k-means clustering algorithm, which has been added with the cosine similarity method as the proposed contribution. The use of the cosine method will determine the initial centroid by calculating the level of similarity of each image feature based on color and dividing them into several categories (low, medium, and high values). Based on the results obtained, the proposed algorithm is able to segment and distinguish between leaf and background images with good results, with the kNN reaching a value of 94.90% for accuracy, 99.50% for sensitivity, and 93.75% for specificity. The results obtained using the kNN method with k-means segmentation obtained a value of 92.46% for accuracy, 96.30% for sensitivity, and 91.50% for specificity. The results obtained using the kNN method without segmentation obtained a value of 90.22% for accuracy, 93.30% for sensitivity, and 89.45% for specificity.