IMPLEMENTATION OF K-MEANS ALGORITHM ELBOW METHOD AND SILHOUETTE COEFFICIENT FOR RAINFALL CLASSIFICATION

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.

Social media has become a central part of daily life in Indonesia, yet the rapid growth of digital platforms presents challenges in analyzing large, unstructured user data. Responding to this issue, this study aims to cluster the behavioral patterns of Indonesian social media users using the K-Means Clustering algorithm, a data mining technique for unsupervised segmentation. Employing a quantitative approach, data were collected through an online questionnaire from 553 respondents aged 15–80 years. After data cleaning, normalization, and feature encoding, the optimal number of clusters was determined using the Elbow method and Silhouette Coefficient, resulting in two clusters with a Silhouette score of 0.177. Cluster 0 (303 respondents) represents highly interactive multi-platform users active on Instagram, TikTok, and YouTube for 3–6 hours daily, showing strong interest in entertainment and motivational content. Cluster 1 (250 respondents) includes more passive users, mainly on Instagram and TikTok, spending 3–4 hours per day with moderate engagement and a preference for motivational and self-development content. The findings demonstrate that K-Means Clustering effectively maps user behavior based on platform use, content preferences, motivations, and interaction patterns. The implications of these findings suggest that digital communication strategies need to be tailored to the characteristics of each user cluster so that the messages and content conveyed are more effective.

One of the educational problems that must be faced by East Java Province is the low reading culture of the community. The level of reading culture can be indicated by the Reading Literacy Activity Index (Alibaca Index). Alibaca Index of East Java is only 33.19 which value is included in the low category. So, this research uses the indicators that compose the Alibaca Index to classify regencies/cities in East Java Province. The analysis process carried out in this research uses one of the unsupervised learning algorithms, namely the K-Means algorithm. Analysis using the K-Means algorithm for grouping regencies/cities in East Java Province based on the indicators that compose the Alibaca index gives the results that the regencies/cities of East Java Province are divided into 3 clusters based on the optimal number of clusters according to the result of the elbow and silhouette method. Cluster 1 consists of 20 regencies and cities, cluster 2 consists of 10 regencies, and cluster 3 consists of 8 cities. Each cluster has different characteristics, cluster 1 is the cluster with the lowest skill dimension, while the cluster 2 area is an area that dominates the access dimension, alternative dimension, and cultural dimension, meanwhile, the third cluster does not have dominance in these 3 dimensions, which means that cluster 3 is the government's priority for improving reading activities, so the result of the analysis can help the government to develop strategic policies to achieve educational equity, especially concerning literacy levels based on the characteristics of each regency/city in East Java Province.

This research presents a comparative analysis of the Elbow and Silhouette methods to identify the ideal number of clusters in applying the K-Prototypes algorithm for customer grouping using purchase transaction data. The K-Prototypes algorithm is employed due to its ability to handle both numerical and categorical data simultaneously. Customer purchase transaction data from the Point of Sale (POS) system is analyzed through preprocessing, feature transformation, and attribute segmentation stages before being clustered using the K-Prototypes algorithm. To identify the optimal cluster count, this study employs two methods: the Elbow and the Silhouette method. The results indicate that the Elbow method produces 2 clusters with a model evaluation score of 0.6368, while the Silhouette method suggests 2 clusters with a slightly lower score of 0.6186. In terms of computational efficiency, the Elbow method also demonstrates a faster processing time results highlight the significance of choosing an appropriate method for identifying the ideal number of clusters, ensuring it aligns with the specific goals of the analysis, whether emphasizing superior inter-cluster distinction or favoring a more parsimonious model configuration.

This study analyzes the spatial distribution patterns of Transjakarta service users in Jakarta using the K-Means Clustering algorithm. The dataset, obtained from the Kaggle platform, consists of 189,501 passenger transaction records, including tap-in and tap-out locations, travel times, and user-related information. The research process involves data collection, preprocessing to remove missing values, application of the K-Means Clustering algorithm, and determination of the optimal number of clusters using the elbow method. Based on the analysis, the optimal number of clusters is identified as four (K=4). A scatter plot visualization presents user distribution patterns based on geographic coordinates and service usage times. Each cluster represents a group of users with similar travel characteristics. This analysis results in a segmentation that reflects variations in Transjakarta passenger mobility patterns and illustrates how travel activity is distributed across spatial and temporal dimensions within the urban area of Jakarta.

This study applies the K-Means clustering algorithm to group 38 regencies and cities in East Java Province based on five Human Development Index (HDI) indicators for the year 2024. These indicators include Life Expectancy (UHH), Expected Years of Schooling (HLS), Mean Years of Schooling (RLS), and Real Expenditure Per Capita (PPK). The aim of this research is to uncover hidden patterns and disparities in regional development, which can be used as a basis for more targeted and data-driven policy interventions.The optimal number of clusters was determined using three evaluation metrics: the Elbow Method, Silhouette Score, and Davies-Bouldin Index. These evaluations collectively identified three distinct clusters. Cluster 0 represents regions with high levels of development across all indicators. Cluster 1 consists of regions with moderate development levels and potential for improvement, while Cluster 2 contains regions with significantly lower values, particularly in education and income metrics.In addition to clustering, a correlation analysis was conducted to examine the relationship between HDI and its supporting indicators. The results show that Mean Years of Schooling (RLS) and Real Expenditure Per Capita (PPK) have the strongest positive correlation with HDI across all clusters. This highlights the key role of education and economic well-being in improving human development. The findings emphasize the importance of clustering analysis in shaping equitable and region-specific development strategies.

Melasma management is challenged by heterogeneity in patient presentation, particularly among individuals with darker skin tones. This study applied k-means clustering, an unsupervised machine learning algorithm that partitions data into k distinct clusters based on feature similarity, to identify patient subgroups that could provide a hypothesis-generating framework for future precision strategies. We analysed clinical and demographic data from 150 South African women with melasma using k-means clustering. The optimal number of clusters was determined using the Elbow Method and Bayesian Information Criterion (BIC), with t-distributed stochastic neighbour embedding (t-SNE) visualization for assessment. The k-Means algorithm identified seven exploratory patient clusters explaining 52.6% of the data variability (R2 = 0.526), with model evaluation metrics including BIC = 951.630 indicating optimal model fit and a Silhouette Score of 0.200 suggesting limited separation between clusters consistent with overlapping clinical phenotypes, while the Calinski-Harabasz index of 26.422 confirmed relatively well-defined clusters that were characterized by distinct profiles including “The Moderately Sun Exposed Young Women”, “Elderly Women with Long-Term Melasma”, and “Younger Women with Severe Melasma”, with key differentiators being age distribution and menopausal status, melasma severity and duration patterns, sun exposure behaviours, and quality of life impact profiles that collectively define the unique clinical characteristics of each subgroup. This study demonstrates how machine learning can identify clinically relevant patient subgroups in melasma. Aligning interventions with the characteristics of specific clusters can potentially improve treatment efficacy.

Korean dramas are highly popular in Indonesia, but it is a challenge for marketers to understand the diverse tastes of the audience. This study aims to identify audience preference segments by applying the K-Means algorithm to perform clustering. The analysis was conducted on 500 Korean dramas from the MyDramaList platform released in the period 2020 to 2023. Features used in the clustering process include rating, number of viewers (no_of_viewers), year of release (year), and genre. To overcome the multi-label genre, this research uses one-hot encoding technique to convert categorical data into numerical format. The optimal number of clusters was determined as four (4) based on analysis using the Elbow Method. The analysis successfully identified four distinct audience segments. Cluster 1 is the largest market segment which includes 323 dramas with a dominant genre of “Drama and Romance” and an average rating of 7.64. In contrast, Cluster 2 is a high-quality niche segment consisting of only 16 dramas but has the highest average rating (8.29) as well as the highest average viewership (25,739), with the dominant genre of “Drama and Mystery”. The other two segments are Cluster 0 (58 dramas) which focuses on the “Thriller” and ‘Mystery’ genres, and Cluster 3 (147 dramas) which features the “Comedy, fantasy and romance” genres. These data-driven findings enable the development of more specific and targeted marketing strategies for each audience profile, thereby improving promotional effectiveness as well as the viewing experience.

PurposeCombining the collected human body variables by a 3D body scanner and the research results of medical computed tomography (CT) imaging, this research aims to develop a military bulletproof vest that is both protective and fit. In particular, the protective part must be able to cover the vital human internal organs completely. The results of this research help to make military bulletproof vests of different sizes for Taiwanese male and female soldiers. At the same time, the research results can provide a reference for the industry of making special-purpose clothing.Design/methodology/approach17 important human body variables of 988 participants (male: 716, 72.5%; female 272, 27.5%) are used for the analysis. The K-means algorithm firstly builds clusters of different body shapes for both sexes; the silhouette coefficient helps to determine the optimal number of clusters to be six. Thus, the standard size of the bulletproof vest for soldiers is determined. The specifications of the bulletproof vest's inner core and textile vest are calculated for each cluster user. Our research then makes twelve prototypes of the bulletproof vest. After that, 12 subjects are invited to try on the new version (the vest designed in this study) and the old version (the vest currently used) to contrast the differences between the two.FindingsAccording to the index of the silhouette coefficient, the optimal number of clusters is determined to be six for both male and female clusters. Therefore, this study has designed six sizes of the bulletproof vest for male and female soldiers in Taiwan. After trying the new and old vests on, the subjects all indicate that the new vest fits better than the old one. In addition, the coverage of the bulletproof vest designed in this study is 94.38% for male users and 92.75% for female users.Originality/valueThe design of bulletproof vests must take note of the fit of the clothing itself and its protective function. Apart from the size design of general clothing only focusing on the human shape exteriorly, the bulletproof vest also needs to pay attention to the relative positions of vital organs inside the human body. Besides, for practical applications, it is quite effective to use the silhouette coefficient to determine the results of cluster analysis. Thus, the value of this research lies in the cross-field combination, enabling the integration of body measurement, data science and clothing design. Generally, bulletproof vests of newly designed sizes can meet the requirements of Taiwan's military. The research results can be used in the development of various military clothing for Taiwanese military personnel. At the same time, the results can be provided to the clothing industry as relevant parameters for designing unique functional clothing.

Stunting is a condition of malnutrition status that is chronic in growth and development from the beginning of life. Malnutrition puts children at greater risk of death. One of the efforts to overcome stunting is to determine in advance the provinces that need to be prioritized in handling the factors that cause stunting by grouping 34 provinces in Indonesia. This study uses k-means clustering to partition data according to their respective characteristics into the form of two or more clusters, determining the optimal number of clusters through elbow optimization methods, gap statistics, and silhouette. The method used to test the best cluster results is the Davies Bouldin Index (DBI) method. The results of the elbow method clustering test produce K = 3 with a DBI value of 0.6392677; the gap statistics method produces K = 1 without DBI testing because only 1 cluster is formed, while the silhouette method produces K = 2 with a DBI value of 0.2116945. This shows that the results of clustering k-means with the silhouette method produce better cluster quality because it has a lower DBI value than other methods.

Automatic segmentation of tissue sections using the multielement information provided by LA-ICP-MS imaging and k-means cluster analysis

To find an optimal cluster size and number of clusters for a reasonable estimate of the prevalence of cataract blindness in people aged > or = 50 years in 19 rural districts of a state in India. Cluster sampling methodology was used in 19 rural districts of Karnataka State, India. In each district, 15 clusters were randomly selected and 90 people aged > or = 50 years were examined in each cluster. As a result the visual acuity and lens status of a total of 22,218 people were assessed. For each district, the design effect for cluster size ranging from 20 to 90 was calculated and the optimal cluster size and the required number of clusters to achieve an accuracy of 1% errors and 80% confidence was assessed. The age and gender adjusted prevalence of cataract blindness varied from 1.58% to 7.24%, which justifies district level surveys. The design effect is nearly 1.5 for clusters of sizes 30 and 40. With an average prevalence of 4.93% with 1% error and 80% confidence level, the optimal number of clusters is 37 and 28 for a cluster size of 30 and 40 respectively and the average sample size for a district around 1100. Rapid assessments for cataract blindness in those aged > or = 50 years can be conducted at district level in India with existing resources and at affordable costs. These provide reliable data, essential for effective monitoring and planning. Other parameters, for instance, surgical coverage can also be assessed. The availability of standardized software for data entry and analysis and strict adherence to survey procedures is essential.

Background Bladder pain syndrome/interstitial cystitis (BPS/IC) is a chronic condition characterized by pelvic pain and urinary symptoms. Despite its significant impact on patients' quality of life, the heterogeneity of BPS/IC symptoms and the presence of comorbidities such as vulvodynia may not be adequately captured by validated questionnaires. Identifying vulvodynia in BPS/IC patients is crucial for providing appropriate treatment options. This study aimed to identify subtypes of BPS/IC patients using unsupervised machine learning and to investigate the prevalence of vulvodynia in each subtype. Methods We conducted a prospective cross-sectional study of 123 BPS/IC patients and 64 age-matched controls. Hierarchical clustering was performed using data from validated questionnaires, including the Numerical Rating Scale-11, Interstitial Cystitis Symptom Index (ICSI), Interstitial Cystitis Problem Index (ICPI), Pelvic Pain and Urgency/Frequency scores, Overactive Bladder Questionnaire Short Form (OABq SF), Overactive Bladder Symptom Score (OABSS), and Pelvic Floor Distress Inventory-20. The optimal number of clusters was determined using the elbow method, and the characteristics of each cluster were analyzed. All participants underwent a vulvodynia swab test to assess vulvodynia symptoms. Results Unsupervised machine learning revealed three distinct clusters of BPS/IC patients. Clusters 0 and 2 differed significantly, with Cluster 2 characterized by significantly higher vulvodynia scores compared to other clusters (P < 0.001). In contrast, Cluster 2 had lower bladder pain scores (ICSI and ICPI) and overactive bladder symptom scores (OABq SF and OABSS) compared to other clusters. Clusters 0 and 1 were characterized by a predominance of bladder pain and urinary frequency symptoms, with Cluster 0 exhibiting more severe symptoms. Conclusions Our study identified distinct subtypes of BPS/IC patients using unsupervised machine learning, with Cluster 2 representing a vulvodynia-predominant subtype. This finding, along with the potential of targeted therapies such as non-ablative erbium YAG laser for vulvodynia, underscores the importance of assessing extravesical symptoms, particularly vulvodynia, for the diagnosis and treatment of BPS/IC. A tailored approach, including laser therapy for vulvodynia-predominant patients, may be necessary for optimal management of BPS/IC. The vulvodynia swab test plays a crucial role in assessing vulvodynia symptoms, underlining the limitations of validated questionnaires in capturing the full spectrum of BPS/IC symptoms. A comprehensive evaluation of patients, including the vulvodynia swab test, is essential for accurate subtyping and management of BPS/IC. Further research with larger sample sizes and investigation of the relationship between identified subtypes and other clinical data is warranted to advance our understanding and management of BPS/IC.

One of the major new concepts in 5G cellular communications is a shift in the way services are delivered to users. In the new 5G protocol, individual users are recognized and tracked through beams, which are targeted and specific to individual users. The millimeter‐wave (mmWave) communications impose a directionality which results in a significant challenge in serving mobile terminals and unmanned aerial vehicles. This challenge can be relieved in mmWave systems using analog beamforming. Based on the identification of the patterns in the reference signal received power (RSRP) measurements, some classifications are employed. Some trajectories are defined for different users in Hallways. Therefore, the angle of arrival (AoA) would be the same for the users following the same trajectory. The users based on the received RSRP values are clustered by K‐means and I‐Kmeans algorithms. To this end, our algorithms to find the beamforming coefficient are employed for only one user in each cluster and the complexity of the algorithms can be lower. The proposed algorithms are spatial frequency‐based beam tracking and angular domain beam tracking algorithms. Simulation results show that tracking the sine function of AoA achieves better performance compared to tracking the AoA. Moreover, the optimal number of clusters is obtained by using the Elbow method.

With the rapid increase in electric vehicle ownership, charging infrastructure faces issues of insufficient quantity and unreasonable distribution, making the rational layout of charging stations critical. This paper introduces the K-means clustering algorithm, integrating data such as charging station power and number of charging piles to construct a demand feature dataset encompassing five dimensions: charging start time concentration, off-peak electricity utilization rate, and others. After data preprocessing and standardization, clustering analysis is conducted. The optimal number of clusters is determined using the elbow method. Clusters are formed by calculating the Euclidean distance between samples and cluster centers, categorizing stations into three groups: low utilization(average daily utilization <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$&lt;20 \%$</tex>), high utilization(average daily utilization <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$&gt;60 \%$</tex>), and medium utilization(average daily utilization <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$30-40 \%$</tex>, with weekend utilization exceeding weekdays). Cluster characteristics were visualized using radar charts and bar charts. Finally, differentiated optimization strategies were proposed for each category: low-utilization sites should revitalize resources through demand diversion and cost reduction; medium-utilization sites should balance supply and demand via time-differentiated pricing; high-utilization sites should address peak load pressures through facility expansion and fault early warning systems. This research provides scientific grounds for charging station operation, maintenance, and layout planning, supporting the efficient development of charging infrastructure.