Davies-Bouldin Index Research Articles

A Review on Appropriateness of Partitional Clustering Algorithms in Handling Transactional Data

Clustering is an unsupervised learning that widely used in vast researches area. The technique also utilized in any disciplines that involves multivariate data analysis. In term of transactional data handling, the partitional clustering is promoted as the one method to explore knowledge from several attributes that are related the business. In this paper, we investigate the use of partitional clustering algorithms including k-means, k-medoids, Fuzzy C Means, CLARA, and CLARANS. The present article delineates the various stages that are integral to accomplishing a review. These stages encompass data collection, data pre-processing, determination of the number of clusters, implementation of algorithms, and evaluation of clustering. The study pointed out that k-medoids as the most potential to be implemented in handling transactional data. The algorithm has achieved commendable scores in two out of three metrics, namely Calinski-Harabasz Index and Silhouette Index but not for the Davies-Bouldin Index. Nevertheless, k-medoids algorithm emerges as a formidable tool in handling the transactional data and facilitating enhanced decision-making. It is our hope that the knowledge acquired from this research will leading to progress in diverse fields where transactional data holds a crucial position. Keywords: Partitional Clustering, Transactional Data, k-means, k-medoids, Fuzzy C Mean, CLARA, CLARANS

Service quality dealer identification: the optimization of K-Means clustering

Service quality and customer satisfaction directly influence company branding, reputation and customer loyalty. As a liaison between producers and consumers, dealers must preserve valuable consumer relationships to increase customer satisfaction and adherence. Lack of comprehensive measurement and standardization regarding service quality emerges as a consideration issue towards the company service excellence. Therefore, identifying the service quality performance and grouping develops into valuable contributions in decision-making to control and enhance the company's intention. This study applies the K-Means Algorithm by optimizing the number of clusters in identifying dealer service quality performance. Hence, the ultimate service quality formation will be performed. The analysis found three dealer identification categories, including Cluster One, with 125 dealers grouped as good performance; Cluster Two, with 30 dealers grouped as very good performance; and Cluster Three, with 38 dealers grouped as not good performance. In order to evaluate the efficacy of optimum k value, the lists of testing approaches are conducted and compared, whereby Calinski-Harabasz, Elbow, Silhouette Score, and Davies-Bouldin Index (DBI) contribute in k=3. As a result, the optimum clusters are determined through the highest performance of k values as three. These three clusters have successfully identified the service quality level of dealers effectively and administered the company guidelines for corrective actions and improvements in customer service quality instead of the standardized normal distribution grouping calculation.

Comparison of K-Means & K-Means++ Clustering Models using Singular Value Decomposition (SVD) in Menu Engineering

The menu is one of the most fundamental aspects of business continuity in the culinary industry. One of the tools that can be used for menu analysis is menu engineering. Menu engineering is an analytical tool that assists restaurants, companies, and small and medium-sized enterprises (SMEs) in assessing and making decisions on marketing strategies, menu design, and sales so that it can produce maximum profit. In this study, several menu engineering models were proposed, and the performance of these models was analyzed. This study used a dataset from the Point of Sales (POS) application in an SME engaged in the culinary field. This research consists of three stages. First, pre-processing the data, comparing the models, and evaluating the models using the Davies Bouldin index. At the model comparison stage, four models are being compared: K-Means, K-Means++, K-Means using Singular Value Decomposition (SVD), and K-Means++ using SVD. SVD is used in the dataset transformation process. K-Means and K-Means++ algorithms are used for grouping menu items. The experiments show that the K-Means++ model with SVD produced the most optimal cluster in this research. The model produced an average cluster distance value of 0.002; the smallest Davies-Bouldin Index (DBI) value is 0.141. Therefore, using the K-Means++ model with SVD in menu engineering analysis produces clusters containing menu items with high similarity and significant distance between groups. The results obtained from the proposed model can be used as a basis for strategic decision-making of managing price, marketing strategy, etc., for SMEs, especially in the culinary business.

STGNNks: Identifying cell types in spatial transcriptomics data based on graph neural network, denoising auto-encoder, and [formula omitted]-sums clustering

Background:Spatial transcriptomics technologies fully utilize spatial location information, tissue morphological features, and transcriptional profiles. Integrating these data can greatly advance our understanding about cell biology in the morphological background. Methods:We developed an innovative spatial clustering method called STGNNks by combining graph neural network, denoising auto-encoder, and k-sums clustering. First, spatial resolved transcriptomics data are preprocessed and a hybrid adjacency matrix is constructed. Next, gene expressions and spatial context are integrated to learn spots’ embedding features by a deep graph infomax-based graph convolutional network. Third, the learned features are mapped to a low-dimensional space through a zero-inflated negative binomial (ZINB)-based denoising auto-encoder. Fourth, a k-sums clustering algorithm is developed to identify spatial domains by combining k-means clustering and the ratio-cut clustering algorithms. Finally, it implements spatial trajectory inference, spatially variable gene identification, and differentially expressed gene detection based on the pseudo-space-time method on six 10x Genomics Visium datasets. Results:We compared our proposed STGNNks method with five other spatial clustering methods, CCST, Seurat, stLearn, Scanpy and SEDR. For the first time, four internal indicators in the area of machine learning, that is, silhouette coefficient, the Davies-Bouldin index, the Caliniski-Harabasz index, and the S_Dbw index, were used to measure the clustering performance of STGNNks with CCST, Seurat, stLearn, Scanpy and SEDR on five spatial transcriptomics datasets without labels (i.e., Adult Mouse Brain (FFPE), Adult Mouse Kidney (FFPE), Human Breast Cancer (Block A Section 2), Human Breast Cancer (FFPE), and Human Lymph Node). And two external indicators including adjusted Rand index (ARI) and normalized mutual information (NMI) were applied to evaluate the performance of the above six methods on Human Breast Cancer (Block A Section 1) with real labels. The comparison experiments elucidated that STGNNks obtained the smallest Davies-Bouldin and S_Dbw values and the largest Silhouette Coefficient, Caliniski-Harabasz, ARI and NMI, significantly outperforming the above five spatial transcriptomics analysis algorithms. Furthermore, we detected the top six spatially variable genes and the top five differentially expressed genes in each cluster on the above five unlabeled datasets. And the pseudo-space-time tree plot with hierarchical layout demonstrated a flow of Human Breast Cancer (Block A Section 1) progress in three clades branching from three invasive ductal carcinoma regions to multiple ductal carcinoma in situ sub-clusters. Conclusion:We anticipate that STGNNks can efficiently improve spatial transcriptomics data analysis and further boost the diagnosis and therapy of related diseases. The codes are publicly available at https://github.com/plhhnu/STGNNks.

Analysis of risk factors in diabetics resulted from polycystic ovary syndrome in women by EDA analysis and machine learning techniques

This study discusses the relationship between Polycystic Ovary Syndrome (PCOS) and diabetes in women, which has become increasingly prevalent due to changing lifestyles and environmental factors. The characteristic that distinguishes women with PCOS is hyperandrogenism which results from abnormal ovarian or adrenal function, which leads to the overproduction of androgens. Excessive androgens in women increase the risk of Type 2 diabetes (T2D) and insulin resistance (IR). Nowadays, diabetes affects people of all ages and is linked to factors such as lifestyle, genetics, stress, and aging. Diabetes, the uncontrolled high blood sugar level can potentially harm kidneys, nerves, eyes, and other organs and there is no cure, making it a concerning disease in developing nations. This research tried to submit the evidence through feature-wise correlation analyses between PCOS and diabetes. Hence, this model utilized the Exploratory Data Analysis (EDA) and the Elbow clustering algorithms for the experimental purpose in which the EDA deeply analyzed the features of PCOS and diabetes and recorded a positive correlation of 95%. The Elbow clustering technique is employed for verifying the correlations identified through EDA. Although limited research exists on this specific disease, this work provides potential evidence for the research community by evaluating the clustering results using Silhouette Score, Calinski-Harabasz Index, and Davies-Bouldin Index.

A Comparative Investigation of Wavelet Families for Classification of EOG Signals Related to Healthy and ADHD Children.

Based on previous research, there are differences between eye movements of people with attention-deficit hyperactivity disorder (ADHD) and of healthy people, as a result, the existence of differences regarding the electrooculogram (EOG) signals of the 2 groups exists. Thus, this study aimed to examine the recorded EOG signals of 30 ADHD children and 30 healthy children while performing an attention-related task. For this purpose, the EOG signals of these 2 groups were decomposed utilizing various wavelet functions. Afterward, features, including mean, energy, and standard deviation (SD) of approximation and detail wavelet coefficients were calculated. The Davies-Bouldin (DB) index was used for the evaluation of the feature space quality. Finally, the 2 groups were classified using one-dimensional feature vector and support vector machine (SVM). The SD of detail coefficients (db4) was selected as the most effective feature for separating the 2 groups. Statistical analysis revealed that the values of energy and SD of EOG signals' detail coefficients were significantly lower in the ADHD group in comparison with the healthy group (P<.001). These results showed that the speed of the ADHD group's eye movements was slower due to the fact that the high-frequency band activity of EOG signals in the healthy group was higher. In addition, the EOG signals were classified with a detection accuracy of 83.42 ± 3.8%. The results of this study can be applied in designing an EOG biofeedback protocol to treat or mitigate the symptoms of ADHD patients.

Pengelompokan Pupuk Bersubsidi Di Kabupaten Bojonegoro Menggunakan Metode K -Means Clustering

Subsidized fertilizer is a form of the government's commitment to increasing agricultural productivity, increasing food production and sustainable food security, now the price of fertilizer in Bojonegoro district is getting more expensive, this encourages researchers to raise it as the title of the thesis. The purpose of the K-Means Clustering method is to increase knowledge and understanding of computer-based systems. The K-Means algorithm is an iterative clustering algorithm that partitions datasets into a number of K Clusters that have been set at the beginning. The K-Means algorithm is simple to implement and execute, relatively fast, adaptable, commonly used in practice. From the problem of clustering subsidized fertilizers in Bojonegoro Regency, it can be solved using the ¬K-Means method. The K-Means algorithm can precisely group large amounts of data. The determination of the central point (centroid) in the initial process of the K-Means algorithm has a significant influence on the cluster yield. Based on the research conducted, the authors tested the best cluster grouping using the Davies Bouldin Index (DBI). It was found that the results of 3 clusters were the best with a DBI value of 0.527 while 4 clusters with a DBI value of 0.649 and 5 clusters with a DBI value of 0.677. The smaller the resulting value in the test, the better the result will be. Meanwhile, the Mean Square Error (MSE) produced in fertilizer clustering is 0.588 and RMSE is 0.962.&#x0D;

Load profiling of commercial and residential building using clustering technique

Data mining is a promising tool used in processing energy data collected from energy consumers. The knowledge derived from energy data is very pertinent in the formulation of various demand-side management programs. This paper uses clustering techniques to segment the energy consumption patterns of residential and commercial buildings; situated at different geographical locations. The two (2) commonly used clustering techniques: K-Means and Agglomerative Hierarchical Clustering, were employed. The result indicates that the choice of clustering technique for load profiling is highly subjective to the nature of the dataset. Hence, using Davies-Bouldin Index (DB) Index and Silhouette Index (SI) as clustering indicators to select an optimum number of clusters and the best clustering technique. Hierarchical clustering was identified as the most appropriate clustering for the two buildings.

Analysis Of Wordle Games Based on Multiple Logistic Regression and Clustering

The development of social media has led to an increasing number of people participating in the online guessing game Wordle, which has become a popular phenomenon on Twitter. Understanding the difficulty of the Wordle game is important for both players and game designers. This article aims to gain an in-depth understanding of the game by analyzing its gameplay reports and word difficulty. Firstly, this article predicts the distribution of Wordle report results. Using a multivariate logistic regression model, the probability distribution prediction is converted into a classification problem, with word attributes and the average number of guesses per player as independent variables for prediction. At the same time, this article introduces random noise into the model prediction to address low probability issues. The model is evaluated using MAE and RMSE, and sensitivity analysis is conducted using k-fold cross-validation. In order to further evaluate the difficulty of words in the game, this article uses the entropy weight-TOPSIS method combined with the Bi-Kmeans classification model to classify word difficulty. The model results show that word difficulty can be divided into five categories. Finally, this article evaluates the performance of the model using Davies-Bouldin Index and the Silhouette Coefficient, and the results show that the model has strong reliability and persuasiveness.

Comparison Of K-Means, K-Medoids, and Fuzzy C-Means Algorithms for Clustering Drug User’s Addiction Levels

Narcotics, psychotropics, and addictive substances are drugs that can activate brain systems, affect dopamine levels, and cause addiction. In Indonesia, there is a law requiring drug addicts to receive treatment and care. To properly treat a drug addict, it is first necessary to determine the level of addiction. Data mining methods such as clustering can be used to assess a user's level of drug addiction. This study uses the clustering algorithms Fuzzy C-means, K-Medoids, and K-means. The performance of the three clustering algorithms will then be evaluated based on the average similarity of clusters. Data such as how many types of drugs that used, the length of time they were used, the psychiatric status, and the physical condition status, are used. Clustering was accomplished using the data mining software RStudio. The clustering algorithms were then evaluated with the Davies Bouldin Index (DBI). The K-Medoids algorithm was found to have the best average similarity value of cluster for determining drug users' addiction levels based on the results of the analysis.&#x0D; &#x0D;

PERBANDINGAN PERFORMA ALGORITMA K-MEANS, K-MEDOIDS, DAN DBSCAN DALAM PENGGEROMBOLAN PROVINSI DI INDONESIA BERDASARKAN INDIKATOR KESEJAHTERAAN MASYARAKAT

One of the development orientations in Indonesia is to improve the welfare of society. Therefore, it is important to identify and understand the characteristics of community welfare in each province in order to determine effective and targeted development strategies. Cluster analysis is one of the analyses that can be used to group provinces in Indonesia that have homogeneous characteristics within a cluster. The partition method is the simplest and fundamental approach to cluster analysis, but it can only find clusters with spherical-shaped forms. On the other hand, DBSCAN is a density-based clustering algorithm that can be used to find clusters with arbitrary shapes. In this study, the performance of the K-Means, K-Medoids, and DBSCAN algorithms was compared using data that had been dimensionally reduced using the t-SNE method. The data used was the indicator data of community welfare in the year 2022. The evaluation results of clustering based on the highest Silhouette coefficient (0.917) and the lowest Davies-Bouldin index (0.089) indicate that the best clustering methods are K-Means and DBSCAN with parameters perplexity = 1, minPts = 2, and epsilon = 9. Both methods produce the same result, which is the formation of eight clusters.

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.

Analisa Clustering untuk Mengelompokan Data Penayangan Film Bioskop Menggunakan Algoritma K-Means

The purpose of this study is one of the analyzes to obtain film screening data, the approach used in this study is the K-means algorithm using the parameter measure type Numerical Measure with Numerical Measure Euclidean Distance to get the best Davies Bouldin Index (DBI), with the intention of getting helps grouping datasets of film screenings at the Ramayana Cirebon XXI Cinema. Results from the evaluation of the Davies Bouldin Index (DBI) obtained is (K-2) with a Davies Bouldin Index (DBI) value of 0.864, because the value obtained is the smaller the Davies Bouldin Index (DBI) value, it shows the optimum performance of the resulting cluster.

Comparison Performance of K-Medoids and K-Means Algorithms In Clustering Community Education Levels

Education is a mandatory right of all citizens and the key to the nation's superiority in global competition that must get top priority to be examined critically and comprehensively. It is known that compulsory education is at least 12 years, but not all people can do it because of minimal economic conditions. In past years, COVID-19 has also had an impact on the economy, school dropout rates, and falling academic achievement, for example in Central Kalimantan. The size of Central Kalimantan, however, makes it difficult for the government to identify the areas with the worst levels of education. To determine which regions fall into the low and high education categories, it is required to group the province's educational levels. This study also compares two algorithms by measuring their accuracy. By looking at which algorithm has the lowest Davies Bouldin Index (DBI) value, the best degree of performance can be ascertained. To process the data from as many as 1,565 sources, data mining techniques, including the clustering method, were used. K-Means and K-Medoids algorithms were employed in this work as clustering techniques. Based on the outcomes of the cluster created, both algorithms are also put to the test for performance. The results of this study obtained 6 clusters in K-Means with the lowest DBI value of -0.439, while the results in K-Medoids were in 3 clusters with the lowest DBI of -0.866. Based on accuracy testing using DBI, it is known that K-Means results are more optimal with the lowest DBI value in the grouping of education levels compared to K-Medoids. It is also known from the formation of 6 clusters of the K-Means algorithm that the low education level is in cluster_0 which is 1484 villages and the higher education level is as many as 3 villages in cluster_3.

Analysis of Elbow, Silhouette, Davies-Bouldin, Calinski-Harabasz, and Rand-Index Evaluation on K-Means Algorithm for Classifying Flood-Affected Areas in Jakarta

Jakarta is the capital city of Indonesia, which has a high population density, and is an area that is frequently hit by floods. This study aims to determine the classification of flood-affected areas in Jakarta between severe, moderate, and low. Design/method/approach: The study was conducted using the elbow, Silhouette, Davidson-Bouldin, and Calinski-Harabasz methods on the K-means algorithm, as well as the Rand method. index for evaluation. Grouping with 3 and 6 groups is the best grouping value based on Calinski-Harabasz. By using the davies bouldin index from the observations, the K value with a value of 6 has the smallest Davies-Bouldin value with a value of 0.2737. By using sillhoute, the experimental results obtained the best values sequentially, namely K=2, K=3, and K=6 with silhouette values of 0.866, 0.854, and 0.803. In this experiment, based on the elbow method, it was found that the best K value was K=3. This was obtained because it was based on observations on the appearance of the SSE data compared to the value of K. In the graph above, it can be seen that the largest decrease in data occurred at K=3 and after this decrease, the decline began to slope. The rand index is a method used to compare several cluster methods. If the value is &gt;= 90 it is a very good result, if the value is in the range 80 to 90 it identifies a good index, whereas if it is below 80 it indicates a bad index. The results show that cluster three is verified as the best cluster with a value of 1, followed by a second alternative with cluster 2 of 0.9182. From several validation and evaluation methods it can be concluded that the best grouping can be done using 3 clusters. The results of the study yielded a value of 75.4% in low areas, 21.1% in moderate areas, and 3.5% in severe areas.

3D pseudo-lithologic modeling via iterative weighted k-means++ algorithm from Tengger Desert cover area, China

The bedrock beneath the Tengger Desert is covered by Quaternary deposits, making it difficult to directly observe the underlying geological information using traditional geological methods. In areas with limited prior geological information, employing geophysical methods to obtain deep-seated information, constructing a multi-source geophysical dataset, and performing three-dimensional modeling can significantly enhance our understanding of the underground geological structures. Cluster analysis is a fundamental unsupervised machine learning technique employed in data mining to investigate the data structure within the feature space. This paper proposes an iterative weighted distance-based extension to the k-means clustering algorithm, referred to as the Iterative Weighted Distance K-means (IW k-means++) algorithm. It incorporates the farthest distance method to select the initial centroid, performs iterative centroid updates based on weighted distance, and dynamically adjusts feature weights during training. The Davies-Bouldin index shows that the performance of IW k-means ++ clustering algorithm is better than the traditional K-Meme ++ clustering algorithm in 3D pseudo-lithology modeling.

Comparison of the DBSCAN Algorithm and Affinity Propagation on Business Incubator Tenant Customer Segmentation

The increasingly complex business environment necessitates businesses to design more effective and efficient strategies for company development, including market expansion. To understand customer behaviors, customer data analysis becomes crucial. One common approach used to group customers is segmentation based on RFM analysis (Recency, Frequency, and Monetary). This study aims to compare the performance of two clustering algorithms, namely DBSCAN and Affinity Propagation (AP), in providing customer profile segment recommendations using RFM analysis. DBSCAN algorithm is employed due to its ability to identify arbitrarily shaped clusters and handle data noise. On the other hand, Affinity Propagation (AP) algorithm is chosen for its capability to discover cluster centers without requiring a pre-defined number of clusters. The transaction dataset used in this research is obtained from one of the business incubator tenants at STIKOM Bali. The dataset undergoes preprocessing steps before being segmented using both DBSCAN and AP algorithms. Performance evaluation of the algorithms is conducted using the Silhouette Scores and Davies-Bouldin Index (DBI) matrices. The research findings indicate that the AP algorithm outperforms DBSCAN in this customer segmentation case. The AP algorithm yields Silhouette Scores of 0.699 and DBI of 0.429, along with recommendations for 4 customer segments. Furthermore, further analysis is performed on the AP results using a statistical approach based on the mean values of each segment for the RFM variables. The four customer segments generated by the AP algorithm, based on the mean values of the RFM variables, can be associated with the concept of customer relationship management.

Cluster analysis of type II Diabetes Mellitus Patients with the Fuzzy C-means method

Cluster analysis has been widely used in the fields of mathematics and health sciences. This study aims to classify distance-based data which are divided into several clusters. Accurate prediction from the outcome or survival rate of diabetic patients can be the key for the stratification of prognosis and therapy. A retrospective study of 447 medical record data of type II diabetes mellitus patients aged 18 years old or above and were hospitalized in the PKU Muhammadiyah Gamping Hospital from 2015-2019. Clustering is using the PCA-Fuzzy C-Means method based on patients’ survival status, demographic characteristics, therapy, and blood glucose (BG) levels. Clustering evaluation by Davies Bouldin Index (DBI). Data analysis is using Jupyter Notebook programme. Cluster formation are first cluster consists of 171 members, second cluster consists of 9 members, third cluster consists of 267 members with DBI 2,2645. 401 patients (89,7%) were recorded as alive and 46 patients (10,3%) were recorded as dead. A total of 447 patients: 54,1% were male; 90,6% were ≥ 45 years old; 66,4% has comorbidities; 51,7% had BG level of more than 200 mg/dl, and 57,7% received combination insulin+oral antidiabetic therapy.

Towards Detecting Influential Members and Critical Topics from Dark Web Forums

Conventionally, the Internet consists of three parts: Surface, Deep, and Dark Webs. Inthe last two decades, a massive increase in illicit activities took place on the differentplatforms of the Dark Web. Moreover, social networks on Dark Web implicateextremism dissemination on a wide scale. In this paper, we propose an approach togenerate textual patterns from discussions on Dark Web terrorist forums employingData Mining techniques. The discovered patterns help identify the influential membersand extract critical topics. We describe our system modules that perform datapreprocessing, text preprocessing with TF-IDF weighting, outlier detection, clusteringevaluation, clustering, and clustering validation, implemented with the RapidMinertool. We apply K-Means as the Clustering method with different distance metrics,evaluate the clustering process using Elbow and Silhouette methods, and validate itusing Davies-Bouldin Index. Furthermore, we investigate the effects of altering thedistance metrics for outlier detection on the Clustering results.

A Study on Enhanced Spatial Clustering Using Ensemble Dbscan and Umap to Map Fire Zone in Greater Jakarta, Indonesia

This research investigated ensemble clustering algorithms and dimensionality reduction for fire zone mapping, specifically DBSCAN + UMAP. We evaluated six clustering methods: DBSCAN, ensemble DBSCAN, DBSCAN + UMAP, ensemble DBSCAN + UMAP, HDBSCAN and Gaussian Mixture Model (GMM). We evaluated our results based on the Silhouette Score and the Davies-Bouldin (DB) index, emphasizing handling irregular cluster shapes, smaller clusters and resolving incompact clusters. Our findings suggested that ensemble DBSCAN + UMAP outperformed five other methods with zero noise clusters indicating clustering results are resistant to outliers, leading to a clearer identification of fire-prone areas, a high Silhouette Score of 0.971, indicating accurate cluster separation of distinct areas of potential fire hazards and an exceptionally low DB Index of 0.05 that indicates compact clusters to identify well-defined and geographically concentrated areas prone to fire hazards. Our findings contribute to the advanced techniques for minimizing the impacts of fires and improving fire hazard assessments in Indonesia.