Cluster Validity Research Articles

Sounds in common: Time-frequency as the classification parameters for pulsed sounds produced by Delphinus delphis

Sounds produced by dolphins can be grouped into tonal (whistles) and pulsed sounds (e.g., echolocation clicks and burst sounds). Clicks are broadband pulses temporarily spaced to allow echo processing between the sound source and the object. Echolocation is related mainly to prey detection and environmental recognition. Echolocation click trains tend to present a decreasing inter-click interval due to a continuous changing of the target's location when the animal approaches to capture the prey. In addition to foraging and feeding contexts, burst pulsed sounds have been associated with short social communication. Although echolocation clicks are relatively well documented, there is no consensus regarding the broad variety of the burst pulsed signals. The present study analyzed time-frequency characteristics by conducting a clustering and discrimination analysis to classify pulsed sounds. A total of 64 click trains were analyzed from short-beaked common dolphins recorded in the slope region of the western South Atlantic Ocean. Three analyses (time; frequency; and combined time-frequency parameters) were compared through k-means clustering and posterior cluster validation using Random forest analysis. The k-means clustering resulted in four clusters for all groups of analysis. The time parameters were the most accurate among the comparisons, with the first two-dimensional axis corresponding to 87 % (Dim1 = 70.2 % and Dim2 = 17.2 %). The random forest analysis showed that the time-frequency dataset was the best classification of pulsed sounds in D. delphis (Accuracy = 84.6 %; confidence interval CI = 65.1 %-95.6 %; p < 0.01). This result considers the animal an acoustical identity, emphasizing the importance of certain parameters that influence this identity and thus reflecting the energy-cost optimization for sound production.

ANALISIS PERBANDINGAN SILHOUETTE COEFFICIENT DAN METODE ELBOW PADA PENGELOMPOKKAN PROVINSI DI INDONESIA BERDASARKAN INDIKATOR IPM DENGAN K-MEDOIDS

Development is a process of change that is carried out consistently with the aim of improvement in all aspects of life with the prevailing values in society to achieve predetermined life goals. The quality of life of the community is measured by the Human Development Index (HDI) at the provincial level through three indicators, including: economic level, health, and education. K-medoids is a method used to group objects that contain outliers. In determining the optimal number of clusters using the Silhouette Coefficient method which has the advantage of determining the best number of clusters that can measure how close the relationship between objects and measure how far a cluster is separated from other clusters. The technique called the Elbow method is employed to ascertain the optimal quantity of clusters, which is done by examining the percentage outcomes derived from comparing the quantity of clusters that form an elbow at a certain point. Then cluster evaluation is carried out using the Davies Bouldin Index (DBI) as a comparison for cluster validation. The results of this study using the Silhouette Coefficient method produced the best cluster, namely 3 clusters with a Silhoutte Coefficient value of 0,3129 and a DBI value of 1,3184. Meanwhile, using the Elbow method produced the best cluster, namely 4 clusters with an SSE value of 54,5548 with a DBI value of 1,1754. So that the best cluster is 4 clusters with the Elbow method with the smallest DBI value.

Radial Basis Function Neural Network with ensemble clustering for modeling mathematics achievement in Indonesia based on cognitive and non-cognitive factors

Mathematics achievement could be influenced by cognitive and non-cognitive factors. The potential variable of cognitive factor is metacognition, whereas non-cognitive factors include Economic, Social, and Cultural Status (ESCS), resilience, life satisfaction, happiness, pride, fear, sadness, and gender. Those variables involve numerical and categorical data. For this reason, this study aims to apply the Radial Basis Function Neural Network (RBFNN) model with ensemble clustering to model the relation between cognitive and non-cognitive aspects and mathematics achievement. The RBFNN is a soft computing approach based on the neural network model and has been shown as an effective model and free of assumption. The ensemble clustering is a process in RBFNN modeling to capture the independent variables involving the numerical and categorical data. It employs K-means clustering for the numerical data and K-modes for categorical data and combines the results of those two methods. The data used in this study are published by PISA (Program for International Student Assessment) 2018. The results show that the RBFNN with ensemble clustering deliver good performance in modeling the students’ mathematics achievement based on the cognitive and non-cognitive factors in terms of prediction accuracy. Other than RBFNN model, the use of cognitive and non-cognitive factors involving in this study also contributes to the high accuracy prediction. This further emphasizes that these factors are good predictors of mathematic achievement. Additionally, we suggest the silhouette cluster validation in the clustering process, since it leads to the number of hidden neurons of the best RBFNN model.

Implementation of Density-Based Spatial Clustering of Applications with Noise and Fuzzy C – Means for Clustering Car Sales

This study compares the performance of two clustering algorithms, Density-Based Spatial Clustering of Applications with Noise (DBSCAN) and Fuzzy C-Means (FCM), in clustering car sales data at PT. XYZ. The dataset, comprising sales transactions from 2020 to 2023, includes information about vehicles, customers, and transactions. Preprocessing methods such as data transformation and normalization were applied to prepare the data. The results indicate that DBSCAN produces clusters with better validity, measured using the Silhouette Score, compared to FCM. Specifically, DBSCAN achieves the highest Silhouette Score of 0.7874 in cluster 2, while FCM reaches a maximum score of 0.3666 in cluster 3. Thus, DBSCAN proves to be more optimal for clustering car sales data at PT. XYZ, highlighting its superior performance in terms of cluster validity.

Centroid-based clustering validity: method and application to quantification of optimal cluster-data space

Centroid-based clustering validity: method and application to quantification of optimal cluster-data space

From A-to-Z review of clustering validation indices

Data clustering involves identifying latent similarities within a dataset and organizing them into clusters or groups. The outcomes of various clustering algorithms differ as they are susceptible to the intrinsic characteristics of the original dataset, including noise and dimensionality. The effectiveness of such clustering procedures directly impacts the homogeneity of clusters, underscoring the significance of evaluating algorithmic outcomes. Consequently, the assessment of clustering quality presents a significant and complex endeavor. A pivotal aspect affecting clustering validation is the cluster validity metric, which aids in determining the optimal number of clusters. The main goal of this study is to comprehensively review and explain the mathematical operation of internal and external cluster validity indices, but not all, to categorize these indices and to brainstorm suggestions for future advancement of clustering validation research. In addition, we review and evaluate the performance of internal and external clustering validation indices on the most common clustering algorithms, such as the evolutionary clustering algorithm star (ECA*). Finally, we suggest a classification framework for examining the functionality of both internal and external clustering validation measures regarding their ideal values, user-friendliness, responsiveness to input data, and appropriateness across various fields. This classification aids researchers in selecting the appropriate clustering validation measure to suit their specific requirements.

Spatially constrained statistical approach for determining the optimal number of regions in regionalization

Determining the optimal number of regions is a challenging issue in regionalization. Although cluster validity indices developed for non-spatial clustering have been used to determine the optimal number of regions, spatial contiguity constraints for regionalization are often neglected. Consequently, different regionalization results can share the same validity index value, which reduces the reliability of identifying the optimal number of regions in regionalization. To overcome this limitation, this study proposes a spatially constrained statistical approach for determining the optimal number of regions using two metrics: (i) a permutation-based variance for measuring the homogeneity within regions and (ii) a proportion index based on spatially constrained k-nearest neighbors to quantify the separation between regions. Furthermore, a distance-based method is employed to balance these two metrics to automatically determine the optimal number of regions. Experimental results on five synthetic datasets, the US presidential election and climate datasets show that the statistical approach developed in this study outperforms three widely used cluster validity indices in determining the optimal number of regions. The proposed statistical approach is straightforward to implement and can effectively reduce subjectivity in regionalization.

Educational Data Clustering in Secondary School Sensor-Based Engineering Courses Using Active Learning Approaches

The authors investigated the impact of active learning STEM and STEAM approaches on secondary school students’ general engineering knowledge, intrinsic relevance, and creativity. Three out-of-school sensor-based courses were held successively. Every sensor-based course involved the final project development. A structured questionnaire was administered to 379 students and consisted of two critical factors: creativity and intrinsic relevance. The third factor was dedicated to the students’ engineering learning outcomes. Two factors were addressed to secondary school students, while the third factor was addressed to the tutors’ observations of the students’ general sensor-based knowledge. Clustering validation analysis quantified the obtained results and justified the significant differences in all estimated factors for different educational modes. Moreover, the study showcases the value of the arts in sensor-based learning-by-doing courses when tackling complex issues like engineering topics. The authors suggest that broader research be undertaken, involving a larger sample, a greater scale, and a diversity of factors.

Revised clusters of annotated unknown sounds in the Belgian part of the North sea

Acoustic signals, especially those of biological source, remain unexplored in the Belgian part of the North Sea (BPNS). The BPNS, although dominated by anthrophony (sounds from human activities), is expected to be acoustically diverse given the presence of biodiverse sandbanks, gravel beds and artificial hard structures. Under the framework of the LifeWatch Broadband Acoustic Network, sound data have been collected since the spring of 2020. These recordings, encompassing both biophony, geophony and anthrophony, have been listened to and annotated for unknown, acoustically salient sounds. To obtain the acoustic features of these annotations, we used two existing automatic feature extractions: the Animal Vocalization Encoder based on Self-Supervision (AVES) and a convolutional autoencoder network (CAE) retrained on the data from this study. An unsupervised density-based clustering algorithm (HDBSCAN) was applied to predict clusters. We coded a grid search function to reduce the dimensionality of the feature sets and to adjust the hyperparameters of HDBSCAN. We searched the hyperparameter space for the most optimized combination of parameter values based on two selected clustering evaluation measures: the homogeneity and the density-based clustering validation (DBCV) scores. Although both feature sets produced meaningful clusters, AVES feature sets resulted in more solid, homogeneous clusters with relatively lower intra-cluster distances, appearing to be more advantageous for the purpose and dataset of this study. The 26 final clusters we obtained were revised by a bioacoustics expert. We were able to name and describe 10 unique sounds, but only clusters named as ‘Jackhammer’ and ‘Tick’ can be interpreted as biological with certainty. Although unsupervised clustering is conventional in ecological research, we highlight its practical use in revising clusters of annotated unknown sounds. The revised clusters we detailed in this study already define a few groups of distinct and recurring sounds that could serve as a preliminary component of a valid annotated training dataset potentially feeding supervised machine learning and classifier models.

Pengelompokan Kabupaten dan Kota di Jawa Timur berdasarkan Percepatan Pemulihan Ekonomi Menggunakan Pendekatan Hirearki

The Covid-19 pandemic's diverse impact on Indonesia's economy, particularly in East Java, spurred the government to formulate a comprehensive work plan targeting three key objectives, one of which is to expedite economic recovery. This plan focuses on three key indicators: economic growth, open unemployment rate (TPT), and the gini ratio. It is known that during the pandemic, East Java initially experienced economic growth that contracted until eventually showing positive growth in the second quarter of 2021, which has been supported by national policies. This study explores district and city classification in East Java based on economic recovery indicators through hierarchical clustering. The analysis identifies Ward's linkage as the most effective model, with a cophenetic correlation coefficient of 0.9311. Internal clustering validation tests reveal two optimal clusters. Cluster 1 is characterized by a notably high average acceleration of economic recovery across all three indicators. The findings suggest that the government should optimize the economic stimulus program for cluster 2 and focus on enhancing income redistribution and job opportunities for cluster 1.

A New Approach In Metaheuristic Clustering: Coot Clustering

As a result of technological advancements, the increase in vast amounts of data in today's world has made artificial intelligence and data mining significantly crucial. In this context, the clustering process, which aims to explore hidden patterns and meaningful relationships within complex datasets by grouping similar features to conduct more effective analyses, holds vital importance. As an alternative to classical clustering methods that face challenges such as large volumes of data and computational complexities, a metaheuristic clustering method utilizing Coot Optimization (COOT), a swarm intelligence-based algorithm, has been proposed. COOT, inspired by the hunting stages of eagles and recently introduced into the literature, is a metaheuristic method. Through the proposed COOT metaheuristic clustering method, the aim is to contribute to the literature by leveraging COOT's robust exploration and exploitation processes, utilizing its dynamic and flexible structure. Comprehensive experimental clustering studies were conducted to evaluate the consistency and effectiveness of the COOT-based algorithm using randomly generated synthetic data and the widely used Iris dataset in the literature. The same datasets underwent analysis using the traditional clustering algorithm K-Means, renowned for its simplicity and computational speed, for comparative purposes. The performance of the algorithms was assessed using cluster validity measures such as Silhouette Global, Davies-Bouldin, Krznowski-Lai, and Calinski-Harabasz indices, along with the Total Squared Error (SSE) objective function. Experimental results indicate that the proposed algorithm performs clustering at a competitive level with K-Means and shows potential, especially in multidimensional datasets and real-world problems. Despite not being previously used for clustering purposes, the impressive performance of COOT in some tests compared to the K-Means algorithm showcases its success and potential to pioneer different studies aimed at expanding its usage in the clustering domain.

Settling Time vs. Accuracy Tradeoffs for Clustering Big Data

We study the theoretical and practical runtime limits of k-means and k-median clustering on large datasets. Since effectively all clustering methods are slower than the time it takes to read the dataset, the fastest approach is to quickly compress the data and perform the clustering on the compressed representation. Unfortunately, there is no universal best choice for compressing the number of points -- while random sampling runs in sublinear time and coresets provide theoretical guarantees, the former does not enforce accuracy while the latter is too slow as the numbers of points and clusters grow. Indeed, it has been conjectured that any sensitivity-based coreset construction requires super-linear time in the datase size. We examine this relationship by first showing that there does exist an algorithm that obtains coresets via sensitivity sampling in effectively linear time -- within log-factors of the time it takes to read the data. Any approach that significantly improves on this must then resort to practical heuristics, leading us to consider the spectrum of sampling strategies across both real and artificial datasets in the static and streaming settings. Through this, we show the conditions in which coresets are necessary for preserving cluster validity as well as the settings in which faster, cruder sampling strategies are sufficient. As a result, we provide a comprehensive theoretical and practical blueprint for effective clustering regardless of data size. Our code is publicly available at https://github.com/Andrew-Draganov/Fast-Coreset-Generation and has scripts to recreate the experiments.

Partitioning of wind pressure coefficients on a tall building under interference effect: A cluster analysis approach

This study proposed a cluster analysis-based approach for partitioning wind pressure on tall buildings in densely-packed areas, considering interference effects. By utilizing a modified GK cluster algorithm and leveraging the coordinate positions of pressure taps along with their corresponding wind pressure coefficients (WPC), the study aimed to distinguish different parts of the building surface exhibiting varying wind load characteristics. The adoption of cluster validation indices (CVIs) allowed for the determination of the optimal number of clusters, enhancing the accuracy and reliability of the partitioning process. The resulting clusters effectively captured the distribution of wind pressure, providing valuable insights for wind-resistant design considerations. Overall, the proposed approach demonstrates promising potential in facilitating the design and analysis of tall buildings subjected to complex wind loads in urban environments.

A new framework for evaluating the virgin compression curves of reconstituted clays at different initial water contents

The influence of initial water content on the virgin compression of reconstituted clays is a topic of great importance. This study introduces a novel perspective based on the concept of intrinsic compression. It is demonstrated that the virgin compression curves of the reconstituted clays are similar in shape to the intrinsic compression line and can be obtained through vertical shifting and stretching. Building upon this concept, the intrinsic compression line is further extended to the compression curve cluster, enabling a direct evaluation of the influence of initial water content. The validity of the compression curve cluster is verified using independent data from the literature as well as data collected by our research team. In addition, a comparison with other relevant theories further underscores the superiority of the proposed framework.

Capacitated Clustering via Majorization-Minimization and Collaborative Neurodynamic Optimization.

This paper addresses capacitated clustering based on majorization-minimization and collaborative neurodynamic optimization (CNO). Capacitated clustering is formulated as a combinatorial optimization problem. Its objective function consists of fractional terms with intra-cluster similarities in their numerators and cluster cardinalities in their denominators as normalized cluster compactness measures. To obviate the difficulty in optimizing the objective function with factional terms, the combinatorial optimization problem is reformulated as an iteratively reweighted quadratic unconstrained binary optimization problem with a surrogate function and a penalty function in a majorization-minimization framework. A clustering algorithm is developed based on CNO for solving the reformulated problem. It employs multiple Boltzmann machines operating concurrently for local searches and a particle swarm optimization rule for repositioning neuronal states upon their local convergence. Experimental results on ten benchmark datasets are elaborated to demonstrate the superior clustering performance of the proposed approaches against seven baseline algorithms in terms of 21 internal cluster validity criteria.

Application of the K-Medoids Algorithm in Clustering PAM Customers Based on Provinces in Indonesia

Application of the K-Medoids Algorithm in Clustering PAM Customers Based on Provinces in Indonesia

Prediction of PM2.5 with a piecewise affine model considering spatial-temporal correlation

Over the past several decades, several air pollution prevention measures have been developed in response to the growing concern over air pollution. Using models to anticipate air pollution accurately aids in the timely prevention and management of air pollution. However, the spatial-temporal air quality aspects were not properly taken into account during the prior model construction. In this study, the distance correlation coefficient (DC) between measurements made in various monitoring stations is used to identify appropriate correlated monitoring stations. To derive spatial-temporal correlations for modeling, the causality relationship between measurements made in various monitoring stations is analyzed using Transfer Entropy (TE). This work explores the process of identifying a piecewise affine (PWA) model using a larger dataset and suggests a unique hierarchical clustering-based identification technique with model structure selection. This work improves the BIRCH (Balanced Iterative Reducing and Clustering using Hierarchies) by introducing Kullback-Leibler (KL) Divergence as the dissimilarity between clusters for handling clusters with arbitrary shapes. The number of clusters is automatically determined using a cluster validity metric. The task is formulated as a sparse optimization problem, and the model structure is selected using parameter estimations. Beijing air quality data is used to demonstrate the method, and the results show that the proposed strategy may produce acceptable forecast performance.

Ship trajectory segmentation and semisupervised clustering via geospatial background knowledge

Cluster analysis is a common application of maritime traffic pattern recognition. However, most current methods are unsupervised clustering algorithms that rely solely on the features of the trajectories themselves for clustering, making them susceptible to uneven density distributions. To address this issue, we propose a semisupervised clustering algorithm that utilizes geospatial data to segment trajectories and generate clustering constraints. First, shoreline and anchorage information are employed for trajectory segmentation to enhance the consistency of local trajectory features. Second, cannot-link constraints derived from shoreline data are used to modify the distance between two trajectories, thereby preventing the clustering of trajectories separated by nonnavigable waters into a single cluster. Last, experimental verification is conducted using automatic identification system data, and the results are compared with those of existing algorithms. The results demonstrate more concentrated trajectory segmentation points, easier selection of clustering parameters, and significantly improved evaluation outcomes based on external clustering validity indices.

Validation of graph sequence clusters through multivariate analysis: application to Rovash scripts

This paper introduces the concept of pattern systems that evolve, with a focus on scripts, a specific type of pattern system. The study analyses the development of different script systems, known as scriptinformatics, with a focus on the historical Rovash scripts used in the Eurasian steppe. The aim is to assess the traditional classification of historical inscriptions, referred to as script relics, into distinct Rovash scripts. Clustering and ordination techniques were used to perform multivariate analyses on Rovash scripts and inscriptions. The study presents two new measures, the script-specific holophyletic index and the joint holophyletic index, for evaluating trees produced by hierarchical clustering. The results indicate that holophyletic indices can validate the traditional assignment of inscriptions to scripts through phylogenetic tree evaluation. This method can be extended to include pattern systems with evolutionary properties and graph sequences derived from them, as well as additional scripts and inscriptions.

Evaluating the Performance of FedCLUS Algorithm Using FedCI: A New Federated Cluster Validity Metric

Evaluating the Performance of FedCLUS Algorithm Using FedCI: A New Federated Cluster Validity Metric