Unsupervised Clustering by Means of Hierarchical Differential Evolution Algorithm

Analyzing the electricity price plays a vital role in market players in deregulated electricity markets. In this regard, proper clustering methods are more beneficial. In this paper, a comparative study of three major clustering algorithms, including K-Means, Fuzzy C-Means, and Hierarchical algorithm on the Italian National Single Price, has been carried out. Moreover, the impact of various parameters of the algorithms on the clustering results has been analyzed. The performance of the clustering methods has been compared through several clustering validity indexes, including the Silhouette index, Calinski-Harabasz index, and Davies-Bouldin indicator. Two distinct patterns consisting of working days and weekends (or holidays) are observable in the particular dataset.

PDBI: A partitioning Davies-Bouldin index for clustering evaluation

Identification of the correct number of clusters is an important consideration in clustering where several cluster validity indexes, primarily utilizing the Euclidean distance, have been used in the literature. The property of symmetry is observed in most clustering solutions. In this paper, the symmetry versions of nine cluster validity indexes, namely, Davies-Bouldin index, Dunn index, generalized Dunn index, point symmetry (PS) index, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> index, Xie-Beni index, FS index, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> index, and SV index, are proposed. It is empirically established that incorporation of the property of symmetry significantly improves the capabilities of these indexes in identifying the appropriate number of clusters. A recently developed PS-based genetic clustering technique, GAPS clustering, is used as the underlying partitioning algorithm. Results on six artificially generated and five real-life datasets show that symmetry-distance-based <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> index performs the best as compared to all the other eight indexes.

There are two notoriously hard problems in cluster analysis, estimating the number of clusters, and checking whether the population to be clustered is not actually homogeneous. Given a dataset, a clustering method and a cluster validation index, this paper proposes to set up null models that capture structural features of the data that cannot be interpreted as indicating clustering. Artificial datasets are sampled from the null model with parameters estimated from the original dataset. This can be used for testing the null hypothesis of a homogeneous population against a clustering alternative. It can also be used to calibrate the validation index for estimating the number of clusters, by taking into account the expected distribution of the index under the null model for any given number of clusters. The approach is illustrated by three examples, involving various different clustering techniques (partitioning around medoids, hierarchical methods, a Gaussian mixture model), validation indexes (average silhouette width, prediction strength and BIC), and issues such as mixed type data, temporal and spatial autocorrelation.

Determining the most proper number of cluster in fuzzy clustering by using artificial neural networks

Transmissions in the mmWave spectrum benefit from a-priori knowledge of radio channel propagation models. This paper is concerned with one important task that helps provide a more accurate channel model, namely, the clustering of all multipath components arriving at the receiver. Our work focuses on directive transmissions in urban outdoor scenarios and shows the importance of the correct estimation of the number of clusters for mmWave radio channels simulated with a software ray-tracer tool. We investigate the effectiveness of k-means and k-power-means clustering algorithms in predicting the number of clusters through the use of cluster validity indices (CVIs) and score fusion techniques. Our investigation shows that clustering is a difficult task because the optimal number of clusters is not always given by one or by a combination of more CVIs. However, using score fusion methods, we find the optimal partitioning for the k-means algorithm based on the power and time of arrival of the multipath rays or based on their angle of arrival. When the k-power-means algorithm is used, the power of each arriving ray is the most important clustering factor, making the dominant received paths pull the other ones around them, to form a cluster. Thus, the number of clusters is smaller and the decision based on CVIs or score fusion factors easier to be taken.

Exploratory data-driven methods such as unsupervised clustering are considered to be hypothesis-generating procedures, and are complementary to the hypothesis-led statistical inferential methods in functional magnetic resonance imaging (fMRI). The major problem with clustering of real bioimaging data is that of deciding how many clusters are present. This motivates the application of cluster validity techniques in order to quantitatively evaluate the results of the clustering algorithm. In this paper, we apply three different cluster validity techniques, namely, Kim's index, Calinski Harabasz index, and the intraclass index to the evaluation of the clustering results of fMRI data. The benefits and major limitations of these cluster validity techniques are discussed based on the achieved results of several datasets.

IMI2: A fuzzy clustering validity index for multiple imbalanced clusters

Because of the complexity of data sets from the real world, it is difficult to classify the data sets clearly and effectively, thus we prefer to adopt fuzzy clustering approaches to analyze the data sets. However, due to the variety of fuzzy clustering algorithms, the different number of clusters will lead to different clustering results. The number of clusters is closely related to the clustering division, so how to determine the number of fuzzy clustering (k ) has become a problem. Until now, many researchers have proposed utilizing fuzzy clustering validity indexes to deal with this kind of problem. However, the effectiveness index of fuzzy clustering can only be evaluated on the basis of the fuzzy clustering algorithm FCM to divide the clusters. When the range of k value is too large, FCM’s clustering for different k values is quite time-consuming. From this perspective, this paper proposes a fuzzy clustering optimal k selection method based on multi-objective optimization (FMOEA-K). Different from the traditional methods, this method combines the fuzzy clustering effectiveness index with multi-objective optimization algorithm (MOEA), and uses multi-objective optimization algorithm to search the appropriate cluster center concurrently. Because of the concurrency of the multi-objective optimization algorithm, the calculation time is shortened. The experimental results show that compared with the traditional method, the FMOEA-K can shorten the calculation time and improve the accuracy of calculating the optimal k value.

Unsupervised classification needs no prior knowledge of interested region and has less human interference that is suitable for processing messes of digital images acquired from earth observation satellites. A typical sequence for unsupervised classification might begin with the analyst specifying minimum and maximum numbers of categories to be generated by the classification algorithm. Usually, a larger cluster number is assigned in advance for the initial clustering. Then, several classified clusters are merged into a larger group so that the number of clusters can be reduced. The selection of an appropriate cluster number is up to the analyst's experience. This paper illustrates the convergence of cluster-center optimization and the optimal cluster number varying with the dimension in Minkowski space. One of the simplest and most popular is Euclidean distance while Minkowski distance is measured in two dimensions. The experiment was executed on several digital images by a classifier employing Genetic Algorithm as a searching tool and Davies-Bouldin index as a cluster validity measure. The results show that a smaller dimension, e.g. one-, two-, and infinity dimensions, in Minkowski space derives less clusters, while the assignment of a larger dimension results in a larger cluster number with a more detailed segmentation.

Ground truth bias in external cluster validity indices

This paper introduces a novel hierarchical fuzzy algorithm for clustering categorical attributes, which consists of three basic design steps. It incorporates a potential-based clustering scheme with a cluster validity index into a framework that is based on the use of the weighted fuzzy c-modes. The novelty of the contribution lies in the following properties: (a) the potential-based clustering scheme reduces the dependence of the algorithm on initialization, (b) the weighted fuzzy c-modes provides flexibility in detecting the real data structure, and (c) the cluster validity index determines the appropriate number of clusters. The algorithm is applied to model (classify) cultural data related to a number of painters of the seventeenth century, where its performance is compared to the respective performance of an agglomerative hierarchical clustering algorithm.

This research is an applied research that aims to determine the clusters of areas affected by floods in bone regency. This study user the K-means method in clustering flood data in 2020 and 2021. The data is grouped based on the number of families affected and the resulting damage. In determining the number of clusters to be used, this study validated 3, 4 and 5 clusters using the davis bouldin index (DBI) validation in determining the best cluster. The results of this validation resulted in the best number of clusters, namely k=4 for 2020 data with a minimum DBI of 0,73 and k=4 for 2021 data with a minimum DBI of 0,44. After clustering, the cluster number for data for 2020 from the firs to fourth cluster member are 34, 7, 2 and 3 sequentially, while the data for years 2021 sequentially are 3, 22, 3 and 1. Then the cluster results are displayed in a spatial form that is created using ArcGIS.

Software Defined Networking (SDN) is quickly becoming a vital technology for the future Internet. SDN provides a worldwide network with the capacity to manage network traffic dynamically. One of the main advantages of SDN over traditional networks is that it provides better network security due to centralised control. However, the flexibility offered by SDN architecture raises several additional network security concerns that must be addressed to improve SDN network security. This study proposes an unsupervised learning method to address attacks in the SDN controller. 7 extracted features from southbound traffic have been used to train KMeans, MeanShift, Density-Based Spatial Clustering of Applications with Noise (DBSCAN), AgglomerativeClustering, Balanced Iterative Reducing and Clustering using Hierarchies (BIRCH), MiniBatchKMeans, Ordering Points To Identify Cluster Structure (OPTICS), and SpectralClustering, which are all well-known unsupervised classifiers. In terms of various well-known performance measuring criteria, such as Silhouette Score (SS), Calinski Harabasz Index (CHI), and Davies Bouldin Index (DBI), BIRCH outperforms all other classifiers.

Text mining is a powerful modern technique used to obtain interesting information from huge datasets. Text clustering is used to distinguish between documents that have the same themes or topics. The absence of the datasets ground truth enforces the use of clustering (unsupervised learning) rather than others, such as classification (supervised learning). The “no free lunch” (NFL) theorem supposed that no algorithm outperformed the other in a variety of conditions (several datasets). This study aims to analyze the k-means cluster algorithm variations (three algorithms (k-means, mini-batch k-means, and k-medoids) at the clustering process stage. Six datasets were used/analyzed in chapter Al-Baqarah English translation (text) of 286 verses at the preprocessing stage. Moreover, feature selection used the term frequency–inverse document frequency (TF-IDF) to get the weighting term. At the final stage, five internal cluster validations metrics were implemented silhouette coefficient (SC), Calinski-Harabasz index (CHI), C-index (CI), Dunn’s indices (DI) and Davies Bouldin index (DBI) and regarding execution time (ET). The experiments proved that k-medoids outperformed the other two algorithms in terms of ET only. In contrast, no algorithm is superior to the other in terms of the clustering process for the six datasets, which confirms the NFL theorem assumption.