A new hierarchical clustering algorithm

This work aims to expand the knowledge of the area of data analysis through persistence homology and representations of directed graphs. To be specific, we looked for how we can analyze homology cluster groups using agglomerative Hierarchical Clustering algorithms and methods. Additionally, the Wine data, which is offered in R studio, was analyzed using various cluster algorithms such as Hierarchical Clustering, K-Means Clustering, and PAM Clustering. The goal of the analysis was to find out which cluster's method is proper for a given numerical dataset. We tried to find the agglomerative hierarchical clustering method by testing the data that will be the optimal clustering algorithm among these three; K-Means, PAM, and Random Forest methods. By comparing each model's accuracy value with cultivar coefficients, we concluded that K-Means methods are the most helpful when working with numerical variables. On the other hand, PAM clustering and Gower with Random Forest are the most beneficial approaches when using categorical variables. These tests can determine the optimal number of clustering groups, given the data set, and by doing the proper analysis. Using those the project, we can apply our method to several industrial areas such that clinical, business, and others. For example, people can make different groups based on each patient who has a common disease, required therapy, and other things in the clinical society. Additionally, people can expect to get several clustered groups based on the marginal profit, marginal cost, or other economic indicators for the business area.

Photovoltaic is attracting attention as one of the renewable energy sources that replace existing fossil fuel-based power generation. Photovoltaic power generation data clustering is becoming increasingly popular because it allows us to identify PV systems without extensive analysis and simulation. Generally, clustering method of PV power data analyzes only the meaning of each cluster, so it is difficult to grasp the similarity between clusters. In this paper, clustering of PV power data through hierarchical clustering algorithm is performed to calculate the relationship between clusters. The hierarchical clustering method was used to analyze the similarity of PV power data between clusters. As a result, PV power data were classified into seasonal clusters and defective clusters.

Community welfare is one of the important points for a region and is also the essence of national development. The welfare of the people in Indonesia is fairly unequal, especially in East Java. To be able to map an area to the welfare of its people in East Java, one way that can be used is to use clustering. The hierarchical clustering method is one of the clustering methods for grouping data. In hierarchical clustering, single linkage, complete linkage, and average linkage methods are suitable methods for grouping data, which will compare the best method to use. The results of the calculation show that the average linkage method with three clusters is the best calculation with a silhouette index value of 0.6054, with the 1st cluster there are 23 regions, namely the city/district with the highest community welfare, the 2nd cluster there are 11 regions, namely cities/districts with moderate social welfare, and in the third cluster there are 4 regions, namely cities/districts with the lowest community welfare.

Deep learning has been popular for a few years, and it shows great capability on unsupervised leaning of representation. Deep belief network consists of multi layers of restricted Boltzmann machine(RBM) and a deep auto-encoder, which uses a stack architecture learning feature layer by layer. The learning rule is that one deeper layer learns more complex representations, which are the high level features of the input data, from the representations learnt by the layer before. Fuzzy C-Means(FCM) is one of the most popular clustering algorithms, which allows one piece of data belong to several clusters. In this paper the authors propose a novel clustering model, and introduce a novel clustering technique(DBNOC) which combines deep belief network and fuzzy c-means. The main idea is that: first, it clusters with the high level representations learnt by stacked RBM to produce the initial cluster center, then it uses the fine-tune step including one center holding clustering algorithm and deep auto-encoder to optimize the cluster center and membership between input data and every cluster by cross iteration. The authors use FCM clustering algorithm to fulfill the model and do experiment on both low dimensional datasets and high dimensional datasets. The experiment results suggest that the proposed deep belief network oriented clustering method is better than the standard K-Means and FCM algorithm on the test datasets. Even on high dimensional datasets, the DBNOC clustering method show more generalization. What's more, the proposed model is suitable both in theoretical and practical.

Clustering has been used in literature to enhance classification accuracy. But most partitional clustering methods need the number of clusters as input and also they are sensitive to initialization. Although hierarchical clustering methods may be more effective in finding clustering structure of the dataset than partitional methods but hierarchical clustering methods give tree structure known as dendrogram which is a sequence of clustering solutions. Hence hierarchical clustering algorithms are not generally applied in the preprocessing step to classification methods. This problem can be solved by cutting the dendrogram to get single clustering solution. In this paper we propose a framework for classification which uses Optimal Clustering Genetic Algorithm (OCGA) to obtain optimal level of cutting the dendrogram. A single clustering solution is obtained by cutting the dendrogram at optimal level. The clusters obtained are used to enhance classification accuracy of the classification methods. The proposed classification methods have been applied for the diagnosis of diabetes disease.

Application of hierarchical clustering, singularity mapping, and Kohonen neural network to identify Ag-Au-Pb-Zn polymetallic mineralization associated geochemical anomaly in Pangxidong district

We present a novel pairwise clustering method. Given a proximity matrix of pairwise relations (i.e. pairwise similarity or dissimilarity estimates) between data points, our algorithm extracts the two most prominent clusters in the data set. The algorithm, which is completely nonparametric, iteratively employs a two-step transformation on the proximity matrix. The first step of the transformation represents each point by its relation to all other data points, and the second step re-estimates the pairwise distances using a statistically motivated proximity measure on these representations. Using this transformation, the algorithm iteratively partitions the data points, until it finally converges to two clusters. Although the algorithm is simple and intuitive, it generates a complex dynamics of the proximity matrices. Based on this bipartition procedure we devise a hierarchical clustering algorithm, which employs the basic bipartition algorithm in a straightforward divisive manner. The hierarchical clustering algorithm copes with the model validation problem using a general cross-validation approach, which may be combined with various hierarchical clustering methods. We further present an experimental study of this algorithm. We examine some of the algorithm's properties and performance on some synthetic and ‘standard’ data sets. The experiments demonstrate the robustness of the algorithm and indicate that it generates a good clustering partition even when the data is noisy or corrupted.

The paper presents the theoretical justification and software for an effective method of data identification in intelligent control systems, which is based on the use of the stages of clustering and classification of objects represented by their parametric description. The author proposed a method of data clustering with fixation of cluster boundary points based on the principle of finding their surface tension. The application of this method of cluster analysis allows to increase the efficiency of identification of objects in control systems using the SVM type classifier. The SVM (Support Vector Machine) type classifier is currently the most advanced and, due to the use of generalized decision functions, is able to operate with both linear and non-linearly distributed images of objects in the parameter space. Today, a significant number of cluster analysis methods and algorithms are known. They can be divided into classical, based on the general algorithm of Fu K.S., and the latest, based on taking into account the nature and structure of data and the purpose of their use. Examples of such methods include: k-means, density-based (DBSCAN), Mean-Shift, using Gaussian mixture models (GMM), methods of hierarchical agglomerative clustering (HAC) . Their common drawback is that they form clusters of points in the parameter space, but do not fix their boundary points. The last characteristic (the presence of marked cluster boundary points) is very useful when building classifiers that implement the task of object identification. In this paper, the author proposed and theoretically substantiated the method of clustering with the definition of surface points by analogy with the physical principle of surface tension of a liquid. The work developed an algorithm for the implementation of this method, as well as software in the Python language in the form of the ClusterBorderFinder application. The author's certificate was obtained for the developed program.

Clustering is one of the techniques used to obtain useful information from web log file for better understanding of customer behaviour. Two clustering techniques that commonly used are Greedy Hierarchical Item Set-Based Clustering (GHIC) algorithm and Hierarchical Clustering Algorithm (HCA). The algorithms, however, have its weaknesses in terms of processing times and time complexity. This paper proposes a new approach called Hierarchical Pattern-Based Clustering (HPBC) algorithm to improve the processing times based on the difference of mean support values of each cluster. The simulation revealed that the proposed algorithm outperformed the HCA and GHIC up to 100% and 50% respectively, with less time complexity.

Hierarchical clustering, a traditional clustering method, has been getting attention again. Among several reasons, a credit goes to a recent paper by Dasgupta in 2016 that proposed a cost function that quantitatively evaluates hierarchical clustering trees. An important question is how to combine this recent advance with existing successful clustering methods. In this paper, we propose a hierarchical clustering method to minimize the cost function of clustering tree by incorporating existing clustering techniques. First, we developed an ensemble tree-search method that finds an integrated tree with reduced cost by integrating multiple existing hierarchical clustering methods. Second, to operate on large and arbitrary shape data, we designed an efficient hierarchical clustering framework, called integrating divisive and ensemble-agglomerate (IDEA) by combining it with advanced clustering techniques such as nearest neighbor graph construction, divisive-agglomerate hybridization, and dynamic cut tree. The IDEA clustering method showed better performance in minimizing Dasgupta's cost and improving accuracy (adjusted rand index) over existing cost-minimization-based, and density-based hierarchical clustering methods in experiments using arbitrary shape datasets and complex biology-domain datasets.

In Indonesia, Dengue Fever (DF) is a contagious disease that is a significant issue in public health. The Kediri Regency in East Java, as reported by the Ministry of Health in 2019, had the highest number of DF cases. If not addressed promptly, DF can lead to outbreaks, creating a health emergency. The lack of a thorough investigation into the diversity of risk within a spatial and temporal region exacerbates this issue. Therefore, spatial-temporal analysis is crucial in developing a warning system to prevent and control DF. This paper proposes a method that combines the Euclidean Distance calculation with the Hierarchical Clustering method. We collected data from the Kediri Regency health department and conducted pre-processing and classification processes, considering the number of DF victims, death rate, population, rainfall, and public facilities. The hierarchical clustering algorithm was used to categorize the 344 village analyses into low, medium, and high vulnerability categories. This method allows for a comparison of yearly single, average, complete, and centroid linkage in DF vulnerability levels. We also employed spatial-temporal visualization based on cellular applications to create a clear picture of areas vulnerable to DF. The experimental results in clustering showed a satisfactory level of matching, with variant values calculated using the hierarchical clustering method. The variants for single linkages were 0.113; for average linkages, they were 0.120; for complete linkages, they were 0.178; and for centroid linkages, they were 0.106. The grouping validation results indicated that the centroid linkage method produced the best variant level. We suggest further enhancing the methods with better process steps using other pre-processing methods to improve the validation quality.

Web services (WS) is called composite or compound when its execution involves interactions with other WS to utilize their features. The service providers published the web services through the internet as independent software components that are fulfilling the requirements of customer request. Clustering is more necessary for efficient web service discovery and web service composition processes. Clustering process groups the similar type of web services. In this paper, efficient clustering methods such as k-means clustering, Hierarchical agglomerative clustering and Balanced Iterative Reducing and Clustering using Hierarchies (BIRCH) clustering are introduced for web service clustering. The k-means clustering is a kind of partitional clustering where the web pages are divided into subsets with no hierarchy defined over them and the hierarchical agglomerative clustering is a type of hierarchical clustering where the web pages are arranged in tree structure in which leaves represents the data points and nodes denotes the clusters. BIRCH is an integrated hierarchical clustering algorithm uses the clustering features and cluster feature tree for general cluster description. Based on these clustering methods, web pages are clustered which are used for web service discovery and web service composition. The experiments are conducted on number of web services and the efficiency is evaluated in terms of accuracy, precision, recall and run time.

Clustering is a group of unsupervised statistical techniques commonly used in many disciplines. Considering their applications to fish abundance data, many technical details need to be considered to ensure reasonable interpretation. However, the reliability and stability of the clustering methods have rarely been studied in the contexts of fisheries. This study presents an intensive evaluation of three common clustering methods, including hierarchical clustering (HC), K-means (KM), and expectation-maximization (EM) methods, based on fish community surveys in the coastal waters of Shandong, China. We evaluated the performances of these three methods considering different numbers of clusters, data size, and data transformation approaches, focusing on the consistency validation using the index of average proportion of non-overlap (APN). The results indicate that the three methods tend to be inconsistent in the optimal number of clusters. EM showed relatively better performances to avoid unbalanced classification, whereas HC and KM provided more stable clustering results. Data transformation including scaling, square-root, and log-transformation had substantial influences on the clustering results, especially for KM. Moreover, transformation also influenced clustering stability, wherein scaling tended to provide a stable solution at the same number of clusters. The APN values indicated improved stability with increasing data size, and the effect leveled off over 70 samples in general and most quickly in EM. We conclude that the best clustering method can be chosen depending on the aim of the study and the number of clusters. In general, KM is relatively robust in our tests. We also provide recommendations for future application of clustering analyses. This study is helpful to ensure the credibility of the application and interpretation of clustering methods.

Clustering is an effective unsupervised machine learning method that can be used as a stand-alone heuristic or as a part of a data mining process. The goal of clustering analysis is to partition data into groups with high intra-cluster association, and low inter-cluster association. Hierarchical clustering requires minimal parameters, has flexibility with similarity measure, and has strong visualization power, all of which makes it ideal for exploratory analysis. Hierarchical clustering is a particular branch of clustering algorithms where the results are not given as partitions, but rather a nested structure, which can represent the ordering among elements within a dataset. The study of the performance of hierarchical structure on time series data is limited. In this paper, we examine the hierarchical structure of time series datasets. The most popular hierarchical structured clustering heuristics include the Hierarchical Agglomerative Clustering, which is distance based; and Ordering Points To Identify the Clustering Structure, which is density based. Both share many similar characteristics and are suitable for time series data processing. We examine the performance of different hierarchical clustering algorithms with time series both internally as well as externally.

Supplementary Material for the manuscript "Drivers of carbon dioxide emissions: An empirical investigation using hierarchical and non- hierarchical clustering methods"