A comparative study of hard clustering algorithms for vegetation data

AimThe unsupervised nature of traditional numerical methods used to classify vegetation hinders the development of comprehensive vegetation classification systems. Each new unsupervised classification yields partitions that are partly inconsistent with previous classifications and change group membership for some sites. In contrast, supervised methods account for previously established vegetation units, but cannot define new ones. Therefore, we introduce the concept of semi‐supervised classification to community ecology and vegetation science. Semi‐supervised classification formally reproduces the existing units in a supervised mode and simultaneously identifies new units among unassigned sites in an unsupervised mode. We discuss the concept of semi‐supervised clustering, introduce semi‐supervised variants of two clustering algorithms that produce groups with crisp boundaries, k‐means and partitioning around medoids (PAM), provide a free software tool to perform these classifications and demonstrate the advantages using example data sets of vegetation plots.MethodsSemi‐supervised methods use a priori information about group membership for some sites to define centroids (k‐means) or medoids (PAM) of site groups that represent previously established vegetation units. They identify these groups in a species hyperspace and assign new sites to them. At the same time, they search for a user‐defined number of new groups. We compared the unsupervised, supervised and semi‐supervised methods using an example of a forest vegetation data set that was previously classified using expert knowledge, and assessed how well these methods reproduced vegetation units defined by experts. Then we compared supervised and semi‐supervised methods in a task when a grassland vegetation classification established in one country was extended to two neighbouring countries.Results and conclusionsExample analyses of vegetation plot data sets demonstrated that semi‐supervised variants of k‐means and PAM are extremely valuable tools for extending existing vegetation classifications while preserving previously defined vegetation units. They can be used both for identifying so far unrecognized vegetation types in the regions where a vegetation classification already exists and for extending a vegetation classification from a particular region to neighbouring regions with partly identical but partly different vegetation types. Both k‐means and PAM provide site groups with crisp boundaries, which makes them a simpler alternative to fuzzy clustering methods.

In view of the considerable applications of data clustering techniques in various fields, such as engineering, artificial intelligence, machine learning, clinical medicine, biology, ecology, disease diagnosis, and business marketing, many data clustering algorithms and methods have been developed to deal with complicated data. These techniques include supervised learning methods and unsupervised learning methods such as density-based clustering, K-means clustering, and K-nearest neighbor clustering. This book reviews recently developed data clustering techniques and algorithms and discusses the development of data clustering, including measures of similarity or dissimilarity for data clustering, data clustering algorithms, assessment of clustering algorithms, and data clustering methods recently developed for insurance, psychology, pattern recognition, and survey data.

Most of the clustering algorithms are designed for such datasets where the dissimilarity between any two points of the dataset can be computed using standard distance measures such as the Euclidean distance. However, many real-life datasets are categorical in nature, where no natural ordering can be found among the elements in the attribute domain. In such situations, the clustering algorithms, such as K-means [238] and fuzzy C-means (FCM) [62], cannot be applied. The K-means algorithm computes the center of a cluster by computing the mean of the set of feature vectors belonging to that cluster. However, as categorical datasets do not have any inherent distance measure, computing the mean of a set of feature vectors is meaningless. A variation of the K-means algorithm, namely Partitioning Around Medoids (PAM) or K-medoids [243], has been proposed for such kinds of datasets.

The development of single-cell ribonucleic acid (RNA) sequencing (scRNA-seq) technology has led to great opportunities for the identification of heterogeneous cell types in complex tissues. Clustering algorithms are of great importance to effectively identify different cell types. In addition, the definition of the distance between each two cells is a critical step for most clustering algorithms. In this study, we found that different distance measures have considerably different effects on clustering algorithms. Moreover, there is no specific distance measure that is applicable to all datasets. In this study, we introduce a new single-cell clustering method called SD-h, which generates an applicable distance measure for different kinds of datasets by optimally synthesizing commonly used distance measures. Then, hierarchical clustering is performed based on the new distance measure for more accurate cell-type clustering. SD-h was tested on nine frequently used scRNA-seq datasets and it showed great superiority over almost all the compared leading single-cell clustering algorithms.

As a new extended form of intuitionistic fuzzy sets, Fermatean fuzzy sets are powerful tools for describing vagueness and uncertainty in complex problems. In the method of handling Fermatean fuzzy information, the distance measure is an essential tool to depict the difference between two Fermatean fuzzy sets. However, how to accurately measure the distance between two Fermatean fuzzy sets is still a problem to be solved. In this paper, we devise two novel distance measure methods for Fermatean fuzzy sets. One is the distance measure of Fermatean fuzzy sets based on the Hellinger distance, which is called the FFSH distance. The other is the distance measure of Fermatean fuzzy sets based on the triangular divergence, which is called the FFSTD distance. Then, we prove that the proposed distance measure methods satisfy the axiomatic requirements of the distance function. Afterward, numerical examples are given to reveal that the proposed distance measures are more effective and reasonable than the normalized Euclidean distance measure, which can overcome the counter-intuitive situation. Besides, we utilize the proposed distance measure methods to address the problems of pattern recognition and medical diagnosis under Fermatean fuzzy environment and achieved excellent results. The experimental results illustrate that the proposed distance measure methods can efficiently handle the practical application under Fermatean fuzzy environment, and are more reliable than the normalized Euclidean distance measure.

This paper studies the generalization and normalization issues of information-theoretic distance measures for clustering validation. Along this line, we first introduce a uniform representation of distance measures, defined as quasi-distance, which is induced based on a general form of conditional entropy. The quasi-distance possesses three properties: symmetry, the triangle law, and the minimum reachable. These properties ensure that the quasi-distance naturally lends itself as the external measure for clustering validation. In addition, we observe that the ranges of the distance measures are different when they apply for clustering validation on different data sets. Therefore, when comparing the performances of clustering algorithms on different data sets, distance normalization is required to equalize ranges of the distance measures. A critical challenge for distance normalization is to obtain the ranges of a distance measure when a data set is provided. To that end, we theoretically analyze the computation of the maximum value of a distance measure for a data set. Finally, we compare the performances of the partition clustering algorithm K-means on various real-world data sets. The experiments show that the normalized distance measures have better performance than the original distance measures when comparing clusterings of different data sets. Also, the normalized Shannon distance has the best performance among four distance measures under study.

Distance and similarity measures are fundamentally important in a variety of scientific fields such as clustering analysis, pattern recognition and decision making, etc. In this paper, by analyzing the existing distance and similarity measures between hesitant fuzzy sets, we show that they are not reasonable in some situations. To this end, we propose a novel concept of hesitancy index of hesitant fuzzy set to measure the hesitancy degree among the possible values in each hesitant fuzzy element of the hesitant fuzzy set. By taking their hesitancy indices into account, new methods for measuring the distances between hesitant fuzzy sets are proposed and their properties are discussed. According to the relationship between the distance measure and the similarity measure, two novel similarity measures for hesitant fuzzy sets are further developed. Afterwards, we propound a novel hesitant fuzzy clustering algorithm on the basis of the novel similarity measures for classifying objects with hesitant fuzzy sets. At length, a real-life example is given to illustrate the detailed implementation process of the proposed clustering approach, and a comparative study on the same example is conducted.

Simulated annealing spectral clustering algorithm for image segmentation

In this study, the concepts of competitive agglomeration clustering algorithm is incorporated into fuzzy c-means (FCM) clustering algorithm for symbolic interval-values data. In the proposed approach, called as IFCMwUNC clustering algorithm, the problems of the unknown clusters number and the initialization of prototypes in the FCM clustering algorithm for symbolic interval-values data are overcome and discussed. Due to the competitive agglomeration clustering algorithm possess the advantages of the hierarchical clustering algorithm and the partitional clustering algorithm, IFCMwUNC clustering algorithm can be fast converges in a few iterations regardless of the initial number of clusters. Moreover, it is also converges to the same optimal partition regardless of its initialization. Experiments results show the merits and usefulness of IFCMwUNC clustering algorithm for the symbolic interval-values data.

Clustering is one of the fundamental techniques of data mining that is used for dataset analysis. Clustering algorithms group available data based on similarity or distance measures. Two important clustering methods used in the literature are hierarchical and density based methods. A lot of algorithms have been developed based on these two concepts separately. Birch and its extensions are samples of hierarchical based methods. DBSCAN and its extensions are samples of density based methods. In this paper, a new algorithm is proposed to use both concepts together to achieve an acceptable speed and results, simultaneously. At first, it tries to make clusters using a hierarchical method. If it decides to make a new cluster, then the algorithm checks for density. In this manner, it tries to postpone splitting the clusters. To show the effect of the proposed algorithm, some evaluations are performed on some synthetic and real datasets which show some improvements over related works.

COVID-19 was discovered near the end of 2019 in Wuhan, China. In a short period, the virus had spread throughout the entire world. One of the primary concerns of managers and decision-makers in all types of hospitals nowadays is to implement detection plans for status of patient (Negative, Positive) in order to provide enough care at the proper moment. To reduce a pandemic of COVID-19, improving health care quality could be advantageous. Making clusters of patients with similar features and symptoms supplies an overview of health quality given to similar patients. In the scope of medical machine learning, the K-means and Partitioning Around Medoids (PAM) clustering algorithms are usually used to produce clusters depend on similarity and to detect helpful patterns from sizes of data. In this paper, we proposed a hybrid algorithm of K-Means and Partitioning Around Medoids (PAM) called K-MP to take benefits of both PAM and K-Means to construct an efficient model for predicting patient status. The suggested model for the real dataset was collected from 400 patients in the many Iraqi clinics using a questionnaire. We evaluated the proposed K-MP by using true negative rate, balance accuracy, precision, accuracy, recall, mean absolute error, F1 score, and root mean square error. From these performance measures, we found that K-MP is more efficient in discovering patient status comparing to K-Means and PAM.

The distance and entropy measures-based intuitionistic fuzzy C-means and similarity matrix clustering algorithms and their applications

Cluster analysis has been used widely as a tool for assessing eutrophic trends in coastal waters. The efficiency of clustering in discriminating between oligotrophic, mesotrophic and eutropic sites, depends on the variables used, the distance measure and the clustering algorithm applied. In the present work seven clustering algorithms were evaluated using sets of data from sampling sites of known water type. The results showed that only the Ward’s algorithm had high resolution in discriminating sampling sites of different trophic status. The remaining clustering algorithms did not show remarkable resolution in classifying different water types. The use of the Ward clustering algorithm is recommended in eutrophication studies where discrete clusters of oligotrophic, mesotrophic and eutrophic water type are under investigation.

Radio frequency identification (RFID) technology has been successfully applied to gather customers' shopping habits from their motion paths and other behavioral data. The customers' behavioral data can be used for marketing purposes, such as improving the store layout or optimizing targeted promotions to specific customers. Some data mining techniques, such as clustering algorithms can be used to discover customers' hidden behaviors from their shopping paths. However, shopping path data has peculiar challenges, including variable length, sequential data, and the need for a special distance measure. Due to these challenges, traditional clustering algorithms cannot be applied to shopping path data. In this paper, we analyze customer behavior from their shopping path data by using a clustering algorithm. We propose a new distance measure for shopping path data, called the Operation edit distance, to solve the aforementioned problems. The proposed distance method enables the RFID customer shopping path data to be processed effectively using clustering algorithms. We have collected a real-world shopping path data from a retail store and applied our method to the dataset. The proposed method effectively determined customers' shopping patterns from the data.

One of the most famous algorithms for time series data clustering is k -means clustering with Euclidean distance as a similarity measure. However, many recent works have shown that Dynamic Time Warping (DTW) distance measure is more suitable for most time series data mining tasks due to its much improved alignment based on shape. Unfortunately, k -means clustering with DTW distance is still not practical since the current averaging functions fail to preserve characteristics of time series data within the cluster. Recently, Shape-based Template Matching Framework (STMF) has been proposed to discover a cluster representative of time series data. However, STMF is very computationally expensive. In this paper, we propose a Shape-based Clustering for Time Series (SCTS) using a novel averaging method called Ranking Shape-based Template Matching Framework (RSTMF), which can average a group of time series effectively but take as much as 400 times less computational time than that of STMF. In addition, our method outperforms other well-known clustering techniques in terms of accuracy and criterion based on known ground truth.