Different Criteria for the Optimal Number of Clusters and Selection of Variables with R

One of the most important problems of clustering is to define the number of classes. In fact, it is not easy to find an appropriate method to measure whether the cluster configuration is acceptable or not. In this paper we propose a possible and non-automatic solution considering different criteria of clustering and comparing their results. In this way robust structures of an analyzed dataset can be often caught （or established） and an optimal cluster configuration, which presents a meaningful association, may be defined. In particular, we also focus on the variables which may be used in cluster analysis. In fact, variables which contain little clustering information can cause misleading and not-robustness results. Therefore, three algorithms are employed in this study： K-means partitioning methods, Partitioning Around Medoids （PAM） and the Heuristic Identification of Noisy Variables （HINoV）. The results are compared with robust methods ones.

The upper bound of the optimal number of clusters in fuzzy clustering

The upper bound of the optimal number of clusters in clustering algorithm is studied in this paper. A new method is proposed to solve this issue. This method shows that the rule cmax≤N^(1/N), which is popular in current papers, is reasonable in some sense. The above conclusion is tested and analyzed by some typical examples in the literature, which demonstrates the validity of the new method.

Knowledge-Driven Possibilistic Clustering with Automatic Cluster Elimination

Traditional Fuzzy C-Means(FCM)and Possibilistic C-Means(PCM)clustering algorithms are data-driven,and their objective function minimization process is based on the available numeric data.Recently,knowledge hints have been introduced to formknowledge-driven clustering algorithms,which reveal a data structure that considers not only the relationships between data but also the compatibility with knowledge hints.However,these algorithms cannot produce the optimal number of clusters by the clustering algorithm itself;they require the assistance of evaluation indices.Moreover,knowledge hints are usually used as part of the data structure(directly replacing some clustering centers),which severely limits the flexibility of the algorithm and can lead to knowledgemisguidance.To solve this problem,this study designs a newknowledge-driven clustering algorithmcalled the PCM clusteringwith High-density Points(HP-PCM),in which domain knowledge is represented in the form of so-called high-density points.First,a newdatadensitycalculation function is proposed.The Density Knowledge Points Extraction(DKPE)method is established to filter out high-density points from the dataset to form knowledge hints.Then,these hints are incorporated into the PCM objective function so that the clustering algorithm is guided by high-density points to discover the natural data structure.Finally,the initial number of clusters is set to be greater than the true one based on the number of knowledge hints.Then,the HP-PCM algorithm automatically determines the final number of clusters during the clustering process by considering the cluster elimination mechanism.Through experimental studies,including some comparative analyses,the results highlight the effectiveness of the proposed algorithm,such as the increased success rate in clustering,the ability to determine the optimal cluster number,and the faster convergence speed.

Performances of Clustering Methods Considering Data Transformation and Sample Size: An Evaluation with Fisheries Survey Data

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 based segmentation of text in complex color images

We propose a novel scheme based on clustering analysis in color space to solve text segmentation in complex color images. Text segmentation includes automatic clustering of color space and foreground image generation. Two methods are also proposed for automatic clustering: The first one is to determine the optimal number of clusters and the second one is the fuzzy competitively clustering method based on competitively learning techniques. Essential foreground images obtained from any of the color clusters are combined into foreground images. Further performance analysis reveals the advantages of the proposed methods.

Automatic Data Clustering Based Mean Best Artificial Bee Colony Algorithm

Fuzzy C-means(FCM)is a clustering method that falls under unsupervised machine learning.The main issues plaguing this clustering algorithm are the number of the unknown clusters within a particular dataset and initialization sensitivity of cluster centres.Artificial Bee Colony(ABC)is a type of swarm algorithm that strives to improve the members’solution quality as an iterative process with the utilization of particular kinds of randomness.However,ABC has some weaknesses,such as balancing exploration and exploitation.To improve the exploration process within the ABC algorithm,the mean artificial bee colony(MeanABC)by its modified search equation that depends on solutions of mean previous and global best is used.Furthermore,to solve the main issues of FCM,Automatic clustering algorithm was proposed based on the mean artificial bee colony called(AC-MeanABC).It uses the MeanABC capability of balancing between exploration and exploitation and its capacity to explore the positive and negative directions in search space to find the best value of clusters number and centroids value.A few benchmark datasets and a set of natural images were used to evaluate the effectiveness of AC-MeanABC.The experimental findings are encouraging and indicate considerable improvements compared to other state-of-the-art approaches in the same domain.