Exact Number Of Clusters Research Articles

Formula omitted]-Means algorithms for clustering analysis with frequency sensitive discrepancy metrics

This paper proposes a new kind of k′-means algorithms for clustering analysis with three frequency sensitive (data) discrepancy metrics in the cases that the exact number of clusters in a dataset is not pre-known. That is, by setting the number k of seed-points for learning clusters to be larger than the true number k′ of actual clusters in the dataset, i.e., k>k′, these algorithms can locate the centers of k′ actual clusters by k′ converged seed-points, respectively, with the extra k-k′ seed-points corresponding to empty clusters, namely containing no winning points in the competition according to the underlying frequency sensitive discrepancy metrics. It is demonstrated by the experiments on both synthetic and real-world datasets that these three new k′-means clustering algorithms can detect the number of actual clusters in a dataset with a classification accuracy rate as high as or higher than that of the original k′-means algorithm. Moreover, they converge more quickly than the original one.

ACOMCD: A multiple cluster detection algorithm based on the spatial scan statistic and ant colony optimization

The spatial scan statistic (SaTScan) has become one of the most popular methods for detecting and evaluating spatial clusters. However, this method can only identify circular or elliptical clusters and is not a good fit for the detection of irregularly shaped clusters. Numerous methods have since been proposed to solve this problem. Nevertheless, if multiple clusters coexist, these methods may not identify the correct situation, because the interference between clusters can easily lead to a tree-like shaped cluster and cause confusion in the results. In this paper, we propose an Ant Colony Optimization based Multiple Cluster Detection (ACOMCD) algorithm, which combines classical SaTScan with the ant colony optimization (ACO) approach. In the initial stage, SaTScan is first used to mark the candidate cluster areas according to the significance of their maximum likelihood evaluations. Then ACO-based scan statistic is carried out separately on these candidate clusters to identify their natural shapes. The algorithm was designed for spatial regional count data only. Comparisons between ACOMCD, SaTScan, GaScan (genetic algorithm-based scan statistic), and FleXScan (flexibly shaped spatial scan statistic) on three kinds of simulated datasets show that ACOMCD performs the best in simultaneously determining the exact number of clusters and identifying multiple irregularly shaped clusters. A case study on esophageal cancer in eastern China further validates the correctness and effectiveness of ACOMCD.

Automatic pattern recognition and color separation of embroidery fabrics

Currently, there is very little literature on automatic image recognition and classification of embroidery fabrics. In today’s embroidery industry, front-end pattern-making still relies greatly on labor, using pattern-making software to carefully depict patterns and images in different colors and regions. Hence, an image analysis system that can recognize colors, regions and patterns automatically is a critical technique of improving the competitiveness of the embroidery industry. In this paper, the mean filtering method, central-weighted median filtering method and morphological operation were employed to filter out the light variation on the embroidery fabric surface structure, and a genetic algorithm was applied to distinguish images of repeat pattern embroidery from that of nonrepeat pattern embroidery. If it is a repeat pattern, then a much smaller sized subimage would be searched in the original image for the same color components and spatial structure, which could lower the computing load of the entire image greatly and is expected to achieve the processing speed required in an online real-time system. As for nonrepeat pattern embroidery images, discrete wavelet transform was applied to acquire low-frequency subimages, which can retain important image features while improving the computing efficiency. Be it a repeat or nonrepeat pattern, after obtaining subimages, specific criteria were used to determine the exact number of clusters, and the weighted fuzzy C-means method was employed to run color separation and region separation. The experiment proved that, in regard to the color embroidery images of repeat and nonrepeat patterns, the method proposed in this paper succeeded in color and region separations with good result.

Improving rival penalized competitive learning using density‐evaluated mechanism

Rival penalized competitive learning (RPCL) and its variants have provided attractive ways to perform clustering without knowing the exact cluster number. However, they are always accompanied by problems of falling in local optima and slow learning speed. Thus we investigate the RPCL and propose a mechanism to directly prune the RPCL's structure by evaluating the data density of each unit. We call the new strategy density‐evaluated RPCL (DERPCL). The communication channel state is estimated by the DERPCL in the simulations, and comprehensive comparisons are made with other RPCLs. Results show that the DERPCL is superior in terms of convergence accuracy and speed.

A quantum-inspired genetic algorithm for k-means clustering

The number of clusters has to be known in advance for the conventional k-means clustering algorithm and moreover the clustering result is sensitive to the selection of the initial cluster centroids. This sensitivity may make the algorithm converge to the local optima. This paper proposes a quantum-inspired genetic algorithm for k-means clustering (KMQGA). In KMQGA, a Q-bit based representation is employed for exploration and exploitation in discrete 0–1 hyperspace using rotation operation of quantum gate as well as the typical genetic algorithm operations (selection, crossover and mutation) of Q-bits. Different from the typical quantum-inspired genetic algorithms (QGA), the length of a Q-bit in KMQGA is variable during evolution. Without knowing the exact number of clusters beforehand, KMQGA can obtain the optimal number of clusters as well as providing the optimal cluster centroids. Both the simulated datasets and the real datasets are used to validate KMQGA, respectively. The experimental results show that KMQGA is promising and effective.

Identifying clusters of user behavior in intranet search engine log files

AbstractWhen studying how ordinary Web users interact with Web search engines, researchers tend to either treat the users as a homogeneous group or group them according to search experience. Neither approach is sufficient, we argue, to capture the variety in behavior that is known to exist among searchers. By applying automatic clustering technique based on self‐organizing maps to search engine log files from a corporate intranet, we show that users can be usefully separated into distinguishable segments based on their actual search behavior. Based on these segments, future tools for information seeking and retrieval can be targeted to specific segments rather than just made to fit the “the average user.” The exact number of clusters, and to some extent their characteristics, can be expected to vary between intranets, but our results indicate that some more generic groups may exist. In our study, a large group of users appeared to be “fact seekers” who would benefit from higher precision, a smaller group of users were more holistically oriented and would likely benefit from higher recall, and a third category of users seemed to constitute the knowledgeable users. These three groups may raise different design implications for search‐tool developers.

An efficient k′-means clustering algorithm

This paper introduces k′-means algorithm that performs correct clustering without pre-assigning the exact number of clusters. This is achieved by minimizing a suggested cost-function. The cost-function extends the mean-square-error cost-function of k-means. The algorithm consists of two separate steps. The first is a pre-processing procedure that performs initial clustering and assigns at least one seed point to each cluster. During the second step, the seed-points are adjusted to minimize the cost-function. The algorithm automatically penalizes any possible winning chances for all rival seed-points in subsequent iterations. When the cost-function reaches a global minimum, the correct number of clusters is determined and the remaining seed points are located near the centres of actual clusters. The simulated experiments described in this paper confirm good performance of the proposed algorithm.

On rival penalization controlled competitive learning for clustering with automatic cluster number selection

The existing rival penalized competitive learning (RPCL) algorithm and its variants have provided an attractive way to perform data clustering without knowing the exact number of clusters. However, their performance is sensitive to the preselection of the rival delearning rate. In this paper, we further investigate the RPCL and present a mechanism to control the strength of rival penalization dynamically. Consequently, we propose the rival penalization controlled competitive learning (RPCCL) algorithm and its stochastic version. In each of these algorithms, the selection of the delearning rate is circumvented using a novel technique. We compare the performance of RPCCL to RPCL in Gaussian mixture clustering and color image segmentation, respectively. The experiments have produced the promising results.

Improving the Robustness of ?Online Agglomerative Clustering Method? Based on Kernel-Induce Distance Measures

Recently, an online agglomerative clustering method called AddC (I. D. Guedalia et al. Neural Comput. {\bf 11} (1999), 521--540) was proposed for nonstationary data clustering. Although AddC possesses many good attributes, a vital problem of that method is its sensitivity to noises, which limits its use in real-word applications. In this paper, based on \hbox{kernel-induced} distance measures, a robust online clustering (ROC) algorithm is proposed to remedy the problem of AddC. Experimental results on artificial and benchmark data sets show that ROC has better clustering performances than AddC, while still inheriting advantages such as clustering data in a single pass and without knowing the exact number of clusters beforehand.

-Means: A new generalized k-means clustering algorithm

This paper presents a generalized version of the conventional k -means clustering algorithm [Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability, 1, University of California Press, Berkeley, 1967, p. 281]. Not only is this new one applicable to ellipse-shaped data clusters without dead-unit problem, but also performs correct clustering without pre-assigning the exact cluster number. We qualitatively analyze its underlying mechanism, and show its outstanding performance through the experiments.

Robust shape detection using fuzzy clustering: practical applications

Abstract Problem of accurate shape detection in practical applications is considered. The work is motivated by several experimental studies in granular flow research, where in general, the objects imaged are spherical particles. A new algorithm called the divide and conquer noise fuzzy c -shells clustering (D&C-NFCS) is proposed, with these particular applications in mind, for detecting circles and ellipses in noisy images without requiring prior knowledge of the exact number of clusters. This unsupervised algorithm uses Hough transform (HT) based methods to provide very rough initial estimates of the cluster prototypes for use in the fuzzy c -shells (FCS) type algorithms. The results of HT are also used to segment the raw data so that the FCS algorithm can be applied to detect one cluster at a time. The concept of recently introduced noise clustering algorithm is also used to make the algorithm robust against noise. Results of this algorithm for several practical examples from granular flow experiments are shown demonstrating high speed and accuracy. When compared with the methods based on HT alone, this approach results in a significant improvement in detection accuracy. Cluster validity issues are also discussed.