• Communications for Statistical Applications and Methods
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• 제22권4호
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• pp.321-331
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• 2015

The K-means clustering algorithm is a popular and widely used method for clustering. For covariance matrices, we consider a geodesic clustering algorithm based on the K-means clustering framework in consideration of symmetric positive definite matrices as a Riemannian (non-Euclidean) manifold. This paper considers a geodesic clustering algorithm for data consisting of symmetric positive definite (SPD) matrices, utilizing the Riemannian geometric structure for SPD matrices and the idea of a K-means clustering algorithm. A K-means clustering algorithm is divided into two main steps for which we need a dissimilarity measure between two matrix data points and a way of computing centroids for observations in clusters. In order to use the Riemannian structure, we adopt the geodesic distance and the intrinsic mean for symmetric positive definite matrices. We demonstrate our proposed method through simulations as well as application to real financial data.

• ETRI Journal
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• 제36권3호
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• pp.333-342
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• 2014

Most hyper-ellipsoidal clustering (HEC) approaches use the Mahalanobis distance as a distance metric. It has been proven that HEC, under this condition, cannot be realized since the cost function of partitional clustering is a constant. We demonstrate that HEC with a modified Gaussian kernel metric can be interpreted as a problem of finding condensed ellipsoidal clusters (with respect to the volumes and densities of the clusters) and propose a practical HEC algorithm that is able to efficiently handle clusters that are ellipsoidal in shape and that are of different size and density. We then try to refine the HEC algorithm by utilizing ellipsoids defined on the kernel feature space to deal with more complex-shaped clusters. The proposed methods lead to a significant improvement in the clustering results over K-means algorithm, fuzzy C-means algorithm, GMM-EM algorithm, and HEC algorithm based on minimum-volume ellipsoids using Mahalanobis distance.

• Journal of Information Processing Systems
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• 제13권6호
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• pp.1467-1486
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• 2017

Fuzzy co-clustering is sensitive to noise data. To overcome this noise sensitivity defect, possibilistic clustering relaxes the constraints in FCM-type fuzzy (co-)clustering. In this paper, we introduce a new possibilistic fuzzy co-clustering algorithm based on information bottleneck (ibPFCC). This algorithm combines fuzzy co-clustering and possibilistic clustering, and formulates an objective function which includes a distance function that employs information bottleneck theory to measure the distance between feature data point and feature cluster centroid. Many experiments were conducted on three datasets and one artificial dataset. Experimental results show that ibPFCC is better than such prominent fuzzy (co-)clustering algorithms as FCM, FCCM, RFCC and FCCI, in terms of accuracy and robustness.

• Journal of Information Processing Systems
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• 제20권2호
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• pp.185-199
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• 2024

In this paper, an improved automated spectral clustering (IASC) algorithm is proposed to address the limitations of the traditional spectral clustering (TSC) algorithm, particularly its inability to automatically determine the number of clusters. Firstly, a cluster number evaluation factor based on the optimal clustering principle is proposed. By iterating through different k values, the value corresponding to the largest evaluation factor was selected as the first-rank number of clusters. Secondly, the IASC algorithm adopts a density-sensitive distance to measure the similarity between the sample points. This rendered a high similarity to the data distributed in the same high-density area. Thirdly, to improve clustering accuracy, the IASC algorithm uses the cosine angle classification method instead of K-means to classify the eigenvectors. Six algorithms-K-means, fuzzy C-means, TSC, EIGENGAP, DBSCAN, and density peak-were compared with the proposed algorithm on six datasets. The results show that the IASC algorithm not only automatically determines the number of clusters but also obtains better clustering accuracy on both synthetic and UCI datasets.

• Communications for Statistical Applications and Methods
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• 제26권1호
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• pp.57-67
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• 2019

Income distribution is a major concern in economic theory. In regional economics, it is often of interest to compare income distributions in different regions. Traditional methods often compare the income inequality of different regions by assuming parametric forms of the income distributions, or using summary statistics like the Gini coefficient. In this paper, we propose a nonparametric procedure to test for heterogeneity in income distributions among different regions, and a K-means clustering procedure for clustering income distributions based on energy distance. In simulation studies, it is shown that the energy distance based method has competitive results with other common methods in hypothesis testing, and the energy distance based clustering method performs well in the clustering problem. The proposed approaches are applied in analyzing data from China Health and Nutrition Survey 2011. The results indicate that there are significant differences among income distributions of the 12 provinces in the dataset. After applying a 4-means clustering algorithm, we obtained the clustering results of the income distributions in the 12 provinces.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제27권2호
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• pp.146-159
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• 2023

This paper proposes a hybrid algorithm combining K-means clustering and watershed algorithms for flower segmentation and counting. We use the K-means clustering algorithm to obtain the main colors in a complex background according to the cluster centers and then take a color space transformation to extract pixel values for the hue, saturation, and value of flower color. Next, we apply the threshold segmentation technique to segment flowers precisely and obtain the binary image of flowers. Based on this, we take the Euclidean distance transformation to obtain the distance map and apply it to find the local maxima of the connected components. Afterward, the proposed algorithm adaptively determines a minimum distance between each peak and apply it to label connected components using the watershed segmentation with eight-connectivity. On a dataset of 30 images, the test results reveal that the proposed method is more efficient and precise for the counting of overlapped flowers ignoring the degree of overlap, number of overlap, and relatively irregular shape.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제11권3호
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• pp.178-183
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• 2011

The deterministic annealing-based clustering algorithm is an EM-based algorithm which behaves like simulated annealing method, yet less sensitive to the initialization of parameters. Pairwise clustering is a kind of clustering technique to perform clustering with inter-entity distance information but not enforcing to have detailed attribute information. The pairwise deterministic annealing-based clustering algorithm repeatedly alternates the steps of estimation of mean-fields and the update of membership degrees of data objects to clusters until termination condition holds. Lacking of attribute value information, pairwise clustering algorithms do not explicitly determine the centroids or medoids of clusters in the course of clustering process or at the end of the process. This paper proposes a method to identify the medoids as the centers of formed clusters for the pairwise deterministic annealing-based clustering algorithm. Experimental results show that the proposed method locate meaningful medoids.

• 한국멀티미디어학회논문지
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• 제6권3호
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• pp.375-383
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• 2003

공간 마이닝에서 클러스터링은 오브젝트간의 거리나 연결 상태, 또는 공간상에서의 상대적인 밀도를 기반으로 서로 비슷한 오브젝트들을 하나의 그룹으로 묶는 과정이다. 실세계에서 공간 상에 분포하는 강이나 호수, 고속도로와 같은 장애물들은 클러스터링의 결과에 영향을 줄 수 있다. 본 논문은 장애물을 고려한 오브젝트 사이의 거리를 정의하고, 이를 이용하여 공간 오브젝트들을 밀도를 기반으로 클러스터링 하면서 동시에 공간상에 존재하는 장애물을 고려하는 새로운 공간 클러스터링 알고리즘(DBSCAN-O)을 제안한다. 또한 실험을 통해 DBSCAN-O가 기존의 밀도 기반 알고리즘인 DBSCAN에서 찾아내지 못한 새로운 형태의 클러스터링 결과를 도출하는 것을 보인다.

• Journal of Information Processing Systems
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• 제19권6호
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• pp.778-790
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• 2023

Although density peak clustering can often easily yield excellent results, there is still room for improvement when dealing with complex, high-dimensional datasets. One of the main limitations of this algorithm is its reliance on geometric distance as the sole similarity measurement. To address this limitation, we draw inspiration from the information bottleneck theory, and propose a novel density peak clustering algorithm that incorporates this theory as a similarity measure. Specifically, our algorithm utilizes the joint probability distribution between data objects and feature information, and employs the loss of mutual information as the measurement standard. This approach not only eliminates the potential for subjective error in selecting similarity method, but also enhances performance on datasets with multiple centers and high dimensionality. To evaluate the effectiveness of our algorithm, we conducted experiments using ten carefully selected datasets and compared the results with three other algorithms. The experimental results demonstrate that our information bottleneck-based density peaks clustering (IBDPC) algorithm consistently achieves high levels of accuracy, highlighting its potential as a valuable tool for data clustering tasks.

• 한국정보처리학회논문지
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• 제7권9호
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• pp.3029-3036
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• 2000

영상분할은 컴퓨터비전 시스템에서 영상정보추출의 중요한 과정 중의 하나이다. 이중에서 퍼지 클러스터링 방법은 영상분할에 광범위하게 사용되고 있다. 대부분의 퍼지 클러스터링 방법으로는 FCM 알고리즘이 사용된다. 그러나 FCM 알고리즘은 클러스터의 중심과 데이터간의 거리에 의존하기 때문에 클러스터 크기가 다를 경우에는 데이터가 오분류될 수 있다. 본 논문에서는 클러스트 크기에 상관없이 데이터를 분류할 수 있는 평균내부거리를 이용한 퍼지 클러스터링 알고리즘을 제안하였다. 평균내부거리는 각 데이터로부터 해당 클러스터 중심까지의 거리를 평균한 값으로 클러스터의 크기와 밀도에 비례한다. 실험 결과를 통하여 제안된 방법이 분류 엔트로피와 적합도 함수에 의해서 좋은 결과를 보여주고 있음을 증명하였다.