On Possibilistic Clustering Methods Based on Shannon/Tsallis-Entropy for Spherical Data and Categorical Multivariate Data

2015 ◽  
pp. 115-128 ◽  
Author(s):  
Yuchi Kanzawa
Keyword(s):  
Multivariate Data ◽  
Tsallis Entropy ◽  
Clustering Methods ◽  
Spherical Data ◽  
Possibilistic Clustering

Possibilistic Clustering Methods for Interval-Valued Data

2014 ◽  
Vol 22 (02) ◽  
pp. 263-291 ◽  
Author(s):  
Bruno Almeida Pimentel ◽  
Renata M. C. R. De Souza
Keyword(s):  
Credit Card ◽  
Data Sets ◽  
Clustering Methods ◽  
Cluster Algorithms ◽  
Research Areas ◽  
Possibilistic Clustering ◽  
Membership Value ◽  
Type Data ◽  
Interval Type ◽  
Better Than

Outliers may have many anomalous causes, for example, credit card fraud, cyberintrusion or breakdown of a system. Several research areas and application domains have investigated this problem. The popular fuzzy c-means algorithm is sensitive to noise and outlying data. In contrast, the possibilistic partitioning methods are used to solve these problems and other ones. The goal of this paper is to introduce cluster algorithms for partitioning a set of symbolic interval-type data using the possibilistic approach. In addition, a new way of measuring the membership value, according to each feature, is proposed. Experiments with artificial and real symbolic interval-type data sets are used to evaluate the methods. The results of the proposed methods are better than the traditional soft clustering ones.

Fuzzy Clustering Methods for Categorical Multivariate Data Based on q-Divergence

2018 ◽  
Vol 22 (4) ◽  
pp. 524-536 ◽  
Author(s):  
Tadafumi Kondo ◽  
◽  
Yuchi Kanzawa
Keyword(s):  
Conventional Method ◽  
Fuzzy Clustering ◽  
Optimization Problems ◽  
Clustering Algorithms ◽  
Multivariate Data ◽  
Clustering Methods ◽  
Kl Divergence ◽  
Fuzzy Clustering Methods ◽  
Conventional Methods ◽  
Vectorial Data

This paper presents two fuzzy clustering algorithms for categorical multivariate data based on q-divergence. First, this study shows that a conventional method for vectorial data can be explained as regularizing another conventional method using q-divergence. Second, based on the known results that Kullback-Leibler (KL)-divergence is generalized into the q-divergence, and two conventional fuzzy clustering methods for categorical multivariate data adopt KL-divergence, two fuzzy clustering algorithms for categorical multivariate data that are based on q-divergence are derived from two optimization problems built by extending the KL-divergence in these conventional methods to the q-divergence. Through numerical experiments using real datasets, the proposed methods outperform the conventional methods in term of clustering accuracy.

Fuzzy Clustering Based on Total Uncertainty Degree

2007 ◽  
Vol 11 (8) ◽  
pp. 897-904
Author(s):  
Tomohito Esaki ◽  
◽  
Tomonori Hashiyama ◽  
Yahachiro Tsukamoto ◽  
◽  
...  
Keyword(s):  
Membership Function ◽  
Fuzzy Clustering ◽  
Numerical Experiments ◽  
Data Distribution ◽  
Membership Functions ◽  
Objective Functions ◽  
Clustering Methods ◽  
Total Uncertainty ◽  
Possibilistic Clustering ◽  
Evidential Theory

Traditional Fuzzy c-Means (FCM) methods have probabilistic and additive restrictions that ∑ μ (x) = 1; the sum of membership values on the identified membership function is one. Possibilistic clustering methods identify membership functions without such constraints, but some parameters used in objective functions are difficult to understand and membership function shapes are independent of clusters estimated through possibilistic methods. We propose novel fuzzy clustering using a total uncertainty degree based on evidential theory with which we obtain nonadditive membership functions whose their shapes depend on data distribution, i.e., they mutually differ. Cluster meanings thus become easier to understand than in possibilistic methods and our proposal requires only one parameter “fuzzifier.” Numerical experiments demonstrated the feasibility of our proposal conducted.

On Sequential Cluster Extraction Based onL1-Regularized Possibilisticc-Means

2015 ◽  
Vol 19 (5) ◽  
pp. 655-661 ◽  
Author(s):  
Yukihiro Hamasuna ◽  
◽  
Yasunori Endo ◽  
Keyword(s):  
Rand Index ◽  
Clustering Methods ◽  
Number Of Clusters ◽  
Numerical Examples ◽  
Allocation Rules ◽  
Possibilistic Clustering ◽  
Extraction Algorithm ◽  
The Relationship

Sequential cluster extraction algorithms are useful clustering methods that extract clusters one by one without the number of clusters having to be determined in advance. Typical examples of these algorithms are sequential hardc-means (SHCM) and possibilistic clustering (PCM) based algorithms. Two types ofL1-regularized possibilistic clustering are proposed to induce crisp and possibilistic allocation rules and to construct a novel sequential cluster extraction algorithm. The relationship between the proposed method and SHCM is also discussed. The effectiveness of the proposed method is verified through numerical examples. Results show that the entropy-based method yields better results for the Rand Index and the number of extracted clusters.

Brain Magnetic Resonance Imaging Segmentation Using Possibilistic Clustering Algorithm Combined with Context Constraints

2020 ◽  
Vol 10 (7) ◽  
pp. 1669-1674
Author(s):  
Zixuan Cheng ◽  
Li Liu
Keyword(s):  
Image Segmentation ◽  
Iterative Process ◽  
Clustering Algorithm ◽  
Spatial Information ◽  
Brain Magnetic Resonance Imaging ◽  
Medical Image Segmentation ◽  
Clustering Methods ◽  
Possibilistic Clustering ◽  
Image Pixels ◽  
Context Constraints

Because the FCM method is simple and effective, a series of research results based on this method are widely used in medical image segmentation. Compared with the traditional FCM, the probability clustering (PCM) algorithm cancels the constraint on the normalization of each sample membership degree in the iterative process, and the clustering effect of the method is improved within a certain range. However, the above two methods only use the gray value of the image pixels in the iterative process, ignoring the context constraint relationship between the high-dimensional image pixels. The two are easily affected by image noise during the segmentation process, resulting in poor robustness, which will affect the segmentation accuracy in practical applications. In order to alleviate this problem, this paper introduces the context constraint information of image based on PCM, and proposes a PCM algorithm that combines context constraints (CCPCM) and successfully applies it to human brain MR image segmentation to further improve the noise immunity of the new algorithm. Expand the applicability of new algorithms in the medical field. Through simulation results on medical images, it is found that compared with the previous classical clustering methods, such as FCM, PCM, etc., the CCPCM has better anti-interference to different noises, and the segmentation boundary is clearer. At the same time, CCPCM algorithm introduces the spatial neighbor information adaptive weighting mechanism in the clustering process, which can adaptively adjust the constraint weight of spatial information and optimize the clustering process, thus improving the segmentation efficiency.

scholarly journals An Instinctive Method for Lesion Detection in Diabetic Retinopathy Images using a Novel Spatial Possibilistic C means Clustering in Kernel Space

2019 ◽  
Vol 8 (2S11) ◽  
pp. 2380-2386
Keyword(s):  
Diabetic Retinopathy ◽  
Spatial Information ◽  
Light Sensitivity ◽  
Lesion Detection ◽  
Clustering Methods ◽  
Kernel Space ◽  
Endothelial Lining ◽  
Blurred Vision ◽  
Blood Capillaries ◽  
Possibilistic Clustering

Diabetic Retinopathy (DR) is the prime cause of vision impediment which originates due micro vascular changes and hyperglycemia stimulated by Diabetes Mellitus (DM). Endothelial lining of the blood capillaries absorbs excess amount of glucose (glycoproteins), hence become thick but are fragile. The swollen capillaries may burst and leak water, proteins, and lipids and tends to fovea expansion. Further it triggers the revascularization to nourish retinal fundus. These new blood capillaries are weak and fragile and can further progress the state to chronic. Pupil dilation for fundus observation leads to many ill effects like head ache, brow pain, blurred vision and light sensitivity. Ophthalmologists cannot administer the pathos well if the symptoms are indolently addressed by the patient and therefore reliability during subjective diagnosis lags. This paper address a qualitative evaluation of novel possibilistic clustering methods with induced spatial constraint in kernel domain to detect the presence of exudates in non-dilated DR images. This methods are compiled in an N dimensional Kernel space which helps to easily segregate the non-linear data regions present in the lower dimensional input space. Also the inclusion of spatial information of a pixel neighborhood will improves the noise handling capability of the proposed methods by easily extricating the noisy pixels from the target lesions and hence improves the system’s accuracy in attaining reliable data. Statistical evaluation reveals that the proposed algorithms has attained better sensitivity and specificity compared to existing state-of-art works.

Power-Regularized Fuzzy Clustering for Spherical Data

2018 ◽  
Vol 22 (2) ◽  
pp. 163-171
Author(s):  
Yuchi Kanzawa ◽  
Keyword(s):  
Fuzzy Clustering ◽  
Numerical Experiments ◽  
Clustering Methods ◽  
Clustering Method ◽  
Spherical Data ◽  
Fuzzy Clustering Method ◽  
Fuzzy Clustering Methods ◽  
Artificial Datasets

In this paper, a power-regularization-based fuzzy clustering method is proposed for spherical data. Power regularization has not been previously applied to fuzzy clustering for spherical data. The proposed method is transformed to the conventional fuzzy clustering method, entropy-regularized fuzzy clustering for spherical data (eFCS), for a specified fuzzification parameter value. Numerical experiments on two artificial datasets reveal the properties of the proposed method. Furthermore, numerical experiments on four real datasets indicate that this method is more accurate than the conventional fuzzy clustering methods: standard fuzzy clustering for spherical data (sFCS) and eFCS.

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