scholarly journals Fuzzy Clustering Algorithms for Image Segmentation

2011 ◽  
Author(s):  
Alberto Rey ◽  
Alfonso Castro ◽  
Bernardino Arcay
Keyword(s):  
Fuzzy Clustering ◽  
Euclidean Distance ◽  
Spatial Information ◽  
Multicore Processors ◽  
Clustering Algorithms ◽  
Source Code ◽  
Spatial Constraints ◽  
3D Images ◽  
Fuzzy C Means ◽  
The Membership Function

In this document we present the implementation of three fuzzy clustering algorithms using the Insight Toolkit ITK. Firstly, we developed the conventional Fuzzy C-Means that will serve as the basis for the rest of the proposed algorithms. The next algorithms are the FCM with spatial constraints based on kernel-induced distance and the Modified Spatial Kernelized Fuzzy C-Means. Both of these introduce a Kernel function, replacing the Euclidean distance of the FCM, and spatial information into the membership function.These algorithms have been implemented in a threaded version to take advantage of the multicore processors. Moreover, providing an useful implementation make it possible that classes work with 2D/3D images, different kernels and spatial shapes.We included the source code as well as different 2D/3D examples, using several input parameters for the algorithms and obtaining the results generated on 2D/3D CT lung studies.

Construct Knowledge Structure of Linear Algebra

2011 ◽  
Vol 211-212 ◽  
pp. 793-797
Author(s):  
Chin Chun Chen ◽  
Yuan Horng Lin ◽  
Jeng Ming Yih ◽  
Sue Fen Huang
Keyword(s):  
Knowledge Management ◽  
Linear Algebra ◽  
Fuzzy Clustering ◽  
Mahalanobis Distance ◽  
Clustering Algorithms ◽  
Knowledge Structure ◽  
Interpretive Structural Modeling ◽  
Cognitive Characteristics ◽  
Fuzzy C Means ◽  
Fuzzy C Means Algorithm

Apply interpretive structural modeling to construct knowledge structure of linear algebra. New fuzzy clustering algorithms improved fuzzy c-means algorithm based on Mahalanobis distance has better performance than fuzzy c-means algorithm. Each cluster of data can easily describe features of knowledge structures individually. The results show that there are six clusters and each cluster has its own cognitive characteristics. The methodology can improve knowledge management in classroom more feasible.

Fuzzyc-Means Algorithms Using Kullback-Leibler Divergence and Helliger Distance Based on Multinomial Manifold

2008 ◽  
Vol 12 (5) ◽  
pp. 443-447 ◽  
Author(s):  
Ryo Inokuchi ◽  
◽  
Sadaaki Miyamoto ◽  
Keyword(s):  
Fuzzy Clustering ◽  
Euclidean Distance ◽  
Geodesic Distance ◽  
Clustering Algorithms ◽  
Multinomial Distribution ◽  
Discrete Data ◽  
Hellinger Distance ◽  
Statistical Manifold ◽  
Data Space ◽  
Leibler Divergence

In this paper, we discuss fuzzy clustering algorithms for discrete data. Data space is represented as a statistical manifold of the multinomial distribution, and then the Euclidean distance are not adequate in this setting. The geodesic distance on the multinomial manifold can be derived analytically, but it is difficult to use it as a metric directly. We propose fuzzyc-means algorithms using other metrics: the Kullback-Leibler divergence and the Hellinger distance, instead of the Euclidean distance. These two metrics are regarded as approximations of the geodesic distance.

scholarly journals Robust Deep Kernel-Based Fuzzy Clustering With Spatial Information for Image Segmentation

2021 ◽  
Author(s):  
Lujia Lei ◽  
Chengmao Wu ◽  
Xiaoping Tian
Keyword(s):  
Image Segmentation ◽  
Kernel Function ◽  
Loss Function ◽  
Fuzzy Clustering ◽  
Clustering Algorithm ◽  
Spatial Information ◽  
Clustering Algorithms ◽  
Noise Robustness ◽  
Neighborhood Information ◽  
Classical Image

Abstract Clustering algorithms with deep neural network have attracted wide attention of scholars. A deep fuzzy K-means clustering algorithm model with adaptive loss function and entropy regularization (DFKM) is proposed by combining automatic encoder and clustering algorithm. Although it introduces adaptive loss function and entropy regularization to improve the robustness of the model, its segmentation effect is not ideal for high noise; At the same time, its model does not use a convolutional auto-encoder, which is not suitable for high-dimensional images.Therefore, on the basis of DFKM, this paper focus on image segmentation, combine neighborhood median and mean information of current pixel, introduce neighborhood information of membership degree, and extend Euclidean distance to kernel space by using kernel function, propose a dual-neighborhood information constrained deep fuzzy clustering based on kernel function (KDFKMS). A large number of experimental results show that compared with DFKM and classical image segmentation algorithms, this algorithm has stronger anti-noise robustness.

scholarly journals Extended Single-Iteration Fuzzy C-Means, and Gustafson-Kessel Algorithms for Medium-Sized (106) Multisource Weber Problem

2019 ◽  
Vol 10 (3) ◽  
pp. 1-15 ◽  
Author(s):  
Tarik Kucukdeniz ◽  
Sakir Esnaf ◽  
Engin Bayturk
Keyword(s):  
Fuzzy Clustering ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Cluster Center ◽  
Medium Size ◽  
Weber Problem ◽  
Solution Approach ◽  
Fuzzy C Means ◽  
Novel Approach ◽  
New Facilities

An uncapacitated multisource Weber problem involves finding facility locations for known customers. When this problem is restated as finding locations for additional new facilities, while keeping the current facilities, a new solution approach is needed. In this study, two new and cooperative fuzzy clustering algorithms are developed to solve a variant of the uncapacitated version of a multisource Weber problem (MWP). The first algorithm proposed is the extensive version of the single iteration fuzzy c-means (SIFCM) algorithm. The SIFCM algorithm assigns customers to existing facilities. The new extended SIFCM (ESIFCM), which is first proposed in this study, allocates discrete locations (coordinates) with the SIFCM and locates and allocates continuous locations (coordinates) with the original FCM simultaneously. If the SIFCM and the FCM, show differences between the successive cluster center values are still decreasing, share customer points among facilities. It is simply explained as single-iteration fuzzy c-means with fuzzy c-means. The second algorithm, also proposed here, runs like the ESIFCM. Instead of the FCM, a Gustafson-Kessel (GK) fuzzy clustering algorithm is used under the same framework. This algorithm is based on single-iteration (SIGK) and the GK algorithms. Numerical results are reported using two MWP problems in a class of a medium-size-data (106 bytes). Using clustering algorithms to locate and allocate the new facilities while keeping current facilities is a novel approach. When applied to the big problems, the speed of the proposed algorithms enable to find a solution while mathematical programming solution is not doable due to the great computational costs.

Identifying the Mastery Concepts in Linear Algebra by Using FCM-CM Algorithm

2010 ◽  
Vol 44-47 ◽  
pp. 3897-3901
Author(s):  
Hsiang Chuan Liu ◽  
Yen Kuei Yu ◽  
Jeng Ming Yih ◽  
Chin Chun Chen
Keyword(s):  
Objective Function ◽  
Linear Algebra ◽  
Fuzzy Clustering ◽  
Distance Function ◽  
Mahalanobis Distance ◽  
Euclidean Distance ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Euclidean Distance Function ◽  
Fuzzy C Means Algorithm

Euclidean distance function based fuzzy clustering algorithms can only be used to detect spherical structural clusters. Gustafson-Kessel (GK) clustering algorithm and Gath-Geva (GG) clustering algorithm were developed to detect non-spherical structural clusters by employing Mahalanobis distance in objective function, however, both of them need to add some constrains for Mahalanobis distance. In this paper, the authors’ improved Fuzzy C-Means algorithm based on common Mahalanobis distance (FCM-CM) is used to identify the mastery concepts in linear algebra, for comparing the performances with other four partition algorithms; FCM-M, GG, GK, and FCM. The result shows that FCM-CM has better performance than others.

scholarly journals Robust Semisupervised Kernelized Fuzzy Local Information C-Means Clustering for Image Segmentation

2020 ◽  
Vol 2020 ◽  
pp. 1-22
Author(s):  
Yao Yang ◽  
Chengmao Wu ◽  
Yawen Li ◽  
Shaoyu Zhang
Keyword(s):  
Image Segmentation ◽  
Fuzzy Clustering ◽  
Clustering Algorithms ◽  
Feature Space ◽  
Iterative Solution ◽  
Segmentation Algorithm ◽  
Gaussian Kernel ◽  
Fuzzy C Means ◽  
Different Types ◽  
Fuzzy C Means Clustering

To improve the effectiveness and robustness of the existing semisupervised fuzzy clustering for segmenting image corrupted by noise, a kernel space semisupervised fuzzy C-means clustering segmentation algorithm combining utilizing neighborhood spatial gray information with fuzzy membership information is proposed in this paper. The mean intensity information of neighborhood window is embedded into the objective function of the existing semisupervised fuzzy C-means clustering, and the Lagrange multiplier method is used to obtain its iterative expression corresponding to the iterative solution of the optimization problem. Meanwhile, the local Gaussian kernel function is used to map the pixel samples from the Euclidean space to the high-dimensional feature space so that the cluster adaptability to different types of image segmentation is enhanced. Experiment results performed on different types of noisy images indicate that the proposed segmentation algorithm can achieve better segmentation performance than the existing typical robust fuzzy clustering algorithms and significantly enhance the antinoise performance.

Adaptive Kernel-Based Fuzzy C-Means Clustering with Spatial Constraints for Image Segmentation

2018 ◽  
Vol 33 (01) ◽  
pp. 1954003 ◽  
Author(s):  
Guang Hu ◽  
Zhenbin Du
Keyword(s):  
Image Segmentation ◽  
Clustering Algorithm ◽  
Spatial Information ◽  
Spatial Constraints ◽  
Fuzzy C Means ◽  
Central Pixel ◽  
Fuzzy C Means Clustering ◽  
Adaptive Kernel ◽  
Fcm Clustering ◽  
Image Pixels

In order to resolve the disadvantages of fuzzy C-means (FCM) clustering algorithm for image segmentation, an improved Kernel-based fuzzy C-means (KFCM) clustering algorithm is proposed. First, the reason why the kernel function is introduced is researched on the basis of the classical KFCM clustering. Then, using spatial neighborhood constraint property of image pixels, an adaptive weighted coefficient is introduced into KFCM to control the influence of the neighborhood pixels to the central pixel automatically. At last, a judging rule for partition fuzzy clustering numbers is proposed that can decide the best clustering partition numbers and provide an optimization foundation for clustering algorithm. An adaptive kernel-based fuzzy C-means clustering with spatial constraints (AKFCMS) model for image segmentation approach is proposed in order to improve the efficiency of image segmentation. Various experiment results show that the proposed approach can get the spatial information features of an image accurately and is robust to realize image segmentation.

Kernelised Rough Sets Based Clustering Algorithms Fused With Firefly Algorithm for Image Segmentation

2019 ◽  
Vol 8 (4) ◽  
pp. 25-38
Author(s):  
Srujan Sai Chinta
Keyword(s):  
Image Segmentation ◽  
Euclidean Distance ◽  
Firefly Algorithm ◽  
Clustering Algorithms ◽  
Kernel Functions ◽  
Gaussian Kernel ◽  
Clustering Methods ◽  
Fuzzy C Means ◽  
Intuitionistic Fuzzy ◽  
Radial Basis

Data clustering methods have been used extensively for image segmentation in the past decade. In one of the author's previous works, this paper has established that combining the traditional clustering algorithms with a meta-heuristic like the Firefly Algorithm improves the stability of the output as well as the speed of convergence. It is well known now that the Euclidean distance as a measure of similarity has certain drawbacks and so in this paper we replace it with kernel functions for the study. In fact, the authors combined Rough Fuzzy C-Means (RFCM) and Rough Intuitionistic Fuzzy C-Means (RIFCM) with Firefly algorithm and replaced Euclidean distance with either Gaussian or Hyper-tangent or Radial basis Kernels. This paper terms these algorithms as Gaussian Kernel based rough Fuzzy C-Means with Firefly Algorithm (GKRFCMFA), Hyper-tangent Kernel based rough Fuzzy C-Means with Firefly Algorithm (HKRFCMFA), Gaussian Kernel based rough Intuitionistic Fuzzy C-Means with Firefly Algorithm (GKRIFCMFA) and Hyper-tangent Kernel based rough Intuitionistic Fuzzy C-Means with Firefly Algorithm (HKRIFCMFA), Radial Basis Kernel based rough Fuzzy C-Means with Firefly Algorithm (RBKRFCMFA) and Radial Basis Kernel based rough Intuitionistic Fuzzy C-Means with Firefly Algorithm (RBKRIFCMFA). In order to establish that these algorithms perform better than the corresponding Euclidean distance-based algorithms, this paper uses measures such as DB and Dunn indices. The input data comprises of three different types of images. Also, this experimentation varies over different number of clusters.

Sign in / Sign up

Export Citation Format

Share Document