Mahalanobis distance based on fuzzy clustering algorithm for image segmentation

Conventional Fuzzy C-means (FCM) algorithm uses Euclidean distance to describe the dissimilarity between data and cluster prototypes. Since the Euclidean distance based dissimilarity measure only characterizes the mean information of a cluster, it is sensitive to noise and cluster divergence. In this paper, we propose a novel fuzzy clustering algorithm for image segmentation, in which the Mahalanobis distance is utilized to define the dissimilarity measure. We add a new regularization term to the objective function of the proposed algorithm, reflecting the covariance of the cluster. We experimentally demonstrate the effectiveness of the proposed algorithm on a generated 2D dataset and a subset of Berkeley benchmark images.     

A novel image segmentation algorithm based on neutrosophic similarity clustering

Segmentation is an important research area in image processing, which has been used to extract objects in images. A variety of algorithms have been proposed in this area. However, these methods perform well on the images without noise, and their results on the noisy images are not good. Neutrosophic set (NS) is a general formal framework to study the neutralities’ origin, nature, and scope. It has an inherent ability to handle the indeterminant information. Noise is one kind of indeterminant information on images. Therefore, NS has been successfully applied into image processing algorithms. This paper proposed a novel algorithm based on neutrosophic similarity clustering (NSC) to segment gray level images. We utilize the neutrosophic set in image processing field and define a new similarity function for clustering. At first, an image is represented in the neutrosophic set domain via three membership sets: T, I and F. Then, a neutrosophic similarity function (NSF) is defined and employed in the objective function of the clustering analysis. Finally, the new defined clustering algorithm classifies the pixels on the image into different groups. Experiments have been conducted on a variety of artificial and real images. Several measurements are used to evaluate the proposed method's performance. The experimental results demonstrate that the NSC method segment the images effectively and accurately. It can process both images without noise and noisy images having different levels of noises well. It will be helpful to applications in image processing and computer vision.     

Learning a Mahalanobis distance metric for data clustering and classification

Distance metric is a key issue in many machine learning algorithms. This paper considers a general problem of learning from pairwise constraints in the form of must-links and cannot-links. As one kind of side information, a must-link indicates the pair of the two data points must be in a same class, while a cannot-link indicates that the two data points must be in two different classes. Given must-link and cannot-link information, our goal is to learn a Mahalanobis distance metric. Under this metric, we hope the distances of point pairs in must-links are as small as possible and those of point pairs in cannot-links are as large as possible. This task is formulated as a constrained optimization problem, in which the global optimum can be obtained effectively and efficiently. Finally, some applications in data clustering, interactive natural image segmentation and face pose estimation are given in this paper. Experimental results illustrate the effectiveness of our algorithm.     

基于马氏距离的FCM图像分割算法

基于模糊C均值聚类的图像分割是应用较为广泛的方法之一,但大多数模糊C均值聚类方法都是基于欧式距离,且存在运算时间过长等问题。提出了一种基于Mahalanobis距离的模糊C均值聚类图像分割算法。实验分析表明,提出的算法在保证分割质量的前提下,能较快提高分割速度。实验结果表明了该方法的有效性。     

基于颜色特征和聚类的马氏距离图像分割法

给出了一种基于颜色特征和聚类的复杂彩图中进行目标图像分割的马氏距离算法.该方法利用目标的颜色进行图像分割.通过对彩图中的物体进行采样和分类,经过对每个像素点进行马氏距离计算和最小值寻找,将图像内的所有像素点进行归类,对目标图像与背景图像进行二值化分割,并对分类后含噪声的目标图像进行自适应滤波.设计了达到以上目的的人机交互式可视化计算机图像处理程序,对在水稻田中试验点上拍摄的水稻照片进行了分析处理,分离出了复杂背景下的水稻植株图像.实验结果表明,该算法能较好地解决复杂彩图中目标图像的分割问题.     

Improved spatial fuzzy c-means clustering for image segmentation using PSO initialization,Mahalanobis distance and post-segmentation correction

In this paper, we propose an improvement method for image segmentation using the fuzzy c-means clustering algorithm (FCM). This algorithm is widely experimented in the field of image segmentation with very successful results. In this work, we suggest further improving these results by acting at three different levels. The first is related to the fuzzy c-means algorithm itself by improving the initialization step using a metaheuristic optimization. The second level is concerned with the integration of the spatial gray-level information of the image in the clustering segmentation process and the use of Mahalanobis distance to reduce the influence of the geometrical shape of the different classes. The final level corresponds to refining the segmentation results by correcting the errors of clustering by reallocating the potentially misclassified pixels. The proposed method, named improved spatial fuzzy c-means IFCMS, was evaluated on several test images including both synthetic images and simulated brain MRI images from the McConnell Brain Imaging Center (BrainWeb) database. This method is compared to the most used FCM-based algorithms of the literature. The results demonstrate the efficiency of the ideas presented.     

基于马氏距离特征加权的模糊聚类新算法

模糊聚类分析是模糊模式识别中一个重要研究领域,而其中最经典的模糊C均值算法认为样本矢量各特征对聚类结果贡献均匀,没有考虑不同的属性特征对模式分类的不同影响,在处理属性高相关的数据集时,该算法分错率增加。针对这些问题,提出了一种基于马氏距离特征加权的模糊聚类算法,利用自适应马氏距离的优点对特征加权处理,对高属性相关的数据集进行更有效的分类。实验证明该方法的可行性和有效性。     

Rough-DBSCAN: A fast hybrid density based clustering method for large data sets

Density based clustering techniques like DBSCAN are attractive because it can find arbitrary shaped clusters along with noisy outliers. Its time requirement is O(n²) where n is the size of the dataset, and because of this it is not a suitable one to work with large datasets. A solution proposed in the paper is to apply the leaders clustering method first to derive the prototypes called leaders from the dataset which along with prototypes preserves the density information also, then to use these leaders to derive the density based clusters. The proposed hybrid clustering technique called rough-DBSCAN has a time complexity of O(n) only and is analyzed using rough set theory. Experimental studies are done using both synthetic and real world datasets to compare rough-DBSCAN with DBSCAN. It is shown that for large datasets rough-DBSCAN can find a similar clustering as found by the DBSCAN, but is consistently faster than DBSCAN. Also some properties of the leaders as prototypes are formally established.     

Color image segmentation using tensor voting based color clustering

A novel color image segmentation method using tensor voting based color clustering is proposed. By using tensor voting, the number of dominant colors in a color image can be estimated efficiently. Furthermore, the centroids and structures of the color clusters in the color feature space can be extracted. In this method, the color feature vectors are first encoded by second order, symmetric, non-negative definite tensors. These tensors then communicate with each other by a voting process. The resulting tensors are used to determine the number of clusters, locations of the centroids, and structures of the clusters used for performing color clustering. Our method is based on tensor voting, a non-iterative method, and requires only the voting range as its input parameter. The experimental results show that the proposed method can estimate the dominant colors and generate good segmented images in which those regions having the same color are not split up into small parts and the objects are separated well. Therefore, the proposed method is suitable for many applications, such as dominant colors estimation and multi-color text image segmentation.     

基于马氏距离和灰色分析的缺失值填充算法

针对kNN算法中欧氏距离具有密度相关性敏感的缺点,提出综合马氏距离和灰色分析方法代替kNN算法中欧式距离的新算法,应用到缺失数据填充方面。其中马氏距离能解决密度相关明显的数据集,灰色分析方法能处理密度相关不明显的情况。因此,该算法能很好处理任何数据集,实验结果显示,算法在填充结果上明显优于现有的其他算法。     

一种基于密度峰值的针对模糊混合数据的聚类算法

将CFSFDP算法拓展到连续型模糊集和离散型模糊集上,提出了一种针对模糊混合数据的拓展型CFSFDP算法,将其命名为FMD-CFSFDP算法。FMD-CFSFDP算法将样本涵盖的经典信息拓展到了模糊集上,利用寻找密度峰值的方法对模糊样本进行聚类,这是一种建立在模糊集上针对模糊混合数据的基于密度的聚类算法。首先简单介绍了CFSFDP算法及其改进,给出了"模糊混合数据"的数学概念;然后结合传统模糊欧氏距离的概念,分别提出了误差更小的针对连续型模糊集与离散型模糊集的改进型欧氏距离,在此基础上,依托权值构建了针对混合型模糊数据的整体距离。参考CFSFDP算法的聚类步骤给出了FMD-CFSFDP算法的聚类步骤。随后,在不同样本量、不同指标数量、不同簇数、不同取数规则的条件下,对算法进行了随机模拟实验并对聚类结果进行了分析。最后分别总结了FMD-CFSFDP算法的优缺点,并在此基础上提出了改进方案,为今后深入研究提供了参考。     

A novel clustering algorithm based on the natural reverse nearest neighbor structure

Cluster analysis plays an important role in identifying the natural structure of the target dataset. It has been widely used in many fields, such as pattern recognition, machine learning, image segmentation, document clustering and so on. There are many different methods to conduct cluster analysis. Namely, most real datasets are non-spherical and have complex shapes. Although these methods are widely used to deal with clustering tasks, they are susceptible to noise and arbitrary shapes. Thus, we propose a novel clustering algorithm (called RNN-NSDC) in this paper, which is based on the natural reverse nearest neighbor structure. Firstly, we apply the reverse nearest neighbors in the algorithm to extract core objects. Secondly, our algorithm uses the neighbor structure information of core objects to cluster. And excluding noise effects, core sets can well represent the structure of clusters. Therefore, the RNN-NSDC can obtain the optimal cluster numbers for the datasets which contain clusters of outliers and arbitrary shapes. To verify the efficiency and accuracy of the RNN-NSDC, synthetic datasets and real datasets are used for experiments. The results indicate the superiority of the RNN-NSDC compared with K-means, DBSCAN, DPC, SNNDPC, DCore and NaNLORE.     

一种基于密度的面向线段的聚类算法

分析了密度聚类算法（DBSCAN）的局限性，在此基础上提出了一种基于密度的面向线段的聚类方法，将DBSCAN中聚类的对象由点转变为线段。在对点聚类的基础上，研究了线段聚类的特点。该算法可以有效处理分布不均匀的线段对象集，发现分布密度不同的各种簇。通过试验证明了该方法的可行性与有效性。     

A particle swarm optimization based simultaneous learning framework for clustering and classification

A particle swarm optimization based simultaneous learning framework for clustering and classification (PSOSLCC) is proposed in this paper. Firstly, an improved particle swarm optimization (PSO) is used to partition the training samples, the number of clusters must be given in advance, an automatic clustering algorithm rather than the trial and error is adopted to find the proper number of clusters, and a set of clustering centers is obtained to form classification mechanism. Secondly, in order to exploit more useful local information and get a better optimizing result, a global factor is introduced to the update strategy update strategy of particle in PSO. PSOSLCC has been extensively compared with fuzzy relational classifier (FRC), vector quantization and learning vector quantization (VQ+LVQ3), and radial basis function neural network (RBFNN), a simultaneous learning framework for clustering and classification (SCC) over several real-life datasets, the experimental results indicate that the proposed algorithm not only greatly reduces the time complexity, but also obtains better classification accuracy for most datasets used in this paper. Moreover, PSOSLCC is applied to a real world application, namely texture image segmentation with a good performance obtained, which shows that the proposed algorithm has a potential of classifying the problems with large scale.     

基于聚类和马氏距离的多角度SURF图像匹配算法

对具有不同旋转角度和变化的图像进行匹配是图像识别中的技术难点,SURF算法在多角度图像的特征点检测和匹配过程中存在易受噪声点干扰、产生误匹配从而导致匹配效率低等不足。结合聚类和马氏距离,提出一种改进的多角度SURF图像匹配算法。首先利用聚类算法对原有算法提取的特征点进行噪声剔除处理,生成新的特征点数据集;然后利用马氏距离能够有效考虑整体相关性及其具有仿射不变性等特点,将SURF算法中的欧式距离用马氏距离替代。实验应用于多角度图像匹配时,改进算法较原SURF算法在匹配效率和准确率上有明显提高。     

A novel differential evolution based clustering algorithm for wireless sensor networks

Clustering is an efficient topology control method which balances the traffic load of the sensor nodes and improves the overall scalability and the life time of the wireless sensor networks (WSNs). However, in a cluster based WSN, the cluster heads (CHs) consume more energy due to extra work load of receiving the sensed data, data aggregation and transmission of aggregated data to the base station. Moreover, improper formation of clusters can make some CHs overloaded with high number of sensor nodes. This overload may lead to quick death of the CHs and thus partitions the network and thereby degrade the overall performance of the WSN. It is worthwhile to note that the computational complexity of finding optimum cluster for a large scale WSN is very high by a brute force approach. In this paper, we propose a novel differential evolution (DE) based clustering algorithm for WSNs to prolong lifetime of the network by preventing faster death of the highly loaded CHs. We incorporate a local improvement phase to the traditional DE for faster convergence and better performance of our proposed algorithm. We perform extensive simulation of the proposed algorithm. The experimental results demonstrate the efficiency of the proposed algorithm.     

GAKREM: A novel hybrid clustering algorithm

We introduce a novel clustering algorithm named GAKREM (Genetic Algorithm K-means Logarithmic Regression Expectation Maximization) that combines the best characteristics of the K-means and EM algorithms but avoids their weaknesses such as the need to specify a priori the number of clusters, termination in local optima, and lengthy computations. To achieve these goals, genetic algorithms for estimating parameters and initializing starting points for the EM are used first. Second, the log-likelihood of each configuration of parameters and the number of clusters resulting from the EM is used as the fitness value for each chromosome in the population. The novelty of GAKREM is that in each evolving generation it efficiently approximates the log-likelihood for each chromosome using logarithmic regression instead of running the conventional EM algorithm until its convergence. Another novelty is the use of K-means to initially assign data points to clusters. The algorithm is evaluated by comparing its performance with the conventional EM algorithm, the K-means algorithm, and the likelihood cross-validation technique on several datasets.     

Single point iterative weighted fuzzy C-means clustering algorithm for remote sensing image segmentation

In this paper, a remote sensing image segmentation procedure that utilizes a single point iterative weighted fuzzy C-means clustering algorithm is proposed based upon the prior information. This method can solve the fuzzy C-means algorithm's problem that the clustering quality is greatly affected by the data distributing and the stochastic initializing the centrals of clustering. After the probability statistics of original data, the weights of data attribute are designed to adjust original samples to the uniform distribution, and added in the process of cyclic iteration, which could be suitable for the character of fuzzy C-means algorithm so as to improve the precision. Furthermore, appropriate initial clustering centers adjacent to the actual final clustering centers can be found by the proposed single point adjustment method, which could promote the convergence speed of the overall iterative process and drastically reduce the calculation time. Otherwise, the modified algorithm is updated from multidimensional data analysis to color images clustering. Moreover, with the comparison experiments of the UCI data sets, public Berkeley segmentation dataset and the actual remote sensing data, the real validity of proposed algorithm is proved.