On mean shift-based clustering for circular data

Cluster analysis is a useful tool for data analysis. Clustering methods are used to partition a data set into clusters such that the data points in the same cluster are the most similar to each other and the data points in the different clusters are the most dissimilar. The mean shift was originally used as a kernel-type weighted mean procedure that had been proposed as a clustering algorithm. However, most mean shift-based clustering (MSBC) algorithms are used for numeric data. The circular data that are the directional data on the plane have been widely used in data analysis. In this paper, we propose a MSBC algorithm for circular data. Three types of mean shift implementation procedures with nonblurring, blurring and general methods are furthermore compared in which the blurring mean shift procedure is the best and recommended. The proposed MSBC for circular data is not necessary to give the number of cluster. It can automatically find a final cluster number with good clustering centers. Several numerical examples and comparisons with some existing clustering methods are used to demonstrate its effectiveness and superiority of the proposed method.     

基于自适应带宽均值漂移聚类算法设计传递函数

本文采用均值漂移聚类算法为三维数据场设计传递函数.首先根据采样点的分布提出了两种自适应的带宽计算方法;然后利用梯度幅值对采样点加权,实现数据场的物质分类;最后对分类的结果设计高斯型的映射函数.实验表明,与固定带宽均值漂移算法相比,该方法提高了算法的速度和分类的准确性,并获得了高质量的绘制效果.     

Segmentation of optic disc in retinal images using an improved gradient vector flow algorithm

Image segmentation plays an important role in the analysis of retinal images as the extraction of the optic disk provides important cues for accurate diagnosis of various retinopathic diseases. In recent years, gradient vector flow (GVF) based algorithms have been used successfully to successfully segment a variety of medical imagery. However, due to the compromise of internal and external energy forces within the resulting partial differential equations, these methods can lead to less accurate segmentation results in certain cases. In this paper, we propose the use of a new mean shift-based GVF segmentation algorithm that drives the internal/external energies towards the correct direction. The proposed method incorporates a mean shift operation within the standard GVF cost function to arrive at a more accurate segmentation. Experimental results on a large dataset of retinal images demonstrate that the presented method optimally detects the border of the optic disc.     

基于张量空间中的均值漂移聚类的极化SAR图像分割

提出了一种基于均值漂移(Mean Shift, MS)聚类的全极化合成孔径雷达(Polarimetric Synthetic Aperture Radar, PolSAR)图像无监督分割算法. 已有的工作在将MS算法应用于全PolSAR图像分割时, 仅使用每个像素点的极化总功率值作为该像素点的特征值, 没有充分利用极化协方差矩阵或者相干矩阵所包含的完整的极化散射信息. 但是如果直接利用每个像素点的极化协方差矩阵作为特征向量, 则这些特征向量构成的空间不再是一个欧氏空间, 而原始的MS算法是定义在欧氏空间中的. 因此, 本文首先将每一个像素点的厄尔米特正定极化协方差矩阵也称为一个张量, 而且使用黎曼流形来描述该张量空间. 然后, 原始的MS算法被扩展到该张量空间中. 直接扩展得到的算法每一步具有明确的含义, 但是运算复杂度较高. 所以本文又进一步对该算法进行了简化, 从而得到了一个实用的分割算法. 通过使用真实的全PolSAR数据以及仿真数据进行实验, 结果验证了新方法的有效性.     

Mean shift spectral clustering

In recent years there has been a growing interest in clustering methods stemming from the spectral decomposition of the data affinity matrix, which are shown to present good results on a wide variety of situations. However, a complete theoretical understanding of these methods in terms of data distributions is not yet well understood. In this paper, we propose a spectral clustering based mode merging method for mean shift as a theoretically well-founded approach that enables a probabilistic interpretation of affinity based clustering through kernel density estimation. This connection also allows principled kernel optimization and enables the use of anisotropic variable-size kernels to match local data structures. We demonstrate the proposed algorithm's performance on image segmentation applications and compare its clustering results with the well-known Mean Shift and Normalized Cut algorithms.     

基于Contourlet变换和均值漂移的SAR图像分割

基于斑噪特性和纹理特征，提出了一种完全无监督的SAR图像分割算法。针对SAR图像的Contourlet变换，提出了子带选取的能量标准，对选定的子带计算能量特征和共生特征；依据特征向量的相似度剔除相近特征向量，用均值漂移算法获取纹理区域数和相应的中心特征，用像素的特征向量与相应中心特征向量的距离确定它们的分类。该文提出的方法不需要先验知识和训练样本。实验表明，基于Contourlet变换的均值漂移分割算法对混合Brodatz图像和SAR图像的分割取得了满意结果。     

大数据集快速均值漂移谱聚类算法及其在图像分割中的应用

均值漂移谱聚类(MSSC)算法为模式识别聚类任务提供了一种较新的方案.然而由于其内嵌均值漂移过程的时问复杂度与样本容量呈平方关系,其在大数据集环境的实用性受到大大削弱.利用快速压缩集密度估计器(FRSDE)替代Parren窗密度估计式(PW)并融合基于图的松弛聚类(GRC)方法,提出了快速均值漂移谱聚类(FMSSC)算法.相比原MSSC,该算法的总体渐进时间复杂度与样本容量呈线性关系,并具有自适应性和便捷性.     

基于串核的音乐风格聚类

给出了一种新的映射音乐到R°空间的方法和基于串核的音乐风格聚类法.利用统计方法分析大量音乐的旋律轮廓线得到合适的编码模式,用它把旋律轮廓线编码为有限字母表(8个字母)的字符串.利用连续子串嵌入法把音乐串显式映射到高维R°空间,并用核表示这一映射.通过用基于核的山方法选择聚类的适合初始点,最后使用基于核的K-means方法聚类音乐数据集,比较了3个不同串核在5个音乐数据集上的聚类性能.     

Nonlinear Mean Shift over Riemannian Manifolds

The original mean shift algorithm is widely applied for nonparametric clustering in vector spaces. In this paper we generalize it to data points lying on Riemannian manifolds. This allows us to extend mean shift based clustering and filtering techniques to a large class of frequently occurring non-vector spaces in vision. We present an exact algorithm and prove its convergence properties as opposed to previous work which approximates the mean shift vector. The computational details of our algorithm are presented for frequently occurring classes of manifolds such as matrix Lie groups, Grassmann manifolds, essential matrices and symmetric positive definite matrices. Applications of the mean shift over these manifolds are shown.     

An algorithm for data-driven bandwidth selection

The analysis of a feature space that exhibits multiscale patterns often requires kernel estimation techniques with locally adaptive bandwidths, such as the variable-bandwidth mean shift. Proper selection of the kernel bandwidth is, however, a critical step for superior space analysis and partitioning. This paper presents a mean shift-based approach for local bandwidth selection in the multimodal, multivariate case. The method is based on a fundamental property of normal distributions regarding the bias of the normalized density gradient. This paper demonstrates that, within the large sample approximation, the local covariance is estimated by the matrix that maximizes the magnitude of the normalized mean shift vector. Using this property, the paper develops a reliable algorithm which takes into account the stability of local bandwidth estimates across scales. The validity of the theoretical results is proven in various space partitioning experiments involving the variable-bandwidth mean shift.     

成对约束的属性加权半监督模糊核聚类算法

在机器学习和数据挖掘中,带约束的半监督聚类是一个活跃的研究领域。为了利用约束条件获得表现更优异的聚类效果,提出了一种成对约束的属性加权半监督聚类算法,该方法充分考虑了属性间的不平衡性,在传统模糊聚类算法中融合半监督学习机制并通过Mercer核把原始的观察空间映射到高维特征空间。实验结果表明,该算法优于相似的成对约束的竞争群算法（PCCA）。     

Spectral clustering with fuzzy similarity measure

Spectral clustering algorithms have been successfully used in the field of pattern recognition and computer vision. The widely used similarity measure for spectral clustering is Gaussian kernel function which measures the similarity between data points. However, it is difficult for spectral clustering to choose the suitable scaling parameter in Gaussian kernel similarity measure. In this paper, utilizing the prototypes and partition matrix obtained by fuzzy c-means clustering algorithm, we develop a fuzzy similarity measure for spectral clustering (FSSC). Furthermore, we introduce the K-nearest neighbor sparse strategy into FSSC and apply the sparse FSSC to texture image segmentation. In our experiments, we firstly perform some experiments on artificial data to verify the efficiency of the proposed fuzzy similarity measure. Then we analyze the parameters sensitivity of our method. Finally, we take self-tuning spectral clustering and Nyström methods for baseline comparisons, and apply these three methods to the synthetic texture and remote sensing image segmentation. The experimental results show that the proposed method is significantly effective and stable.     

Semisupervised Clustering with Metric Learning using Relative Comparisons

Semisupervised clustering algorithms partition a given data set using limited supervision from the user. The success of these algorithms depends on the type of supervision and also on the kind of dissimilarity measure used while creating partitions of the space. This paper proposes a clustering algorithm that uses supervision in terms of relative comparisons, viz., x is closer to y than to z. The proposed clustering algorithm simultaneously learns the underlying dissimilarity measure while finding compact clusters in the given data set using relative comparisons. Through our experimental studies on high-dimensional textual data sets, we demonstrate that the proposed algorithm achieves higher accuracy and is more robust than similar algorithms using pairwise constraints for supervision.     

基于E2LSH-MKL的视觉语义概念检测

多核学习方法(Multiple kernel learning, MKL)在视觉语义概念检测中有广泛应用, 但传统多核学习大都采用线性平稳的核组合方式而无法准确刻画复杂的数据分布. 本文将精确欧氏空间位置敏感哈希(Exact Euclidean locality sensitive Hashing, E2LSH)算法用于聚类, 结合非线性多核组合方法的优势, 提出一种非线性非平稳的多核组合方法—E2LSH-MKL. 该方法利用Hadamard内积实现对不同核函数的非线性加权,充分利用了不同核函数之间交互得到的信息; 同时利用基于E2LSH哈希原理的聚类算法,先将原始图像数据集哈希聚类为若干图像子集, 再根据不同核函数对各图像子集的相对贡献大小赋予各自不同的核权重, 从而实现多核的非平稳加权以提高学习器性能; 最后,把E2LSH-MKL应用于视觉语义概念检测. 在Caltech-256和TRECVID 2005数据集上的实验结果表明,新方法性能优于现有的几种多核学习方法.     

An adaptive unsupervised approach toward pixel clustering and color image segmentation

This paper proposes an adaptive unsupervised scheme that could find diverse applications in pattern recognition as well as in computer vision, particularly in color image segmentation. The algorithm, named Ant Colony-Fuzzy C-means Hybrid Algorithm (AFHA), adaptively clusters image pixels viewed as three dimensional data pieces in the RGB color space. The Ant System (AS) algorithm is applied for intelligent initialization of cluster centroids, which endows clustering with adaptivity. Considering algorithmic efficiency, an ant subsampling step is performed to reduce computational complexity while keeping the clustering performance close to original one. Experimental results have demonstrated AFHA clustering's advantage of smaller distortion and more balanced cluster centroid distribution over FCM with random and uniform initialization. Quantitative comparisons with the X-means algorithm also show that AFHA makes a better pre-segmentation scheme over X-means. We further extend its application to natural image segmentation, taking into account the spatial information and conducting merging steps in the image space. Extensive tests were taken to examine the performance of the proposed scheme. Results indicate that compared with classical segmentation algorithms such as mean shift and normalized cut, our method could generate reasonably good or better image partitioning, which illustrates the method's practical value.     

Mean shift is a bound optimization

We build on the current understanding of mean shift as an optimization procedure. We demonstrate that, in the case of piecewise constant kernels, mean shift is equivalent to Newton's method. Further, we prove that, for all kernels, the mean shift procedure is a quadratic bound maximization.     

一种面向视觉注意区域检测的运动分割方法*

结合视觉显著区检测的特点,本文提出一种面向视觉注意区域检测的运动分割方法。该方法用一种层次聚类方法将特征点的运动轨迹进行聚类。首先用中值偏移算法扩大了不同类型运动之间特征向量的差距,同时缩小了相同运动类型的差别。继而,用一种无监督聚类算法,将不同类型的运动进行分割,同时自动获得运动分类数。最后利用运动分割结果,提出一种结合空间和颜色采样的运动显著区域生成方法。与以往方法相比,该方法能够将不同类型的运动自动进行分割,生成的视觉注意区域更为准确,而且稳定性大幅提高。实验结果证明了该方法的有效性和稳定性。     

Mean shift, mode seeking, and clustering

Mean shift, a simple interactive procedure that shifts each data point to the average of data points in its neighborhood is generalized and analyzed in the paper. This generalization makes some k-means like clustering algorithms its special cases. It is shown that mean shift is a mode-seeking process on the surface constructed with a “shadow” kernal. For Gaussian kernels, mean shift is a gradient mapping. Convergence is studied for mean shift iterations. Cluster analysis if treated as a deterministic problem of finding a fixed point of mean shift that characterizes the data. Applications in clustering and Hough transform are demonstrated. Mean shift is also considered as an evolutionary strategy that performs multistart global optimization     

Mean shift clustering-based moving object segmentation in the H.264 compressed domain

This study presents a mean shift clustering-based moving object segmentation approach in the H.264 compressed domain. The motion information extracted from H.264 compressed video, including motion vectors (MVs) and partitioned block size, are used as segmentation cues. The MVs are processed by normalisation, weighted 3D median filter and motion compensation to obtain a reliable and salient MV field. The partitioned block size is used as a measure of motion texture in the process of the MV field. Based on the processed MV field, the authors employ the mean shift-based mode seeking in spatial, temporal and range domain to develop a new approach for compact representation of the MV field. Then, the MV field is segmented into different motion-homogenous regions by clustering the modes with small spatial and range distance, and each object is represented by some dominant modes. Experimental results for several H.264 compressed video sequences demonstrate good performance and efficiency of the proposed segmentation approach.     

基于特征约束和均值漂移的机动目标粒子跟踪

粒子滤波是适用于非线性非高斯系统下目标跟踪的强有力工具．ＭｉｒｏＳｏｔ足球机器人系统可以作为研究机动目标跟踪问题的平台．对此,在分析ＭｉｒｏＳｏｔ系统目标特征的基础上,提出一种基于目标特征约束的均值漂移粒子滤波算法,利用约束和优化的思想提高粒子的质量并减少其数量．对比实验表明,该方法有效地克服了传统粒子滤波的计算量和粒子退化问题,保证了多机动目标跟踪的准确性和实时性．