基于模糊聚类的非线性系统模糊辨识算法

针对模糊聚类算法中数据和运算耗时很长，不适于在线建模与控制的问题，基于模糊聚类型隶属函数和EUM方法，提出了一种新的模糊辨识算法。该方法省去了求解聚类中心的迭代过程，计算时间显著减少。采用该方法对Box—Jenkins煤气炉数据和Mackey—Glass混沌时间序列进行了仿真，结果证明了该方法的有效性。     

Effective fuzzy c-means clustering algorithms for data clustering problems

Clustering is a well known technique in identifying intrinsic structures and find out useful information from large amount of data. One of the most extensively used clustering techniques is the fuzzy c-means algorithm. However, computational task becomes a problem in standard objective function of fuzzy c-means due to large amount of data, measurement uncertainty in data objects. Further, the fuzzy c-means suffer to set the optimal parameters for the clustering method. Hence the goal of this paper is to produce an alternative generalization of FCM clustering techniques in order to deal with the more complicated data; called quadratic entropy based fuzzy c-means. This paper is dealing with the effective quadratic entropy fuzzy c-means using the combination of regularization function, quadratic terms, mean distance functions, and kernel distance functions. It gives a complete framework of quadratic entropy approaching for constructing effective quadratic entropy based fuzzy clustering algorithms. This paper establishes an effective way of estimating memberships and updating centers by minimizing the proposed objective functions. In order to reduce the number iterations of proposed techniques this article proposes a new algorithm to initialize the cluster centers.In order to obtain the cluster validity and choosing the number of clusters in using proposed techniques, we use silhouette method. First time, this paper segments the synthetic control chart time series directly using our proposed methods for examining the performance of methods and it shows that the proposed clustering techniques have advantages over the existing standard FCM and very recent ClusterM-k-NN in segmenting synthetic control chart time series.     

A new identification method for fuzzy linear models of nonlinear dynamic systems

The most promising methods for identifying a fuzzy model are data clustering, cluster merging and subsequent projection of the clusters on the input variable space. This article proposes to modify this procedure by adding a cluster rotation step, and a method for the direct calculation of the consequence parameters of the fuzzy linear model. These two additional steps make the model identification procedure more accurate and limits the loss of information during the identification procedure. The proposed method has been tested on a nonlinear first order model and a nonlinear model of a bioreactor and results are very promising.     

Fuzzy C-means based clustering for linearly and nonlinearly separable data

In this paper we present a new distance metric that incorporates the distance variation in a cluster to regularize the distance between a data point and the cluster centroid. It is then applied to the conventional fuzzy C-means (FCM) clustering in data space and the kernel fuzzy C-means (KFCM) clustering in a high-dimensional feature space. Experiments on two-dimensional artificial data sets, real data sets from public data libraries and color image segmentation have shown that the proposed FCM and KFCM with the new distance metric generally have better performance on non-spherically distributed data with uneven density for linear and nonlinear separation.     

核空间中智模糊聚类及图像分割应用

目的 为了更有效地提高中智模糊C-均值聚类对非凸不规则数据的聚类性能和噪声污染图像的分割效果,提出了核空间中智模糊均值聚类算法。方法 引入核函数概念。利用满足Mercer条件的非线性问题,用非线性变换把低维空间线性不可分的输入模式空间映射到一个先行可分的高维特征空间进行中智模糊聚类分割。结果 通过对大量图像添加不同的加性和乘性噪声进行分割测试获得的核空间中智模糊聚类算法提高了现有算法的对含噪声聚类的鲁棒性和分类性能。峰值信噪比至少提高0.8 dB。结论 本文算法具有显著的分割效果和良好的鲁棒性,并适应于医学,遥感图像处理需要。     

Nonstationary time series analysis by temporal clustering

The object of this paper is to present a model and a set of algorithms for estimating the parameters of a nonstationary time series generated by a continuous change in regime. We apply fuzzy clustering methods to the task of estimating the continuous drift in the time series distribution and interpret the resulting temporal membership matrix as weights in a time varying, mixture probability distribution function (PDF). We analyze the stopping conditions of the algorithm to infer a novel cluster validity criterion for fuzzy clustering algorithms of temporal patterns. The algorithm performance is demonstrated with three different types of signals.     

弹性核子空间聚类*

现有子空间聚类算法通常假设数据来自多个线性子空间,无法处理时间序列聚类中存在的非线性和时间轴弯曲问题.为了克服这些局限,通过引入核技巧和弹性距离,提出弹性核低秩表示子空间聚类和弹性核最小二乘回归子空间聚类,统称为弹性核子空间聚类,并从理论上证明弹性核最小二乘回归子空间算法的组效应和弹性核低秩表示子空间聚类算法的收敛性.在5个UCR时间序列数据集上的实验表明本文算法的有效性.     

Automatic time series analysis for electric load forecasting via support vector regression

In this work, a strategy for automatic lag selection in time series analysis is proposed. The method extends the ideas of feature selection with support vector regression, a powerful machine learning tool that can identify nonlinear patterns effectively thanks to the introduction of a kernel function. The proposed approach follows a backward variable elimination procedure based on gradient descent optimisation, iteratively adjusting the widths of an anisotropic Gaussian kernel. Experiments on four electricity demand forecasting datasets demonstrate the virtues of the proposed approach in terms of predictive performance and correct identification of relevant lags and seasonal patterns, compared to well-known strategies for time series analysis designed for energy load forecasting and state-of-the-art strategies for automatic model selection.     

基于核模糊聚类的多模型LSSVM回归建模

针对大规模数据采用单模型回归存在精度差和计算量较大的问题,提出一种基于核模糊聚类的多模型最小二乘支持向量回归建模方法.该方法首先使用基于条件正定核的模糊C均值聚类算法对数据集做出聚类划分;然后针对每个聚类做最小二乘支持向量回归估计;同时根据每个聚类内数据分布的特征,给出了一种简单的核参数选择方法.利用数值仿真实验进行非线性函数估计,实验结果表明了所提出的方法具有良好的精度和泛化能力.     

Hierarchical-fuzzy clustering of temporal-patterns and its application for time-series prediction

In a recent paper we presented a new algorithm for hierarchical unsupervised fuzzy clustering (HUFC) and demonstrated its performance for biomedical state identification. In the present paper, a new hybrid algorithm for time series prediction is applying the HUFC algorithm for grouping and modeling related temporal-patterns that are dispersed along a non-stationary signal. Vague and gradual changes in regime are naturally treated by means of fuzzy clustering. An adaptive hierarchical selection of the number of clusters (the number of underlying processes) can overcome the general non-stationary nature of real-life time-series (biomedical, physical, economical, etc.).     

基于改进粒子群优化的移动界面模式聚类算法

聚类是一种非常有效的信息分析方法。针对现有基于粒子群优化的模糊C均值(Fuzzy C-means,FCM)聚类算法的聚类效果不佳的问题,提出一种基于改进粒子群优化的模糊C均值聚类算法,并将该聚类算法应用到移动界面模式的聚类中。首先,利用直觉模糊熵的几何解释和约束构造合理的直觉模糊熵;然后,在粒子群优化中使用直觉模糊熵判断种群的多样性程度,并引入混沌反向学习策略来提高全局搜索能力;最后,为了增强聚类算法的非线性处理能力,在聚类算法中加入高斯核函数,并将该聚类算法应用到移动界面模式的聚类中。移动界面模式聚类的实验表明,与现有聚类算法相比,文中所提聚类算法具有更好的聚类效果。     

基于密度峰值的加权犹豫模糊聚类算法

由于人们对事物认知的局限性和信息的不确定性,在对决策问题进行聚类分析时,传统的模糊聚类不能有效解决实际场景中的决策问题,因此有学者提出了有关犹豫模糊集的聚类算法。现有的层次犹豫模糊K均值聚类算法没有利用数据集本身的信息来确定距离函数的权值,且簇中心的计算复杂度和空间复杂度都是指数级的,不适用于大数据环境。针对上述问题,文中提出了一种基于密度峰值思想的加权犹豫模糊聚类算法(WHFDP),首先给出了犹豫模糊元素集的补齐方法,并结合变异系数理论给出了新的距离函数权重计算公式,然后利用密度峰值选取簇中心,不仅降低了簇中心计算的复杂度,而且提高了对不同规模以及任意形状数据集的适应性,算法的时间复杂度和空间复杂度也降为多项式级,最后采用典型数据集进行仿真实验,证明了所提算法的有效性。     

A spatio-temporal decomposition based deep neural network for time series forecasting

Spatio-temporal problems arise in a broad range of applications, such as climate science and transportation systems. These problems are challenging because of unique spatial, short-term and long-term patterns, as well as the curse of dimensionality. In this paper, we propose a deep learning framework for spatio-temporal forecasting problems. We explicitly design the neural network architecture for capturing various types of spatial and temporal patterns, and the model is robust to missing data. In a preprocessing step, a time series decomposition method is applied to separately feed short-term, long-term and spatial patterns into different components of the neural network. A fuzzy clustering method finds clusters of neighboring time series residuals, as these contain short-term spatial patterns. The first component of the neural network consists of multi-kernel convolutional layers which are designed to extract short-term features from clusters of time series data. Each convolutional kernel receives a single cluster of input time series. The output of convolutional layers is concatenated by trends and followed by convolutional-LSTM layers to capture long-term spatial patterns. To have a robust forecasting model when faced with missing data, a pretrained denoising autoencoder reconstructs the model’s output in a fine-tuning step. In experimental results, we evaluate the performance of the proposed model for the traffic flow prediction. The results show that the proposed model outperforms baseline and state-of-the-art neural network models.     

Hadoop based uncertain possibilistic kernelized c-means algorithms for image segmentation and a comparative analysis

Over the years data clustering algorithms have been used for image segmentation. Due to the presence of uncertainty in real life datasets, several uncertainty based data clustering algorithms have been developed. The c-means clustering algorithms form one such family of algorithms. Starting with the fuzzy c-means (FCM) a subfamily of this family comprises of rough c-means (RCM), intuitionistic fuzzy c-means (IFCM) and their hybrids like rough fuzzy c-means (RFCM) and rough intuitionistic fuzzy c-means (RIFCM). In the basic subfamily of this family of algorithms, the Euclidean distance was being used to measure the similarity of data. However, the sub family of algorithms obtained replacing the Euclidean distance by kernel based similarities produced better results. Especially, these algorithms were useful in handling viably cluster data points which are linearly inseparable in original input space. During this period it was inferred by Krishnapuram and Keller that the membership constraints in some rudimentary uncertainty based clustering techniques like fuzzy c-means imparts them a probabilistic nature, hence they suggested its possibilistic version. In fact all the other member algorithms from basic subfamily have been extended to incorporate this new notion. Currently, the use of image data is growing vigorously and constantly, accounting to huge figures leading to big data. Moreover, since image segmentation happens to be one of the most time consuming processes, industries are in the need of algorithms which can solve this problem at a rapid pace and with high accuracy. In this paper, we propose to combine the notions of kernel and possibilistic approach together in a distributed environment provided by Apache™ Hadoop. We integrate this combined notion with map-reduce paradigm of Hadoop and put forth three novel algorithms; Hadoop based possibilistic kernelized rough c-means (HPKRCM), Hadoop based possibilistic kernelized rough fuzzy c-means (HPKRFCM) and Hadoop based possibilistic kernelized rough intuitionistic fuzzy c-means (HPKRIFCM) and study their efficiency in image segmentation. We compare their running times and analyze their efficiencies with the corresponding algorithms from the other three sub families on four different types of images, three different kernels and six different efficiency measures; the Davis Bouldin index (DB), Dunn index (D), alpha index (α), rho index (ρ), alpha star index (α*) and gamma index (γ). Our analysis shows that the hyper-tangent kernel with Hadoop based possibilistic kernelized rough intuitionistic fuzzy c-means is the best one for image segmentation among all these clustering algorithms. Also, the times taken to render segmented images by the proposed algorithms are drastically low in comparison to the other algorithms. The implementations of the algorithms have been carried out in Java and for the proposed algorithms we have used Hadoop framework installed on CentOS. For statistical plotting we have used matplotlib (python library).     

一种非线性模型的在线辨识方法

提出一种用于非线性模型在线辨识的模糊算法。该算法将非线性输入输出系统用时变线性系统模型来拟和。并把此非线性系统模型表示成模糊模型的形式，用在线调节模糊模型的方法来辨识时变线性模型的相关参数。在以往的模糊辨识方法中，均未给出在线调整非线性系统的模糊辨识算法。将递推模糊聚类方法与卡尔曼滤波法用于在线调整模糊模型参数，仿真算例表明了此算法的有效性与良好的实用价值。     

核空间直觉模糊局部C-均值聚类分割算法研究

针对现有直觉模糊C-均值聚类仅适合呈团状数据的不足,采用非线性函数将数据样本从欧式空间映射至再生希尔伯特高维特征空间,得到核空间直觉模糊聚类算法;同时考虑相邻像素的相互影响,将邻域像素融入核空间直觉模糊聚类的最优化目标函数中,经数学推导便得到嵌入像素局部信息的核空间直觉模糊聚类分割算法。图像分割测试结果表明,核直觉模糊C-均值聚类分割法相比现有直觉模糊C-均值聚类分割法能获得更满意的分割效果;同时,嵌入局部信息的核直觉模糊C-均值聚类分割法表现出良好的抗噪鲁棒性。     

密度敏感模糊核最大熵聚类算法EI北大核心CSCD

提出一种密度敏感模糊核最大熵聚类算法.该算法首先通过核函数将原始非线性非高斯的数据集转化为核空间数据集,然后利用核函数的相似性抵消不属于该聚类的样本数据在聚类过程中对聚类中心求解的干扰,消除正则化系数对聚类结果的影响,进而抑制传统最大熵聚类算法的趋同性.最后通过引入相对密度项,解决因样本数据在特征空间的分布差异而导致的聚类中心求解偏差问题,从而提高聚类结果的准确性.实验部分,本文讨论了算法参数间的关系以及对聚类结果的影响.通过与传统模糊C均值聚类算法、核模糊C均值聚类算法、最大熵聚类算法、最大熵规范化权重核模糊C均值聚类算法以及其他两种改进最大熵聚类算法的聚类结果进行对比分析,结果表明本文提出的密度敏感模糊核最大熵聚类算法的聚类性能明显优于其他算法.     

Fuzzy clustering of time series in the frequency domain

Traditional and fuzzy cluster analyses are applicable to variables whose values are uncorrelated. Hence, in order to cluster time series data which are usually serially correlated, one needs to extract features from the time series, the values of which are uncorrelated. The periodogram which is an estimator of the spectral density function of a time series is a feature that can be used in the cluster analysis of time series because its ordinates are uncorrelated. Additionally, the normalized periodogram and the logarithm of the normalized periodogram are also features that can be used. In this paper, we consider a fuzzy clustering approach for time series based on the estimated cepstrum. The cepstrum is the spectrum of the logarithm of the spectral density function. We show in our simulation studies for the typical generating processes that have been considered, fuzzy clustering based on the cepstral coefficients performs very well compared to when it is based on other features.     

基于模糊核聚类的图像SVM分类辨识

提出一种结合特征场和模糊核聚类支持向量机的图像分类辨识方法。首先,构造符合人类视觉特性的图像彩色和纹理特征数据场,一方面,引入新阈值,建立图像纹理特征;另一方面,在图像彩色特征上,对能够引起注意的像素区域的像素点进行加权处理,并使用彩色空间分布离散度来描述彩色的空间分布。其次,采用模糊核聚类支持向量机对图像进行分类研究。在使用特征空间时,不仅考虑了样本与类中心间的关系,还考虑了类中各个样本间的关系,以模糊连接度来度量类中各个样本间的关系,并以二叉树方式构造子分类器。实验结果表明,该方法可以获得较好的图像分类效果。