谱聚类与维数约简算法及其应用

发布时间：2018-04-17 11:52

本文选题：维数约简 + 谱聚类　；参考：《西安电子科技大学》2016年博士论文

【摘要】：近年来,在很多实际问题中,人们获取的数据具有很高的维数。数据的高维性使得计算机对数据的处理越来越复杂,导致“维数灾难”的现象发生,另外数据的高维性也掩盖了数据的内在特性,使人们不便于发现其中的规律。如何从高维数据中挖掘出有效的数据信息并发现数据的低维本质属性已经成为模式识别、应用数学、计算机视觉等领域的研究者所关注的共同问题。维数约简是人们处理这一问题的有效方法。另外,谱聚类也是数据挖掘的一个重要手段。本文对谱聚类和维数约简方法进行深入的研究,提出了一些新的有效的谱聚类和维数约简方法,并应用于图像分割和人脸识别中。本文的主要工作和创新成果如下：1.针对谱聚类算法对高斯核尺度参数敏感且该参数难以确定的缺陷,首先,利用核模糊C均值聚类算法进行粗聚类,得到隶属度向量构成的划分矩阵；其次,利用隶属度向量的内积,提出了一个无参数的核模糊相似度度量；最后,提出了一个基于核模糊相似度的谱聚类算法。实验结果表明,所提出的谱聚类算法不仅有效克服了算法对参数的敏感性,而且解决了高斯核尺度参数难以确定的问题。2.针对传统谱聚类算法中使用欧氏距离的相似性度量不适用于分布复杂数据及对参数敏感的问题,利用测地线距离,设计了一种基于流形距离的相似度度量,有效改善了算法对参数的敏感性及对分布复杂数据的实用性。在此基础上,针对谱映射空间K-均值聚类对初始聚类中心敏感、容易陷入局部最优的问题,提出了一个新的基于模拟退火的谱聚类方法,并将其应用于图像分割中。实验结果表明,所提出的新谱聚类算法不仅有效降低了算法对参数的敏感性,而且能有效避免算法陷入局部最优,改善了传统谱聚类算法的性能。3.当样本规模较大时,谱聚类方法复杂性过高、计算量大。针对此问题,提出基于超像素的谱聚类方法。该算法首先通过超像素的方法预处理,用超像素代替原来单个的像素；然后利用本文已提出的基于核模糊相似度度量构造加权无向图；最后采用谱聚类算法进行聚类,并将其应用于图像分割。所提方法大大降低了传统谱聚类算法的复杂度,减少了计算量。实验表明,相比较传统谱聚类方法,基于超像素的谱聚类方法获得了更好的分割效果。4.针对判别稀疏邻域保持嵌入(DSNPE)算法类间离散度构造复杂的问题,首先,通过保持平均脸的稀疏重构关系,设置了新的类间离散度；然后,通过同时最大化类间离散度和最小化类内紧凑度构造维数约简的目标函数；最后,提出了一种改进的维数约简算法,并将其应用于人脸识别。所提出算法不仅有效降低了DSNPE算法的复杂度,而且增强了类间判别力。人脸识别的仿真实验结果表明,相比较已有的其他算法,该算法具有较高的识别率。
[Abstract]:In recent years, in many practical problems, the data obtained by people have a high dimension.The high dimension of data makes the processing of data by computer more and more complex, which leads to the phenomenon of "dimensionality disaster". In addition, the high dimension of data also conceals the inherent characteristics of data, which makes it difficult for people to find the rules.How to mine effective data information from high-dimensional data and find the essential attributes of low-dimensional data has become a common concern of researchers in the fields of pattern recognition, applied mathematics, computer vision and so on.Dimension reduction is an effective method to deal with this problem.In addition, spectral clustering is also an important means of data mining.In this paper, spectral clustering and dimension reduction methods are deeply studied, and some new and effective spectral clustering and dimension reduction methods are proposed, which are applied to image segmentation and face recognition.The main work and innovative results of this paper are as follows: 1.Aiming at the limitation that spectral clustering algorithm is sensitive to Gao Si's kernel scale parameter and this parameter is difficult to determine, firstly, the kernel fuzzy C-means clustering algorithm is used for coarse clustering, and the partition matrix of membership vector is obtained.By using the inner product of membership degree vector, a nonparametric kernel fuzzy similarity measure is proposed. Finally, a spectral clustering algorithm based on kernel fuzzy similarity is proposed.The experimental results show that the proposed spectral clustering algorithm not only overcomes the sensitivity of the algorithm to the parameters, but also solves the problem of the difficult determination of Gao Si kernel scale parameters.To solve the problem that Euclidean distance is not suitable for distributed complex data and sensitive to parameters in traditional spectral clustering algorithm, a similarity measure based on manifold distance is designed by using geodesic distance.The sensitivity of the algorithm to the parameters and the practicability of the distributed complex data are improved effectively.On this basis, a new spectral clustering method based on simulated annealing is proposed to solve the problem that K-means clustering in spectral mapping space is sensitive to the center of initial clustering and is prone to fall into local optimal condition, and it is applied to image segmentation.Experimental results show that the proposed new spectral clustering algorithm not only effectively reduces the sensitivity of the algorithm to the parameters, but also effectively avoids the algorithm falling into local optimum, and improves the performance of the traditional spectral clustering algorithm.When the sample size is large, the complexity of the spectral clustering method is too high and the computation is large.To solve this problem, a spectral clustering method based on hyperpixel is proposed.The algorithm uses super-pixel preprocessing method to replace the original single pixel, and then constructs weighted undirected graph based on kernel fuzzy similarity measure proposed in this paper. Finally, spectral clustering algorithm is used to cluster.It is applied to image segmentation.The proposed method greatly reduces the complexity and computational complexity of the traditional spectral clustering algorithm.The experimental results show that compared with the traditional spectral clustering method, the spectral clustering method based on super-pixel has better segmentation effect.In order to solve the complex problem of discriminating the discrete degree between classes of sparse neighborhood preserving embedding (DSNPE) algorithm, firstly, by maintaining the sparse reconstruction relation of the average face, a new inter-class dispersion is set up.The objective function of dimension reduction is constructed by simultaneously maximizing inter-class dispersion and minimizing intra-class compactness. Finally, an improved dimension reduction algorithm is proposed and applied to face recognition.The proposed algorithm not only reduces the complexity of the DSNPE algorithm, but also enhances the discriminant power between classes.The simulation results of face recognition show that compared with other existing algorithms, this algorithm has a higher recognition rate.
【学位授予单位】：西安电子科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP311.13

【相似文献】