稀疏样本自表达的子空间聚类算法

发布时间：2018-05-23 14:34

本文选题：子空间聚类 + 自表示　；参考：《广西师范大学》2016年硕士论文

【摘要】：实际应用中,子空间聚类方法可以从高维数据中寻找一个低维表示,用少量的数据就能去描述整个数据空间。这在很大程度上提升了高维数据处理的效率。目前已存在不同形式的子空间聚类方法有不同的适用环境。其中基于谱聚类的子空间聚类算法是应用较为普遍的一类处理高维数据的聚类方法。现有的基于谱聚类的子空间聚类算法通常围绕数据的局部或全局信息去构建数据的相似度矩阵,然后通过谱聚类对该相似度矩阵进行处理获得最后的聚类结果。这些算法主要的差异在于构建相似度矩阵的方法。一个好的相似度矩阵往往可以更好的体现数据子空间结构,而有利于处理高维数据中数据可能来自多个不同子空间的复杂情况。因此,本文给出了一种基于稀疏样本自表达模型的算法去构建相似度矩阵。该算法主要有以下几个创新点：1.该算法利用样本之间固有相关性找出一组与待测样本相关性强的样本去度量样本之间的相似度,以便更好的体现样本之间的相似关系。2.该算法首先通过l1-范数对自表达矩阵进行全局稀疏,使其更能体现出样本空间的低维子空间属性。然后进一步通过l2,1-范数对自表达系数矩阵进行行稀疏,使其对噪音和离群点更具鲁棒性。3.该算法提出了一种求解稀疏自表达模型的优化算法,该优化算法可以在处理高维数据时快速收敛到最优解,极大的减少了计算的复杂度,提高了子空间聚类的效率。
[Abstract]:In practical application, the subspace clustering method can find a low-dimensional representation from the high-dimensional data, and the whole data space can be described with a small amount of data. This greatly improves the efficiency of high dimensional data processing. There are different subspace clustering methods in different environments. The subspace clustering algorithm based on spectral clustering is a kind of clustering method which is widely used to deal with high dimensional data. The existing subspace clustering algorithms based on spectral clustering usually construct the similarity matrix around the local or global information of the data, and then process the similarity matrix by spectral clustering to obtain the final clustering results. The main difference of these algorithms is the method of constructing similarity matrix. A good similarity matrix can better reflect the structure of the data subspace, and it is helpful to deal with the complex situation that the data in the high-dimensional data may come from many different subspaces. Therefore, this paper presents an algorithm based on sparse sample self-representation model to construct similarity matrix. The algorithm has the following innovations: 1. The algorithm uses the inherent correlation between samples to find a group of samples with strong correlation to measure the similarity between samples, in order to better reflect the similarity between samples. The algorithm firstly sparse the self-representation matrix globally by using l _ 1-norm, so that it can reflect the low-dimensional subspace attributes of the sample space more effectively. Then the self-expression coefficient matrix is sparse by L _ 2N _ 1-norm to make it more robust to noise and outliers. This algorithm proposes an optimization algorithm for sparse self-representation model. The algorithm can quickly converge to the optimal solution when processing high-dimensional data, greatly reduces the computational complexity and improves the efficiency of subspace clustering.
【学位授予单位】：广西师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TP311.13

【相似文献】