学习一致相似度矩阵的图非负矩阵分解

Nonnegative matrix decomposition of the learning consistency similarity matrix

非负矩阵分解(NMF)是一种有效的数据降维方法,广泛应用于图像聚类等领域。然而,NMF不能捕获数据固有的几何结构,所以基于图的非负矩阵分解被提出。基于图的算法大多使用K-近邻来构造相似度图。由于数据中的异常值和错误特征,直接构造图是不准确的。针对上述问题,提出了基于学习一致性相似度矩阵的图非负矩阵分解方法。该方法首先通过自适应学习来获得相似度矩阵,然后通过相似度矩阵构造拉普拉斯图正则项,最后将该正则项加入原始的非负矩阵分解模型中。优化了之前直接使用K-近邻构图的弊端,并且能很好地保持数据的几何结构。新提出的算法在USPS、yale、faces以及ORLdata数据集上进行聚类试验并与一些先进算法进行了比较。数值试验结果证明了本文提出的算法性能很好。

Nonnegative matrix factorization(NMF)is an effective dimension reduction method widely used in image clustering and other fields.However,as NMF cannot capture the inhernt geometric structure of data,graph-based non-negative matrix decomposition is proposed.Most graph-based algorithms use K-nearest neighbors to construct similar graphs.However,the directly constructed graphs are inaccurate due to the outliers and error features in the data.This paper proposes a non-negative matrix decomposition based on the learning consistency similarity matrix.This method firstly obtains the similarity matrix through adaptive learning,then constructs the regular term of the Laplacian graph through it,and finally adds the regular term to the original non-negative matrix factorization model,which optimizes the disadvantages of directly using K-nearest neighbor composition in the previous practice,and finely maintains the geometric structure of data.The algorithm is used in clustering experiments on USPS dataset,yale dataset,faces dataset and ORLdata dataset and is compared with some other advanced algorithms.The numerical test results show that the algorithm proposed in this paper performs quite well.