基于局部学习的受限非负矩阵分解算法

Constrained nonnegative matrix factorization based on local learning

为了利用样本的局部结构信息与少量标记样本的类别信息,提出了一种基于局部学习的受限非负矩阵分解算法,并应用于数据表示.为了考虑样本的局部结构信息,通过每个样本邻域构建出的分类器对样本的类别进行预测;同时,还将样本中存在的类别信息作为硬约束,使得相同类别的高维样本在低维表示空间保持一致.算法不仅利用了样本的几何流形结构信息与鉴别结构信息,还考虑了标记样本的类别信息,因此比传统的非负矩阵算法具有更强的鉴别性.在20Newsgroups文本库和ORL人脸库中的实验结果表明了算法能提高分解准确率和归一化互信息.

In order to make use of the local structure information and the label information of limited labeled data,constrained nonnegative matrix factorization based on local learning（CNMFLL）was proposed for data representation.To take consideration of the local structure information in the data,apredictor was constructed by the neighborhood of each point and its label information was estimated.In addition,the label information of the labeled data was as hard constraints so that the samples sharing the same label in high dimensional space had the same coordinate in new representation space.Therefore,this algorithm not only makes use of the geometry structure information and discriminate structure information,but also considers the label information of labeled data.Thus,CNMFLL has more discriminate power than traditional NMF.The experimental results on 20 Newsgroups text database and ORL face database show that the proposed algorithm can improve the accuracy and normalize mutual information.