Locality Preserving Projection Based on F-norm
Locality Preserving Projection Based on F-norm
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DOI：
10.1609/aaai.v32i1.11518
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发表时间：
2018-04
期刊：
影响因子：
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通讯作者：
Xiangjie Hu;Yanfeng Sun;Junbin Gao;Yongli Hu;Baocai Yin
中科院分区：
文献类型：
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作者：
Xiangjie Hu;Yanfeng Sun;Junbin Gao;Yongli Hu;Baocai Yin
局部保持投影（LPP）是一种众所周知的降维方法，其中保持了数据的邻域图结构。传统的LPP采用平方F范数进行距离测量。这可能会夸大更多的距离误差，并导致模型对离群值敏感。为了解决这个问题，我们提出了两个新的F-范数为基础的模型，称为F-LPP和F-2DLPP，这是基于矢量和矩阵的数据，分别开发。在F-LPP和F-2DLPP中，投影到低维空间的数据的距离由F范数测量。因此，预计这两种方法都可以减少离群值的影响。针对基于F范数的模型，提出了一种迭代优化算法，并给出了算法的收敛性分析。在三个公共数据库上的实验结果证明了我们提出的方法的有效性。
Locality preserving projection (LPP) is a well-known method for dimensionality reduction in which the neighborhood graph structure of data is preserved. Traditional LPP employ squared F-norm for distance measurement. This may exaggerate more distance errors, and result in a model being sensitive to outliers. In order to deal with this issue, we propose two novel F-norm-based models, termed as F-LPP and F-2DLPP, which are developed for vector-based and matrix-based data, respectively. In F-LPP and F-2DLPP, the distance of data projected to a low dimensional space is measured by F-norm. Thus it is anticipated that both methods can reduce the influence of outliers. To solve the F-norm-based models, we propose an iterative optimization algorithm, and give the convergence analysis of algorithm. The experimental results on three public databases have demonstrated the effectiveness of our proposed methods.