适用于小样本的双邻接图判别分析算法
Double Adjacent Graph-Based Discriminant Analysis for Small Size Sample

作为一种常用的降维方法，适用于小样本的监督化拉普拉斯判别分析方法通过使用图嵌入的判别近邻分析得到了很好的降维效果。但该方法在构建近邻图时，在K近邻中寻找同类和异类样本点存在数据不平衡问题；此外，在优化该方法的目标函数时，没有全面考虑到类间信息，从而会在一定程度上降低该方法的性能。针对以上两个问题，本文提出了适用于小样本的双邻接图判别分析方法。首先该方法分别在同类和异类样本中找出K个近邻点，然后使用这K个类内近邻点和K个类间近邻点来构造双邻接图，这样可以确保邻接图中既有同类样本点也有异类样本点，且数目相同。然后该方法在目标函数的推导结果中加入了类间拉普拉斯散度矩阵，从而使优化得到的投影矩阵融入更多的类间信息。在Yale和ORL人脸数据集上进行实验，并与同类方法相比，结果表明本文提出的适用于小样本的双邻接图判别分析方法能够得到更好的降维效果。
As a common dimensionality reduction method, the supervised Laplacian discriminant analysis (SLDA) for small size sample achieves a good result of dimensionality reduction via graph embedding discriminant neighborhood analysis. However, when SLDA finds the inter-class and intra-class data points in K nearest neighbors, there might exist an imbalance problem. Additionally, SLDA does not fully consider the inter-class information, which may decrease the performance of SLDA to a certain extent. To address the two problems mentioned above, we propose a double adjacent graph-based discriminant analysis (DAG-DA) algorithm for small size sample. Firstly, the algorithm tries to find K nearest neighbors in inter-class and intra-class samples, respectively, and then uses these K inter-class neighbors and K intra-class neighbors to construct the double adjacent graph. In this way, we can ensure that the adjacent graph contains both the inter-class and intra-class data points and has the same number. Secondly, the algorithm tries to add the intra-class Laplacian scatter matrix into the objective function of SLDA. Thus, the projection matrix obtained by optimization takes the information between classes into account fully. We perform experiments on Yale and ORL human face datasets. Experimental results show that the proposed algorithm can get better performance compared with other methods.