一种优化的近邻保持嵌入降维算法研究

Research on an Optimized Nearest Neighbor Preserving Embedding Algorithm for Dimensionality Reduction

近邻保持嵌入算法NPE是流形学习领域中一种重要的降维算法,现已成功应用于很多领域,例如人脸识别、语音识别等,但在处理局部邻域信息量不足、存在短路以及流形曲率大等稀疏数据时,原始数据的几何拓扑结构损坏严重。其主要原因是在邻域选择中没有对数据类间信息进行很好的区分。基于此,提出了一种优化的近邻保持算法(ONPE),在NPE算法中对数据类间信息进行优化,构造类间权值矩阵;并在低维局部重建时引入类内密度信息,从数据类内和类间两个维度出发,更好地避免数据在近邻选取方向上的缺失。将ONPE算法应用于图像检索等实验,结果表明在图像检索的实验中该算法有较高的查准率和查全率。ONPE相对于NPE降维的时间复杂度并没有增加,验证了算法的实用性和有效性。

The nearest neighbor preserving embedding algorithm(NPE)is an important dimensionality reduction algorithm in manifold learning,which has been successfully applied to many fields,such as face recognition,speech recognition,etc.However,when dealing with sparse data such as insufficient local neighborhood information,short circuit and large manifold curvature,the geometric topology of the original data is seriously damaged.The main reason is that the information between data classes is not well differentiated in neighborhood selection.Based on this,we propose an optimized nearest neighbor preserving algorithm(ONPE),which optimizes the inter-class information in the NPE algorithm,constructs the inter-class weight matrix,and introduces the intra-class density information in the low-dimensional local reconstruction.Starting from the two dimensions of data class and inter-class,we can better avoid the absence of data in the direction of neighbor selection.The experiment results show that the proposed algorithm has higher precision and recall ratio in the experiment of image retrieval.The time complexity of ONPE is not increased compared with NPE,which verifies the practicability and effectiveness of the algorithm.