基于判别正则化的局部保留投影

Discriminant and regularization locality preserving projections

中文关键词  局部保留投影  流形学习  局部相似度阈值  图描述  特征提取

英文关键词  Locality preserving projections  Manifold learning  Local similarity threshold  Graph description  Feature extraction

中文摘要

      局部保留投影（Locality preserving projections，LPP）是一种常用的线性化流形学习方法，其通过线性嵌入来保留基于图所描述的流形数据本质结构特征，因此LPP对图的依赖性强，且在嵌入过程中缺少对图描述的进一步分析和挖掘。当图对数据本质结构特征描述不恰当时，LPP在嵌入过程中不易实现流形数据本质结构的有效提取。为了解决这个问题，本文在给定流形数据图描述的条件下，通过引入局部相似度阈值进行局部判别分析，并据此建立判别正则化局部保留投影（简称DRLPP）。该方法能够在现有图描述的条件下，有效突出不同流形结构在线性嵌入空间中的可分性。在人造合成数据集和实际标准数据集上对DRLPP以及相关算法进行对比实验，实验结果证明了DRLPP的有效性。

英文摘要

      Locality preserving projections (LPP) is a popular linear manifold learning algorithm, which preserves the intrinsic structure of manifold data based on graph description by linear embedding. As a result, LPP is highly dependent on the graph, and it lacks further analysis and mining of graph description in the process of embedding. When the intrinsic structure is improperly described by the graph, it is not easy for LPP to extract the intrinsic structure of manifold data effectively while embedding. In order to solve this problem, local discriminant analysis is proposed in this paper by introducing a local similarity threshold given the graph description of manifold data, and then discriminant and regularization locality preserving projections (DRLPP) is presented. The proposed method can effectively highlight the separability of different manifolds in the linear embedding space based on the existing graph description of data. Extensive experiments on synthetic data and benchmark datasets illustrate the effectiveness of our proposed method compared with related algorithms.