Abstract: Focusing on the issues that the Principal Component Analysis (PCA) related dimensionality reduction methods are limited to deal with nonlinear distributed datasets and have poor robustness, a new dimensionality reduction method named Robust Cosine-Euclidean Metric (RCEM) was proposed. Considering that Cosine Metric (CM) can handle the outliers efficiently and Euclidean distance can well maintain variance information of samples, the CM was used to describe the geometric characteristics of neighborhood and the Euclidean distance was used to depict the global distribution of dataset. This new proposal method retained local information of dataset while achieving the unification of local and global structure, thus it increased the robustness of local dimensionality reduction algorithm and helped avoiding the problem of small sample size cases. The experimental results on Corel-1000 dataset showed that the retrieval average precision of RCEM was 5.61% higher than that of Angle Optimization Global Embedding (AOGE), and the retrieval time of RCEM was decreased by 42% compared with dimensionality reduction free method. The results indicate that RCEM can improve the efficiency of image retrieval without decreasing the retrieval accuracy, and it can be effectively applied to Content-Based Image Retrieval (CBIR).

Key words: Principal Component Analysis (PCA), Cosine Metric (CM), Euclidean distance, local information, Content-Based Image Retrieval (CBIR)

摘要： 为解决主成分分析（PCA）无法处理非线性数据集以及鲁棒性差的问题，提出一种鲁棒的余弦-欧氏距离度量的降维方法（RCEM）。该方法利用余弦度量（CM）能够处理离群点的特点来提取数据的局部几何特征，并利用欧氏距离能够很好地保持样本的方差信息的特点来刻画数据集的全局分布，在保留数据局部信息的同时实现了局部和全局的统一，提高了局部降维算法的鲁棒性，同时避免了局部小样本问题。实验结果显示，与角度优化全局嵌入（AOGE）方法相比，在Corel-1000数据集下检索查准率提高了5.61%，相比不降维时检索时间减少了42%。结果表明，RCEM算法能在不降低图像检索精度的同时提高图像检索的效率，可以有效应用于基于内容的图像检索（CBIR）。

关键词: 主成分分析, 余弦度量, 欧氏距离, 局部信息, 基于内容的图像检索