线性判别分析中两种空间信息嵌入方法之比较

Comparison between Two Approaches of Embedding Spatial Information into Linear Discriminant Analysis

由"没有免费午餐定理(NFL)"可知:只有充分利用了与问题相关的先验知识的学习器才会拥有好的学习性能,而常用的线性判别分析(LDA)在为图像提取判别特征时对图像向量化的处理导致了空间结构的破坏,以致结构信息未被利用,从而限制了学习性能的进一步提升。空间平滑的LDA(SLDA)通过对LDA目标的空间正则化弥补了此不足,同时图像欧氏距离(IMED)则通过空间平滑欧氏距离实现对空间结构的利用,而后将其用于LDA(IMEDA)。对这两种LDA间的内在联系进行了尝试探究:理论上证明了对于中心化样本,SLDA是IMEDA的特例;分析了算法的时间和空间复杂度;经验上通过Yale、AR和FERET人脸集比较了SLDA和IMEDA的识别性能和运行时间,同时分析了参数对模型性能的影响。

No Free Lunch Theorem says that only taking full advantage of learning machine of priori knowledge related to the problem under consideration can have a good learning performance. However, the vectorization of the images used in conventional linear discriminant analysis （LDA） damages the spatial structure of initial images, and restricts the im- provement of the learning performance of LDA. Spatially smoothing linear discriminant analysis （SLDA） tries to over- come this problem by introducing the spatial regularization to the objective of LDA, whereas IMage Euclidean Distance Discriminant Analysis （IMEDA） substitutes IMage Euclidean Distance （IMED） for the original Euclidean metric in the objective of LDA to utilize the spatially structure information. This paper attempted to explore the intrinsic link between SLDA and IMEDA： theoretically proved that SLDA is the special ease of IMEDA when the sample mean of the data set is zero,analyzed the time complexity and the space complexity of the algorithms. The experiments were conducted to compare SLDA with IMEDA on Yale, AIR and FERET face datasets, and the influences of the parameters on perfor- mance of the algorithms were analyzed.