Abstract: The TRIMAP algorithm redefines the expression of  the distance on the graph, and in order to measure the quality of the projection functions, considers the squared error sum of all pair wise geodesic. This way can better find what is needed from high-dimensional space to low-dimensional vector space conversion. But this measure can’t be well express the contrast relationship between graph distance which is defined in TRIMAP algorithm and actual distance which is projected to low dimensional space. Aiming at this deficiency, this paper uses a new standard expression and defines a parameter m to represent relationship in order to solve the defect, get the best projection and improve the recognition rate. The preliminary experimental results show that it can get a better recognition performance in the ORL face image classification and recognition problem.

Key words: data dimension reduction, manifold learning, geodesic distance, ISOMAP algorithm, locally linear embedding

摘要： TRIMAP算法重新定义了图上距离的表达形式，并用近邻点对的测地距离的误差和作为衡量投影函数好坏的标准，通过这种方法可以较好地找到所需的从高维空间到低维空间转换的媒介，但是这种衡量标准不能很好地表达出TRIMAP中定义的图上距离与投影到低维空间中两点实际距离的对比关系。针对这个不足，采用了一个新的衡量标准表达式，定义一个参数m来代表对比关系，以此来解决这个缺陷，从而更好地获得最佳投影，提高识别率。实验结果表明，在ORL人脸图像的分类识别问题中获得了较好的识别性能。

关键词: 数据降维, 流形学习, 测地距离, 等距离映射算法, 局部线性嵌入