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中文摘要：
TRIMAP算法可以较好地解决一个＂将处于某一不明确的黎曼流形上的高维张量数据投影到一低维子空间,而不改变原流形中任一对数据点的测地距离,同时保留识别能力＂的问题。但发现了TRIMAP算法中对于图上距离定义的不足,并对其做出了新的定义,重新定义了图上距离的TRIMAP算法,不仅汲取了原算法的优点,并考虑到了不同类之间的大小及各类的疏密程度对属于不同类的样本点之间的距离的影响,可以更有效地识别出待识别样本的类别,提高识别率。经初步的实验验证,在ORL人脸图像的分类问题中获得了比原TRIMAP算法更好的识别性能。
英文摘要：
The TRIMAP algorithm can solve the problem of projecting high-dimensional tensor data on an unspecified Rie-mannian manifold onto some lower dimensional subspace without distorting the pair-wise geodesic distances between data points on the Riemannian manifold while preserving discrimination ability.But a shortage of the definition of graph distance has been discovered and a new definition is worked out on it.The TRIMAP which has the new definition not only learns the benefits of the TRIMAP algorithm but also considers the influences which the size and the density level between different classes have on the distances between data points.In addition,it can more effectively identify the type of samples to be identified to improve the recognition rate.The experimental results about ORL face classification demonstrate that the proposed idea has better classification performance than the TRIMAP algorithm.
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