THE TRACE RATIO OPTIMIZATION PROBLEM FOR DIMENSIONALITY REDUCTION
THE TRACE RATIO OPTIMIZATION PROBLEM FOR DIMENSIONALITY REDUCTION
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DOI：
10.1137/090776603
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发表时间：
2010-01-01
影响因子：
1.5
通讯作者：
Saad, Y.
中科院分区：
文献类型：
--
作者：
Ngo, T. T.;Bellalij, M.;Saad, Y.
本文考虑了p列酉阵V上Tr[V-TAv]/Tr[V-TBV]之比的最优化问题，其中A，B是两个正定矩阵。这个问题在有监督学习技术中很常见。然而，由于它的数值解通常是昂贵的，它经常被更简单的优化问题所取代，该优化问题包括在V-TBV=i，单位矩阵的约束下对Tr[V-TAv]进行优化。本文的目的是详细研究这个迹比优化问题，考虑不同的算法来求解它，并说明这些算法在降维方面的使用。
This paper considers the problem of optimizing the ratio Tr[V-T AV]/ Tr[V-T BV] over all unitary matrices V with p columns, where A, B are two positive definite matrices. This problem is common in supervised learning techniques. However, because its numerical solution is typically expensive it is often replaced by the simpler optimization problem which consists of optimizing Tr[V-T AV] under the constraint that V-T BV = I, the identity matrix. The goal of this paper is to examine this trace ratio optimization problem in detail, to consider different algorithms for solving it, and to illustrate the use of these algorithms for dimensionality reduction.