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ACCV

2007

Springer

2007

Springer

Abstract. The trace quotient problem arises in many applications in pattern classiﬁcation and computer vision, e.g., manifold learning, low-dimension embedding, etc. The task is to solve a optimization problem involving maximizing the ratio of two traces, i.e., maxW Tr(f(W ))/Tr(h(W )). This optimization problem itself is non-convex in general, hence it is hard to solve it directly. Conventionally, the trace quotient objective function is replaced by a much simpler quotient trace formula, i.e., maxW Tr h(W )−1 f(W ) ¡ , which accommodates a much simpler solution. However, the result is no longer optimal for the original problem setting, and some desirable properties of the original problem are lost. In this paper we proposed a new formulation for solving the trace quotient problem directly. We reformulate the original non-convex problem such that it can be solved by efﬁciently solving a sequence of semideﬁnite feasibility problems. The solution is therefore globally optimal...

Related Content

Added |
18 Oct 2010 |

Updated |
18 Oct 2010 |

Type |
Conference |

Year |
2007 |

Where |
ACCV |

Authors |
Chunhua Shen, Hongdong Li, Michael J. Brooks |

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