Trace Quotient Problems Revisited

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Trace Quotient Problems Revisited
The formulation of trace quotient is shared by many computer vision problems; however, it was conventionally approximated by an essentially different formulation of quotient trace, which can be solved with the generalized eigenvalue decomposition approach. In this paper, we present a direct solution to the former formulation. First, considering that the feasible solutions are constrained on a Grassmann manifold, we present a necessary condition for the optimal solution of the trace quotient problem, which then naturally elicits an iterative procedure for pursuing the optimal solution. The proposed algorithm, referred to as Optimal Projection Pursuing (OPP), has the following characteristics: 1) OPP directly optimizes the trace quotient, and is theoretically optimal; 2) OPP does not suffer from the solution uncertainty issue existing in the quotient trace formulation that the objective function value is invariant under any nonsingular linear transformation, and OPP is invariant only und...
Shuicheng Yan, Xiaoou Tang
Added 22 Aug 2010
Updated 22 Aug 2010
Type Conference
Year 2006
Where ECCV
Authors Shuicheng Yan, Xiaoou Tang
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