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戴道清, Xiao-Sheng Zhuang and Dao-Qing Dai
,-0001,():
-1年11月30日
This paper addresses the small sample size problem in linear discriminant analysis, which occurs in face recognition applications. Belhumeur, Hespanha and Kriegman (IEEE Trans. on PAMI, Vol. 19 (7) (1997), 711-720.) proposed the FisherFace method. We find out that the FisherFace method might fail since after the PCA transform the corresponding within class covariance matrix can still be singular, this phenomenon is verified with the Yale face database. Hence we propose to use an inverse Fisher criteria. Experiment results suggest that this new approach works well.
linear discriminant analysis,, small sample size problem,, Inverse Fisher discriminate criteria,, face recognition.,
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【期刊论文】On a nonlocal problem for nonlinear pseudoparabolic equation in one space dimension*
戴道清, Dao-Qing Dai and Yu Huang
,-0001,():
-1年11月30日
For a one-dimensional nonlinear pseudoparabolic equation we consider its initial boundary value problem on an interval. The boundary condition on the left endpoint is of Dirichlet type, but the condition on the right endpoint is replaced by a nonlocal one. Because it is given by an integral, the function involved could exhibit singularities, which distinguishes this nonlocal condition from its Dirichlet counterpart. Based on an elliptic estimate and an iteration method we established the well-posedness of solutions in a weighted Sobolev space.
Nonlinear pseudoparabolic equation, weighted Sobolev space, elliptic estimate, nonlocal boundary condition
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【期刊论文】RIEMANN MAPPING THEOREMS FOR BELTRAMI EQUATIONS BY CIRCLE PACKINGS
戴道清, SHI-YI LAN AND DAO-QING DAI
PACIFIC JURNAL OF MATHEMATICS Vol. 217. No.1, 2004,-0001,():
-1年11月30日
We use circle packing techniques to construct approximate solutions to the generalized Beltrami equations with simply and multiply connected regions in the plane. We show convergence of the approximate solutions. This gives a constructive proof for the existence of quasiconformal mappings with a given pair of complex dilations.
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【期刊论文】Galerkin analysis for Schr
戴道清, Dao-Qing Dai, Bin Hana) and Rong-Qing Jia
J. Math. Phys., Vol. 45, No.3, March 2004,-0001,():
-1年11月30日
We consider the perturbed Schr
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【期刊论文】ORTHONORMAL POLYNOMIAL WAVELETS ON THE INTERVAL
戴道清, DAO-QING DAI AND WEI LIN
,-0001,():
-1年11月30日
We use special functions and orthonormal wavelet basis on the real line to construct wavelet-like basis. With these wavelets we can construct polynomial basis on the interval, moreover we can use them to the numerical resolution of degenerate elliptic operators.
Chebyshev polynomials,, Riesz basis,, wavelets,, degenerate elliptic operator.,
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