منابع مشابه
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 G...
متن کاملEquivalence of quotient Hilbert modules
Let M be a Hilbert module of holomorphic functions over a natural function algebra A (Ω), where Ω ⊆Cm is a bounded domain. Let M0 ⊆M be the submodule of functions vanishing to order k on a hypersurface Z ⊆ Ω. We describe a method, which in principle may be used, to construct a set of complete unitary invariants for quotient modules Q = M ⊖M0. The invariants are given explicitly in the particula...
متن کاملThe Trace Formula for Noncompact Quotient
1. In [12] and [13] Selberg introduced a trace formula for a compact, locally symmetric space of negative curvature. There is a natural algebra of operators on any such space which commute with the Laplacian. The Selberg trace formula gives the trace of these operators. Selberg also pointed out the importance of deriving such a formula when the symmetric space is assumed only to have finite vol...
متن کاملA note on the trace quotient problem
The trace quotient problem or the trace ratio problem (TRP) is to find an orthogonal matrix V ∈ Rm× (m ≥ ) that maximizes the quotient tr(V BV )/ tr(V W V ) for a given symmetric matrix B ∈ Rm×m and a symmetric positive definite matrix W ∈ Rm×m . It has a crucial role in linear discriminant analysis and has many other applications in computer vision and machine learning as well. In this short n...
متن کاملQuotient Hilbert Modules Similar to the Canonical Hilbert Module
Let H m be the reproducing kernel Hilbert space with the kernel function (z, w) ∈ B×B → (1− m ∑ i=1 ziw̄i) . We show that if θ : B → L(E , E∗) is a multiplier for which the corresponding multiplication operator Mθ ∈ L(H m ⊗ E , H 2 m ⊗ E∗) has closed range, then the quotient module Hθ, given by · · · −→ H m ⊗ E Mθ −→ H m ⊗ E∗ πθ −→ Hθ −→ 0, is similar to H m ⊗F for some Hilbert space F if and on...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1988
ISSN: 0019-2082
DOI: 10.1215/ijm/1255989004