xviNotation
Notation
U,uDomain, point on domain
x,x(u)∈X(U,C)Signal on the domain of the form x:U→C
f(x)∈F(X)Functionsonsignalsonthedomainoftheformf:
X(U,C)→Y(whendomainUandtargetCareclearfrom
the context)
G,gGroup, element of the group
g.u,ρ(g)Group action, group representation
X∈C
|U|×ばつs
Matrix representing a signal on a discrete domain
x
u
∈C
s
Vector representing a discrete domainsignal Xon element
u∈U
x
uj
∈CScalar representing the jthcomponent of adiscrete domain
signal Xon element u∈U
F(X)Functionondiscretedomainsignalsthatreturnsanother
discrete domain signal, as a matrix
τ:U→UAutomorphism of the domain
η:U→U
′
Isomorphism between two different domains
σ:C→C
′
Activation function (point-wise non-linearity)
G=(V,E)Graph with nodes Vand edges E
M=(V,E,F)Mesh with nodes V, edges E, and faces F
x⋆θConvolution with filterθ
S
v
Shift operator
φ
i
Basis function
T
u
U,TUTangent space at u, tangent bundle
X∈T
u
UTangent vector
g
u
(X,Y)=⟨X,Y⟩
u
Riemannian metric
l(γ),l
uv
Length of a curve γ, discrete metric on edge (u,v)