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x1, x2, ..., xNN N
n
ˆ
f(x) = 1
Nh1h2...hn
N
X
i=1
n
Y
j=1
Kjx−xj
hj,
hj=4
N(n+2) 1
n+4 ×σj
j Kj(·)
j
σj=sN
P
i=1
(xij −¯xj)2
N−1
j
F F =
{f1(x), f2(x), ..., fn(x)}, n > 2k
k
C1,· · · , Ck
k
P
i=1
#Ci=n, #Ci
i
Ci∩Cj=∅, i 6=j, i = 1, k, j = 1, k.
L1
n
f1(x), f2(x), . . . , fn(x),(n>2)
Rmfmax (x) =
max {f(x)1, f2(x), . . . , fn(x)}
n= 2
w(f1, f2)≡kf1−f2k1
2=Z
Rm
fmax (x)x−1
n > 2
w(f1, f2, . . . , fn)≡ kf1, f2, . . . , fnk1
=Z
Rm
fmax (x)dx −1.
g, (g1, g2, ..., gn),(f1, f2, ..., fm)
w[g∪ {(f1, f2, ..., fm)}]
w[{g1, g2, ..., gn}∪{f1, f2, ..., fm}].
SF =
k
P
i=1 P
f∈Ci
kf−fvik2
nmini6=jkfvi−fvjk2,
kfvi−fvjkL1
CiCj
| | |
fvj=
P
fi∈Cj
fi
nj
nj
Cj
k
n f1, f2, . . . , fn(n > 2)
k C1, C2, . . . , Ck
k
P
i=1
#Ci=n C(t)
i
Ci, i =1, k t
n k
1
C(1)
1, C(1)
2, . . . , C(1)
k.
fj,
wfj∪C(1)
i=
fj∪C(1)
i
1, i = 1, k, j = 1, n
fjC(1)
1
fj∈C(1)
h
wfj∪C(1)
h=
mini=1,...,k nwfj∪C(1)
io fj
C(1)
h
C(1)
s
wfj∪C(1)
s= mini=1,...,k nwfj∪C(1)
io
fjC(1)
s
2C(2)
s
C(1)
hfj
C(2)
h
C(2)
1, C(2)
2, . . . , C(2)
kfj
m
k m
C(m)
1, C(m)
2, . . . , C(m)
k
wfj∪C(m)
s= mini=1,...,k nwfj∪C(m)
io.
(f, k, x)
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f
f
k
k
x f
m
d
m
createU (k, n )
k n
B
B
(1∗n , .5, k +.5)
(f, x)
f
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| | |
n
| | |
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n
n
n n
n
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2
2
