Available via license: CC BY

Content may be subject to copyright.

| | |

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)

| | |

f

f

k

k

x f

m

d

m

createU (k, n )

k n

B

B

(1∗n , .5, k +.5)

(f, x)

f

| | |

| | |

n

| | |

| | |

n

n

n n

n

| | |

2

2