17.1.4.
, , .
, (, ). , , . , () , () , ().
, () . (, , ..) .
, . , , . , .
, , (Hierarchical Cluster Analysis)
, . - ,
( ) , . (), . , . () . .
. , , , ( ), - .
, , :
- , , , ;
|
|
- , ;
- (, ).
17.2.
17.2.1.
n +1 x 1, x 2,..., x n, y, , x 1, x 2,..., xn y. , f n . y, x 1, x 2,..., xn f (x 1, x 2,..., xn), y = f (x 1 ,x 2,..., xn) y =y (x 1 ,x 2,..., xn).
x 1, x 2,..., xn , y ‑ n .
- . , , . x y, z.
17.2.2.
, , (x,y) D , f (x,y) f (x,y).
D .
x,y M , z=f (x,y) z = f (M). x,y M.
x, y , M (x,y). , z = f (), .
(x, y, f (x, y)), (x,y)Î D. .
1.
, () . z = f (x,y), 2. M (x,y) X,Y l 1 l 2, . , M f l 1 , l 2 . , M 1, l 1 M, f (M 1) > f (M). M 2 , l 2 M, f (M 2) < f (M).
, , , .
|
|
. z = f (x, y) c , .
17.2.3.
z=C ( XOY Z z=C). z = f (x, y) XOY C z = f (x, y). XOY, f (x, y) = C. C, f (x, y). C, , .
17.2.1.
z = .
, > 0,
< 0, ( = ,
> 0), = 0.
17.2.4.
XOY : M 0(x 0, y 0) M 1(x 1, y 1). r , 17.1.,
.
d ‑ . d - Vd M 0(x 0, y 0) , x,y
.
, d - M 0(x 0, y 0) d ( , )
M 0(x 0, y 0) z = f (x, y), d, M (x, y) Î Vd (x 0, y 0) f (x, y) > f (x 0, y 0).
M 0(x 0, y 0) z = f (x, y), d, M (x, y) Î Vd (x 0, y 0) : f (x, y) < f (x 0, y 0).
.
A z = f (x, y) M 0(x 0, y 0):
,
e > 0 d > 0, M (x, y) d - M 0(x 0, y 0)
| f (x, y) - A |< e.
z = f (x, y) M 0(x 0, y 0),
.
.
, ( ) . - . ,
17.2.5.
x z = f (x, y) M 0(x 0, y 0)
,
. ( ):
; ; .
x z = f (x, y), x y.
y z = f (x, y) M 0(x 0, y 0):
= .
XYZ y = y 0 P, OY y 0. P z = f (x, y), L, 1. XOY L x 0, y 0 x z = f (x, y) . .
|
|
y.
17.2.1
. , x z = f (x, y) y , y x.
1. .
2.
z = f (x, y) , , , :
.
. x y. zxx ¢¢, zyy¢¢, zxy¢¢ . ; . . , , , , . , zxy¢¢ = (zx¢) y¢ zyx¢¢ = (zy¢) x¢.
17.2.1. ( )
, , x y. ( , 1 2.)
. . , ,
.
, OX OY, , XOY, 1. . , (0,0) , . , (0,0) M , f (M) = 1, f (0, 0) = 0. (0,0).
D Oxy z = f(x,y). D - n () D1, D2, D3, , Dn. Dk (k=1,2,,n), dn Dk ( ) Dk Mk (xk, yk)
f(x, y) ≥0, Mk (xk, yk) Dk f(Mk), Vn , , D, , Oz z = f(x,y) (. :)
17.2.2.( )
z =f(x,y) D,
17.2. 6
V f(x,y) D .
,
() D, f(x,y)≥0,
, z=f(x,y), D.
|
|
17.2.7
D Oy (Ox), , Oy (ox) , .
() , () .
, (), .
:
, Oy
, O
17.2.8
, , . . , , () . , f(x,y) g(x) ∙ h(x,y),
, .
17.2.2.
D,
D :
2. ,
3. , :
4. D
D =