, () . , :
I m, II n mxn,
n | min | |||
a11 | a1n | |||
MAX | ||||
m | am1 | amn |
n | |||
a11 | a1n | ||
m | am1 | amn | |
max | MIN |
=0
.
1. min
2. : maxmin - .
:
1. max
2. : minmax
:
1. max min aij ≤ min max aij
I j j i
:
maxminij=minmaxij
, , .
.
() , . . . , .
X Lk. Lm (m≤k), : ( ) , . ( ) , . . , , , ( ). , , , ( ) , .
W m*k, Lk , :
Y = W*(X - μ), Y ∈ Lm, X ∈ Lk.
X - , Y - , μ - X .
(20 ) X. .
|
|
Y X : y1 , y2 y1.
, X = (x1,x2), , .
X .
X n*k (n , k ), Z , :
zi,j =(xi,j - xj)/Sj ,
: xi,j - i - j- X, i=1,2,...,n; j=1,2,...,k,
xj - j- X: xj =∑i xi,j/n,
Sj - j- X:
S2j = ∑i (xi,j - xj)2/(n-1).
R :
R=(Z*Z)/(n-1).
, C :
C = (X*X)/(n-1).
Λ () .
λj | R - λI| = 0. λj - . Σλj xj. , k.
, λj. R. k j = 1,..., k. :
(1-λj)*v1j + r12*v2j +r13*v3j +... +r1k*vkj = 0,
r21*v1j + (1-λj)*v2j +r23*v3j +... +r2k*vkj = 0,
...............................................................
rk1*v1j + rk2*v2j +rk3*v3j +... +(1-λj)*vkj = 0,
, , . , .
A , akj . A k*k Xj, m , m ≤ k. A Λ V A = V*Λ1/2.
G k*n, G = A-1Z. :
g11 | g12 | ... | g1n |
g21 | g22 | ... | g2n |
... | ... | ... | ... |
gk1 | gk1 | ... | gkn |
( k). m m*n. m , λj. , "Statgraphics" , .
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