Дронов С.В. Математические методы в психологии
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I
q
(Z) =
1
1 + ∆(Z)
.
F
Z(X) = (X
i
1
)
, ..., X
(i
q
)
).
I
q
(Z) =
k
X
i,j=1
δ(P
i
(Z), P
j
(Z)),
k δ(., .)
δ(P
i
(Z), P
j
(Z)) =
X
(
¯
X
i
−
¯
X
j
)
2
.
Y aX +b
X
p µ S p×p
I
q
=
P
q
j=1
Dz
(j)
P
p
i=1
Dx
(i)
→ max,
Z = L(X − µ), L − q × p
X
k
k−1
L
(
P
l
(1)
j
x
(j)
→ max,
P
(l
(1)
j
)
2
= 1,
P
i,j
S
i,j
l
(1)
i
l
(1)
j
→ max,
< Sl
(1)
, l
(1)
> → max
l
1
, kl
1
k = 1,
l
(j)
j
S j
λ
j
S
I
q
=
λ
1
λ
1
+ ... + λ
p
,
x
1
x
2
x
3
S =
451, 39 271, 17 168, 70
271, 17 171, 73 103, 29
168, 70 103, 29 66, 65
.
λ
1
= 680, 40, λ
2
= 6, 50 λ
3
= 2, 86.
l
1
=
0, 81
0, 50
0, 31
, l
2
=
−0, 55
0, 83
0, 10
, l
3
=
−0, 21
−0, 25
0.95
.
i z
(i)
= < l
i
, X > X
x
j
Z
λ
1
λ
1
+ λ
2
+ λ
3
= 0, 9864,
x
(1)
, ..., x
(p)
f
(1)
, ..., f
(q)
f
f
(i)
x
(j)
X = QF + U,
Q − p ×q
F
X U
U
F V
U
X
X = AF, Df
(i)
= 1, i = 1, 2...
A F
Z = CF, X = (AC)Z C
A, F F (m)
m A
m
X
ˆ
X(m) = A
m
F (m).
X
ˆ
X(m)
f
(i)
=
1
√
λ
i
˜
f
(i)
,
˜
f
(i)
i i A
√
λ
i
l
i
l
i
S
λ
i
x
(i)
, x
(j)
ˆx
(i)
, ˆx
(j)
Q =
q
1,1
0 0 ... 0
q
2,1
q
2,2
0 ... 0
... ... ... ... ...
q
q,1
q
q,2
q
q,3
... q
q,q
... ... ... ... ...
q
p,1
q
p,2
q
p,3
... q
p,q
,
Q V
x
(1)
, ..., x
(p)
i j
ρ
i,j
Dx
(i)
f
(1)
f
(1)
x
(i1)
= x
(i)
− ˆq
i,1
f
(1)
.
ˆ
Q V
ˆ
V = S −
ˆ
Q
ˆ
Q
t
.
Q, V
F q x
x
(i)
k
=
q
X
j=1
q
i,j
f
(j)
k
+ u
(i)
k
, i = 1, ..., p, k = 1, ..., n.
ˆ
F
k
= (
ˆ
Q
t
ˆ
V
−1
ˆ
Q)
−1
ˆ
Q
t
X
k
, k = 1, ..., n.
c
i,j
ˆ
F =
CX
n
X
k=1
q
X
i=1
M(f
(i)
k
−
p
X
j=1
c
i,j
x
(k)
j
)
2
→ min
C
.
f
(i)
k
M
X
F
X
F
t
!
=
QQ
t
+ V Q
Q
t
I
.
ˆ
F
k
= (I +
ˆ
Q
t
ˆ
V
−1
ˆ
Q)
−1
ˆ
Q
ˆ
V
−1
X
k
, k = 1, ..., n.
x
1
x
2
x
3
x
4
x
5
x
6
q
i,1
q
i,2
x
1
x
2
x
3
x
4
x
5
x
6
f
1
= 0, 245x
1
+ 0, 208x
2
+ 0, 158x
3
+ 0, 278x
4
+ 0, 271x
5
+ 0, 157x
6
,
f
2
= 0, 352x
1
+ 0, 201x
2
+ 0, 309x
3
− 0, 351x
4
− 0, 303x
5
− 0, 126x
6
.
f
1
f
2
∆
l
δ
l
i,j
i j
l
p
q
q < p
∆
l
∆
i j
δ
i,j
=
p
1 − ρ
i,j
,
ρ
i,j
q
ˆx
0
i,k
, i = 1, ...p, k = 1, ..., q
ˆ
d
0
i,j
=
s
X
k
(ˆx
0
i,k
− ˆx
0
j,k
)
2
.
δ
0
i,j
= δ
i,j
,
ˆ
d
0
i,j
S =
v
u
u
t
P
i,j
(δ
i,j
−
ˆ
d
i,j
)
2
P
i,j
ˆ
d
2
i,j
.
(i, j), i, j = 1, ..., p
δ
i,j
ˆ
d
i,j
ˆx
c+1
i,k
= ˆx
c
i,k
−
1
p
P
j
1 −
δ
c+1
i,j
ˆ
d
c
i,j
(ˆx
c
i,k
− ˆx
c
j,k
)
ˆ
d
c+1
i,j
=
q
P
k
(ˆx
c+1
i,k
− ˆx
c+1
j,k
)
2
,
δ
c+1
i,j
c
S
δ
c+1
i,j
ˆ
d
c+1
i,j
X n p
x l
x
c
(x)
j
, j = 1, ..., l
x
n
X
i=1
c
(x)
r(i)
= 0;
1
n
n
X
i=1
(c
(x)
r(i)
)
2
= 1,
r(i) x i
Q =
X
i<j
ρ
2
i,j
,
ρ
i,j
i j
x
(1)
, ..., x
(p)
X
1
q
X
2
p − q
Q
X
1
X
1
X
2
Q = Q
1
+ Q
1,2
+ Q
2
.
Q
2
x
3
x
4
x
5
