Information Technology Reference
In-Depth Information
Ta b l e 3 . 3
Three-dimensional example data set.
Sample no.
X
Y
Z
1
13
.
5471
12
.
6356
21
.
7779
2
15
.
3202
5
.
4330
20
.
4339
3
17
.
7739
12
.
4688
19
.
3321
4
18
.
3664
14
.
7330
28
.
2576
5
18
.
0205
9
.
3600
25
.
1894
6
16
.
9528
11
.
8832
21
.
8291
7
17
.
5986
13
.
0341
21
.
5221
8
13
.
6643
11
.
2316
13
.
9913
9
19
.
3081
11
.
7703
28
.
3937
10
20
.
2114
8
.
0871
22
.
4164
11
15
.
7187
14
.
7718
18
.
7206
12
11
.
6222
17
.
9957
21
.
4343
13
14
.
4965
15
.
3002
20
.
6371
14
19
.
5328
11
.
8101
22
.
1391
15
16
.
1871
10
.
0019
16
.
2823
16
17
.
5598
10
.
0402
20
.
3788
17
17
.
2416
13
.
5807
25
.
4979
18
16
.
2913
14
.
9305
22
.
9105
17
.
7401
15
.
5304
22
.
6354
19
.
.
.
20
20
3395
10
9800
23
1621
21
8
.
5554
12
.
2874
12
.
9827
22
11
.
1397
12
.
4292
18
.
0374
23
11
.
9930
13
.
4574
21
.
6548
24
7
.
8248
4
.
4579
8
.
4648
25
10
.
7568
6
.
6412
17
.
6931
When representing the samples relative to orthogonal axes in
L
, the coordinates of
the projected points are given by
z
=
x
V
r
,
(3.4)
which implies taking the biplot plane in Figure 3.6 and placing it in the x-y plane to
produce a scatter diagram. The steps in creating this scatter diagram are: first, the data
in Table 3.3 are column-centred to
X
, say; then we obtain the SVD
X
=
U
V
with
0
.
5453
−
0
.
4502
0
.
7071
.
V
=
0
.
2784
0
.
8929
0
.
3540
(3.5)
0
.
7907
−
0
.
0038
−
0
.
6122
Finally, using (3.4), the first two columns of
XV
are plotted, and the resulting scatter
diagram is shown in Figure 3.7.
A figure similar to Figure 3.7 can also be constructed with the following call to
PCAbipl
:
PCAbipl(X = as.matrix(Table.3.3.data[,-1]), ax = NULL,
pch.samples = 15, colours = "green")
