Applied Statistics Using SPSS, STATISTICA, MATLAB and R

340 8 Data Structure Analysis
We see that by using the covariance matrix, only one eigenvector has dominant
correlations with the original variables, namely the “compression breaking load”
variables RMCS and RCSG. These variables are precisely the ones with highest
variance. Note also the dominant values of the first two elements of u. When using
the correlation matrix, the f elements are more balanced and express the
contribution of several original features: f1 highly correlated with chemical
features, and f2 highly correlated with density (MVAP), porosity (PAOA), and
water absorption (AAPN).
The scatter plot of Figure 8.6a shows that the pc scores obtained with the
covariance matrix are unable to discriminate the several groups of rocks; u1 only
discriminates the rock classes between high and low “compression breaking load”
groups. On the other hand, the scatter plot in Figure 8.6b shows that the pc scores
obtained with the correlation matrix discriminate the rock classes, both in terms of
chemical composition (f1 basically discriminates Ca vs. SiO2-rich rocks) and of
density-porosity-water absorption features (f2).
Table 8.4. Eigenvectors of the rock dataset computed from the covariance matrix
(u1 and u2) and from the correlation matrix (f1 and f2) with the respective
correlations. Correlations above 0.7 are shown in bold.
u1 u2 r1 r2 f1 f2 r1 r2
RMCS -0.695 0.487 -0.983 0.136 -0.079 0.018 -0.569 0.057
RCSG -0.714 -0.459 -0.984 -0.126 -0.069 0.034 -0.499 0.105
RMFX -0.013 -0.489 -0.078 -0.606 -0.033 0.053 -0.237 0.163
MVAP -0.015 -0.556 -0.089 -0.664 -0.034 0.271 -0.247 0.839
AAPN 0.000 0.003 0.251 0.399 0.046 -0.293 0.331 -0.905
PAOA 0.001 0.008 0.241 0.400 0.044 -0.294 0.318 -0.909
CDLT 0.001 -0.005 0.240 -0.192 0.001 0.177 0.005 0.547
RDES 0.002 -0.002 0.523 -0.116 0.070 -0.101 0.503 -0.313
RCHQ -0.002 -0.028 -0.060 -0.200 -0.095 0.042 -0.689 0.131
SiO 2 -0.025 0.046 -0.455 0.169 -0.129 -0.074 -0.933 -0.229
Al 2O 3 -0.004 0.001 -0.329 0.016 -0.129 -0.069 -0.932 -0.215
Fe 2O 3 -0.001 -0.006 -0.296 -0.282 -0.111 -0.028 -0.798 -0.087
MnO -0.000 -0.000 -0.252 -0.039 -0.090 -0.011 -0.647 -0.034
CaO 0.020 -0.025 0.464 -0.113 0.132 0.073 0.955 0.225
MgO -0.003 -0.007 -0.393 -0.226 -0.024 0.025 -0.175 0.078
Na 2O -0.001 0.004 -0.428 0.236 -0.119 -0.071 -0.856 -0.220
K 2O -0.001 0.005 -0.320 0.267 -0.117 -0.084 -0.845 -0.260
TiO 2 -0.000 -0.000 -0.152 -0.097 -0.088 -0.026 -0.633 -0.079