Quartz Technology Ltd

Home Feedback Contents Search Databank Support

PCA results

 

Home
Up

 

Results of Principal Component Analysis

Implementation of PCA is summarised in steps 1-8 (Manly, 1991).

1.   Input scaled fractional data shown here 

 

Sensor

1

x1

x2

x3

x4

x5

x6

Sample        ¯

 

 

 

 

 

 

65

 

 

 

 

 

 

 

2.  Standardisation of input data

The input data was autoscaled so that each variable (sensor) is mean centred with a standard deviation (s) of one.  The autoscaled element x¢ij of each sensor i for organic vapour j is calculated according to the equation

                                  x¢ij = (xij -`xi )/ sI

 

3.  Calculation of correlation matrix

Sensor

1

2

3

4

5

6

1

1.00000

0.11102

-0.71754

-0.80115

-0.16102

0.05899

2

 

1.00000

-0.53813

-0.19589

-0.71866

-0.54553

3

 

 

1.00000

0.43053

0.17779

-0.12292

4

 

 

 

1.00000

0.17951

0.01731

5

 

 

 

 

1.00000

0.9419

6

 

 

 

 

 

1.00000

 

The calculated correlation matrix shown above suggested the sensors were not highly correlated.

4.  Calculation of eigenvalues

Eigenvalue

1

2

3

4

5

6

 

 

 

% variance

 

2.8191

 

47.0

 

2.0787

 

34.6

 

0.7915

 

13.2

 

0.2996

 

5.0

 

0.0112

 

0.2

 

0.000

 

0.0

The first and second principal components accounts for 81.6% of the variance which suggests these are the most important of the six.  However, the third principal component represents 13.2% of the variation in the measurements therefore should not be ignored.

5.  Calculation of eigenvectors

Principal Component Number

Eigenvectors

 

Thiophenol

OV17

Ethylcellulose

OV225

C20M

FFAP

1

0.374

0.473

-0.395

-0.359

-0.477

-0.353

2

0.488

-0.216

-0.370

-0.397

0.393

0.515

3

-0.253

0.498

-0.563

0.500

0.152

0.314

 

The eigenvectors, more commonly referred to as the loadings, provide the coefficients of the principal components and in this case give an indication of the contribution of a particular sensor to the classification process.

6.   Calculation of Scores

The scores for the individual samples are calculated using the equations:

                    Z1 = 0.374x1 +0.473x2 -0.395x3 -0.359x4 -0.477x5 -0.353x6

                    Z2 = 0.488x1 -0.216x2 -0.370x3-0.397x4 +0.393x5 +0.515x6

                    Z3 = -0.253x1 +0.498x2 -0.563x + 0.500x4 + 0.152x + 0.314x6

7.  Plot Scores

The corresponding scores, Z1 versus Z2 and Z1 versus Z3 for each sample were plotted in 2-dimensional space to complete the PCA.

Figure 1.7  Plot of the first and second principal component of data for 50 second scaled fractional response of the x1   - x6  sensor quartz crystal array to (D) hexane, (ÿ) propan-2-ol, (ÿ) triethylamine, (O) acetone, (ÿ) chloroform, (´) diethylether, (D) toluene, (s)  propan-1-ol, (D)  2-butanone, (O)  ethanol, (´) acetonitrile, (´)  methanol, (O) n-butylacetate

 

 

[ Home ] [ Up ]

Send mail to webmaster@quartztec.com with questions or comments about this web site.
Copyright © 1998-2005 Quartz Technology Limited
Last modified: June 03, 2000