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DFA results

 

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Results of LDFA of the example data set are shown in Table 1.2.  The success rate was found to be 98% using cross-validation (also known as leave-one-out) (Mertens et al. 1994).

 

 

Organic Vapour

 

hexane

propan-2-ol

triethyl-amine

acetone

chloro-form

diethyl-ether

Toluene

propan-1-ol

2-butanone

ethanol

acetonitrile

methanol

butyl-acetate

Hexane

5

0

0

0

0

0

0

0

0

0

0

0

0

propan-2-ol

0

5

0

0

0

0

0

0

0

0

0

0

0

Triethylamine

0

0

5

0

0

0

0

0

0

0

0

0

0

Acetone

0

0

0

5

0

0

0

0

0

0

0

0

0

Chloroform

0

0

0

0

5

0

0

0

0

0

0

0

0

Diethylether

0

0

0

0

0

4

0

0

0

0

0

0

0

Toluene

0

0

0

0

0

1

5

0

0

0

0

0

0

propan-1-ol

0

0

0

0

0

0

0

5

0

0

0

0

0

2-butanone

0

0

0

0

0

0

0

0

5

0

0

0

0

Ethanol

0

0

0

0

0

0

0

0

0

5

0

0

0

Acetonitrile

0

0

0

0

0

0

0

0

0

0

5

0

0

Methanol

0

0

0

0

0

0

0

0

0

0

0

5

0

Butylacetate

0

0

0

0

0

0

0

0

0

0

0

5

5

Total No.

5

5

5

5

5

5

5

5

5

5

5

5

5

No. correct

5

5

5

5

5

4

5

5

5

5

5

5

5

% correct

100

100

100

100

100

80

100

100

100

100

100

100

100

  Table 1.2:  Discriminant function analysis of sensor responses for organic vapours.

 

Results of eigenanalysis for class and corresponding percent variance are shown in Table 1.3.

Eigenvalue

1

2

3

4

5

 

 

% variance

451.030

 

53.1

287.283

 

33.8

89.875

 

10.6

17.220

 

2.0

4.465

 

0.5

Table 1.3:  Results of eigenanalysis for class (MANOVA) using responses from sensors x1   - x5 .

 

The first two canonical variates account for a high percentage of variation in the data.  The coefficients of the canonical variates are shown in Table 1.4.  The values suggest the remaining sensors are not highly correlated.

Canonical variate

Variable

 

Thiophenol

OV17

Ethylcellulose

OV225

C20M

1

-0.1628

-0.1551

-0.2355

-0.1145

-0.0372

2

0.0986

0.1030

0.0815

0.1835

0.0272

Table 1.4  Coefficients of the canonical variates.

 

Therefore, the equations generated through eigenanalysis for class (MANOVA) using responses from sensors x1   - x5    were:

Z1 = -0.1628x1 - 0.1551 x2 - 0.2355x3 - 0.1145 x4 - 0.0372 x5

Z2 = 0.0986x1 + 0.1030 x2 + 0.0815x3 + 0.1835 x4 + 0.0272 x5

A plot of Z1 versus Z2 is shown in Figure 1.8.

The location of the propan-1-ol, ethanol and methanol cluster suggests similarities in vapour/coating interaction mechanisms.  However, the propan-2-ol cluster was well separated from the main group of alcohols that may suggest other factors are also important, for example, the branched nature of this solute.

Figure 1  Application of MANOVA to responses from sensors x1   - x5  obtained at 50 seconds for (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.

 

 

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