Fisher ratio

Because of the correlation between variables, univariate methods can select some variables that give the same information. The decorrelation method, used in the program SELECT of the software package ARTHUR, selects the first variable according to Fisher ratio, then this variable (let it be xp is subtracted from the remaining variables ... 

Instead of the imivariate Fisher ratio, SLDA considers the ratio between the generalized within-category dispersion (the determinant of the pooled within-category covariance matrix) and total dispersion (the determinant of the generalized covariance matrix). This ratio is called Wilks lambda, and the smaller it is, the better the separation between categories. The selected variable is that that produces the maximum decrease of Wilks lambda, tested by a suitable F statistic for the input of a new variable or for the deletion of a previously selected one. 

Figure 6 Refolded Fisher ratios are visualized in the left pane (summed over all m/z of interest). Locations identified in the Fisher ratios indicating features of interest can be analyzed in the full dataset, in the right pane, using PARAFAC or other methods.

The Fisher ratio F. of feature i for a binary classification problem is given by equation (99) C376, 4163. 

Fisher ratios have a great dynamic range variing from zero if the classes have the same mean to some large value for well separated classes. 

Instead of the Fisher ratio an easier to calculate weight was proposed by Coomans et.al. C553 (equation (100)). 

A maximum number of 102 features were selected by use of the Fisher ratios. The authors emphazised that an averaged predictive ability of 76 % which was found with 2000 unknowns is a level which should be of substantial help in spectral interpretations when combined with additional information. 

Another method of variable selection for use in classification problems involves use of the Fisher ratio, whereby a value is calculated for each variable according to the following formulae. 

When deaUng with binary classification problems using a single descriptor, Fisher ratios (FR) can be used to select the best predictor [60,315,324]. Such ratios are defined as... 

Further, the descriptors exhibiting highest Fisher ratios... 

The following step consists in the computation of the Fisher ratio, Fcaic., i.e., the ratio between MSEC and MSE. 

Finally, the p-value, p-v., is computed as a fimction of Fcaic., ssbc and yssE, considering the Fisher distribution of the Fisher ratio. This outcome leads to the F-test, where the p-v. is compared to a significance level a. The final response is that the factor has a significant impact on the output, if p-v.< a. Otherwise, it is concluded that the output is not significantly affected by the factor. The level a is usually assumed as 5%, as suggested in many References, such as [22],... 

In classification problems the features with highest discrimination power are selected. An often applied criterion is the Fisher ratio which is defined for a binary classification problem by equation (12) as... 

Observe the unprecedented improvement in the statistical parameters of the cleansed regression based on 10 benzenoids. The standard error is about 10 times smaller than when all 14 benzenoids are used in a regression, and the Fisher ratio has increased by a factor of 15. The numerical values for the parameters Ri, Rz, and Rs changed somewhat when various outliers were disregarded, but these changes remained relatively small. In all cases, the relative magnitudes of Ri, Rz, and Rz are approxi-... 

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