Fuzzy entropy and similarity based feature selection method

In data analytics and machine learning it is common on the era of big data that there
is a wealth of information present as available features for real world problems. However
not all the feature are relevant for the problem at hand and because of it feature selection
where purpose is to find the most important features for the problem is often used.
Aim of the feature selection is to find most important features for the analysis task at hand 
(e.g. statistical classification or regression analysis).
Fuzzy entropy and similarity based feature selection method was created in 2011. It is a feature selection method for selecting most important features in any classification problems. Basic idea in short is to use training data to create ideal vectors for each class and then compute similarities of the samples and ideal vectors. Once this has been done next step is to use similarity values to calculate fuzzy entropy values for each feature. Lower entropy values indicate structureness while higher entropy values indicate randomness and hence lower importance. Algorithm in short goes as follows.
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where xd denotes data samples feature "d" and we restrict the mean calculation to only those samples that belong to class "i".
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where the similarity for feature "d" of a sample "xj" with ideal vector "vi" of class "i" is summed over all samples (j=1...,n) and classes (i=1...,N)
For fuzzy entropy "H" commonly used fuzzy entropy measure is De luca & Termini's fuzzy entropy measure 
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where now elements formula_9 membership degree formula_10 to fuzzy set is simply replaced by similarity degree formula_3. 
Also other fuzzy entropy measures can be used e.g. Parkash et al. fuzzy entropy. There fuzzy entropy is calculated as formula_12
Scaling factor to FES was later suggested in. There scaling factor is calculated as
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Purpose there in short is that if the feature in a class takes on average largely different values than in other classes, then this leads to smaller entropy values. Scaled entropy (SE) value is then calculated as
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FES has been implemented in matlab, python and R.
References.
 