## 5 Discriminant Analysis
### Sequential Forward Feature Selection  
In order to elucidate the most discriminant descriptors, a discriminant analysis was done by means of a Sequential Forward Feature Selection (SFFS), also known as the floating search method [39]. The algorithm selects a subset of features that best predict the objects to be classified. Thus, features are sequentially added to an empty candidate set until the addition of further features does not decrease the misclassification error rate (i.e., the number of misclassified observations divided by the number of observations) of a learning algorithm (quadratic discriminant analysis). Another variant of the method is Backward Selection (SBS), in which features are sequentially removed from a full candidate set until the removal of further features increases the misclassification error. This methodology gives a list of features ordered by discrimination capacity. In Table 5, such a list is shown for the first 100 most discriminant handcrafted features. The percentage of morphological descriptors is only 4%, although two of them are on the top. For the rest of descriptors, the percentages are as follows: statistical (28%); logGabor (40%) and LBP (30%). \begin{table}
\begin{tabular}{c l l l l l l l} \hline
1 & M & _Shape_ & 35 & LBP & _Cantras (d = 3, 0\({}^{\circ}\))_ & 69 & G1 & _Cantras (d = 1, 90\({}^{\circ}\))_ \\
2 & S & _Ist Quartile_ & 36 & G4 & _Correlation 1 (d = 1, 90\({}^{\circ}\))_ & 70 & S & \(\Sigma\)_Average (d = 1, 45\({}^{\circ}\))_ \\
3 & M & _Asymmetry_ & 37 & G4 & _Correlation 1 (d = 1, 135\({}^{\circ}\))_ & 71 & G4 & _Entropy_ \\
4 & S & _Cantras (d = 1, 45\({}^{\circ}\))_ & 38 & S & _Energy (d = 1, 0\({}^{\circ}\))_ & 72 & LBP & _Cluster Prominence (d = 1, 0\({}^{\circ}\))_ \\
5 & S & _Energy_ & 39 & S & _Correlation 1 (d = 3, 45\({}^{\circ}\))_ & 73 & G4 & _Cluster Shade (d = 1, 0\({}^{\circ}\))_ \\
6 & S & _Cantras (d = 1, 0\({}^{\circ}\))_ & 40 & S & _Homogeneity 1 (d = 1, 45\({}^{\circ}\))_ & 74 & LBP & _Correlation 1 (d = 3, 0\({}^{\circ}\))_ \\
7 & G4 & _Correlation 1 (d = 3, 90\({}^{\circ}\))_ & 41 & S & _Correlation 1 (d = 3, 90\({}^{\circ}\))_ & 75 & S & _Entropy_ \\
8 & S & _Interquartile Range_ & 42 & LBP & _AVariance (d = 1, 0\({}^{\circ}\))_ & 76 & G3 & \(\Delta\)_Entropy (d = 1, 45\({}^{\circ}\))_ \\
9 & G4 & _AEtrupy (d = 1, 90\({}^{\circ}\))_ & 43 & G & _Correlation 1 (d = 3, 0\({}^{\circ}\))_ & 77 & LBP & _Correlation 1 (d = 4, 45\({}^{\circ}\))_ \\
10 & LBP & _Ist Quartile_ & 44 & G2 & _Cantras (d = 1, 90\({}^{\circ}\))_ & 78 & LBP & _Cantras (d = 1, 90\({}^{\circ}\))_ \\
11 & LBP & _Correlation 1 (d = 3, 135\({}^{\circ}\))_ & 45 & LBP & _Correlation 1 (d = 3, 45\({}^{\circ}\))_ & 79 & G3 & _Energy (d = 1, 0\({}^{\circ}\))_ \\
12 & LBP & _Max. Probability (d = 1, 45\({}^{\circ}\))_ & 46 & LBP & _Correlation 1 (d = 3, 135\({}^{\circ}\))_ & 80 & G4 & _Correlation 1 (d = 5, 0\({}^{\circ}\))_ \\
13 & LBP & _Cantras (d = 3, 45\({}^{\circ}\))_ & 47 & LBP & _Max. Probability (d = 1, 0\({}^{\circ}\))_ & 81 & LBP & _Homogeneity 1 (d = 1, 135\({}^{\circ}\))_ \\
14 & S & _Variance_ & 48 & S & _Correlation 1 (d = 5, 90\({}^{\circ}\))_ & 82 & G4 & _Avariance (d = 1, 90\({}^{\circ}\))_ \\
15 & LBP & _Correlation 1 (d = 1, 45\({}^{\circ}\))_ & 49 & G4 & _Avariance (d = 1, 45\({}^{\circ}\))_ & 83 & LBP & _Max. Probability (d = 3, 135\({}^{\circ}\))_ \\
16 & S & _Kurtosis_ & 50 & S & _3 rd Quartile_ & 84 & G4 & _Entropy (d = 1, 0\({}^{\circ}\))_ \\
17 & LBP & _Autocorrelation (d = 3, 135\({}^{\circ}\))_ & 51 & S & _Correlation 1 (d = 5, 90\({}^{\circ}\))_ & 85 & G4 & _Correlation 1 (d = 1, 90\({}^{\circ}\))_ \\
18 & G4 & \(\Delta\)_Entropy (d = 3, 0\({}^{\circ}\))_ & 52 & S & _Dissimilarity (d = 5, 135\({}^{\circ}\))_ & 86 & G3 & \(\Delta\)_Variance (d = 1, 45\({}^{\circ}\))_ \\
19 & S & _Autocorrelation (d = 1, 0\({}^{\circ}\))_ & 53 & S & _Max.