# Automatic Classification of Morphologically Similar Fish Species Using Their Head Contours
## 3 Results
### Features Based on the Dct and the Dft. a Comparative Study
#### 3.1.2 LOO-CV Tests  
The following tests are intended to determine both the size of the network and the optimal number of characteristics that achieve the best classification rate. The tests that were carried out using features coming from the DFT were then repeated; however, this time using features coming from the DCT, and their results are summarized in Figures 9 and 10. In all these tests, LOO-CV was used to obtain realistic results, and the experiments were repeated 100 times in order to show existing tendencies. Mean values of accuracy, the quotient between the number of correct predictions divided by the number of the predictions done, are represented by color balls and their corresponding standard deviations are shown by vertical lines. The SLFN weights, \(\mathbf{W}\) and \(\mathbf{b}\), were randomly selected according to a zero-mean Gaussian distribution with a standard deviation of one, where \(H\) indicates the number of hidden nodes and \(L\) the number of input features. In Figures 9 and 10, \(N\) number of transformed coefficients were used. In these figures, note that in the case of the DCT, the number of features (N) is the same as the number of coefficients (L), but in the DFT, \(L=2N-1\) instead. Figures 9 and 10 share the same structure. In both, the Figures 9a,b and 10a,b show the results of the binary classification problem and Figures 9c,d and 10c,d portray the results of the multi-class classification problem. When it comes to the binary problem, the optimal number of DFT-based features is \(L=5\), quite independently of the size of the network (see Figure 9a). The best accuracy values were obtained for \(H\) values of around 10 (see Figure 9b). The best results achieved using the DCT-based features were also obtained for when \(L=5\) independently of the size of the network (see Figure 10a). In the same way, the best accuracy results were obtained when \(H=10\) (see Figure 10b). In both cases, the best average value for the accuracy was around 0.9 (90%). To obtain the first five features, the first three and five DFT and DCT coefficients were required, respectively. The two encoding alternatives behave in a very similar way, and to decide which one is the best one, the tests need to be refined. Regarding the multi-class classification problem, when using DFT-based features, the best results were attained when \(L=5\). In this context, the optimum network size increases to values of about \(H=30\) (see Figure 9c). Above \(H=30\), there is a wide range of \(H\) values for which networks work properly (see Figure 9d). When the DCT is used in this context, the results are very similar, and so from \(L=5\) (see Figure 10c) and from \(H=30\) (see Figure 10d) there is a wide range of values of \(L\) and \(H\) for which the networks work correctly. In both cases, independently of the use of DFT/DCT, the average accuracy values are also similar and in the better configurations appear to be slightly above 80%. From the previous graphs, it is difficult to determine which coding (DFT/DCT) provides the best accuracy, since they behave in a very similar way. In the tests performed below, the number of  
Figure 9: The accuracy obtained by training a single-hidden layer feed-forward neural (SLFN) with the DFT-based features. Leave-one-out cross-validation (LOO-CV). iterations is incremented to 1000 for a small range of values of \(H\) and \(L\) near the optimal point of network operation. LOO-CV is always performed. The results are presented in tables indicating the accuracy regarding the average value, standard deviation, and both the maximum and minimum values obtained. The optimal values are represented in bold. We found that the optimum number of features was 5, independently of which transform (DCT or DFT) was used. Using more than five features reduces the performance of the networks. The only case that differs from the others in the sense of optimal number of features used is that of the binary classification case if the DFT is used, where the best accuracy scores were obtained with three features.