## 1 Introduction
[15] derived some methods for phytoplankton identification based on neural networks, but again, they do not provide a fully-automatic method. [PERSON] et al. [16] have proposed a hybrid optical-digital method for the identification of five different species of phytoplankton through the use of operators invariant to translation rotation and scale. [PERSON] and [PERSON] 2003 [19], used form descriptors by Legendre polynomials and principal component analysis in the identification of the _Cymbella cistula_ species. An important attempt to automate diatom classification was conducted for the ADIAC project (Automatic Diatom Identification And Classification) [18; 20]. Several accuracy results were reported with a database composed of different numbers of diatom taxa ranging from 37-55 classes. In ADIAC, 171 features were used for diatom classification. These features are intended to describe the diatom symmetry, shape, geometry and texture by means of different descriptors, such as: rectangularity, circularity, compactness, shape of poles, length, width, length-width ratio, size, stria density orientation, horizontal frequency, Gray-Level Co-occurrence Matrix (GLCM), moment invariants, Gabor wavelets, Fourier and Scale-invariant Feature Transform (SIFT) descriptors. The classifiers that perform better are bagging of decision trees and random forest of predictive clustering trees, all of them evaluated with 10-fold cross-validation (10 fcv). The best results, up to 97.97% accuracy, were obtained with 38 classes using Fourier and SIFT descriptors with random forest. Performance decreased down to 96.17% when classifying 55 classes with the same descriptors and classifier [21]. New techniques based on Convolutional Neural Networks (CNN) have also been explored to classify sea plankton ([PERSON] 2015 [22], and [PERSON] et al., 2016 [23]). Note, however, that these images are different than those studied in this paper since this type of plankton varies from phytoplankton (diatoms). In [22], a database of 30,000 images belonging to 121 classes was used. The results were poor with a maximum performance of 73.90%. In [23], a database of 30,000 images belonging to 33 classes was used. They obtained an accuracy up to 96.3%. The other work related to CNN applied to diatoms is the one published by the authors (see the next paper companion [24]). The work presented here and the methodology have been compared to the CNN approach [24]. Thus, most of the efforts are still carried out with handcrafted approaches or \"hand-designed\" methods where a set of fixed features is used. That is, the methods rely on expert knowledge to extract the most relevant features versus CNN approaches that learn features from data. However, still,the handcrafted methods present limited results as in [25], where 14 classes were classified with Support Vector Machine (SVM) 10 fcv, using 44 GLCM features that describe only geometric and morphological properties. They obtained an accuracy of 94.7%. Therefore, the automated classification of diatoms (in terms of pattern recognition) or taxon identification remains a challenge. At present, there is no system capable of taking into account variations in both the contour and the texture in a relatively large number of species. One of the reasons is the difficulty in acquiring a big dataset of tagged data with a sufficient number of samples per species. The classification of diatoms is tedious and laborious, even for an expert diatomist. In this paper, we present a complete study of relevant features to describe and classify diatoms. The main purpose is to define the most discriminant features and to make a comparison of classifiers based on these features versus the CNN approach. For that, we collected an important database of 80 diatom taxa with 300 samples per taxon described in Section 2. The database was composed of an average of 100 distinct diatoms per class and augmented by means of computational simulations up to 300 samples per class.