## 2 Materials and Methods
### Method
#### 2.3.2 Image Classification and Accuracy Assessment  
Two supervised classification methods were used for image classification: support vector machine (SVM) and neural network (NN). SVM is a supervised classification method derived from statistical learning theory that often yields good classification results from complex and noisy data [30; 31; 32]. It separates the classes with a decision surface that maximizes the margin between the classes. The surface is often called the optimal hyperplane, and the data points closest to the hyperplane are called support vectors. The support vectors are the critical elements of the training set. SVM can be adapted using nonlinear kernels to become a nonlinear classifier. While SVM is a binary classifier in its simplest form, it can function as a multiclass classifier by combining several binary SVM classifiers (creating a binary classifier for each possible pair of classes). SVM includes a penalty parameter that allows a certain degree of misclassification, which is particularly important for non-separable training sets. The penalty parameter controls the trade-off between allowing training errors and forcing rigid margins. It creates a soft margin that permits some misclassifications, such as it allows some training points on the wrong side of the hyperplane. Increasing the value of the penalty parameter increases the cost of misclassifying points and forces the creation of a more accurate model that may not generalize well. NN applies a layered feed-forward neural network classification technique. The NN technique uses standard backpropagation for supervised learning [33; 34]. You can select the number of hidden layers to use and can choose between a logistic or hyperbolic activation function. Learning occurs by adjusting the weights in the node to minimize the difference between the output node activation and the output. The error is back propagated through the network, and the weight is adjusted using a recursive method. NN classification can be used to perform non-linear classification. To evaluate the potential of integrating microwave data with optical data into the classification process, the following pairs of images were considered: (1) SPOT-5 30 April and Sentinel-1A 19 April and (2) SPOT-5 15 May and Sentinel-1A 13 May. For the first pair, the SPOT-5 image of 15 April would be more suitable; however, this image has an almost total cloud cover. Other possible pairs between SPOT-5 and Sentinel-1A images were not used because most of the crops were all in the senescence phase and because the northern part of the later images (6 June, 24 July and 17 August) was lacking. Four band combinations were tested to evaluate which combination produced the best results: (1) SPOT-5 bands; (2) SPOT-5 bands + Sentinel-1A VV band; (3) SPOT-5 bands + Sentinel-1A VH band; and (4) SPOT-5 bands + Sentinel-1A VV + VH bands. All of the multispectral bands of the SPOT-5 HRG2 sensor, e.g., B1 (green), B2 (red), B3 (NIR) and SWIR bands, were considered for classification. A crop mask was created for use during classification to reduce misclassifications among crops, surrounding natural/semi-natural vegetation, water and artificial areas. After selecting which band combination and classifier to use, images were added cumulatively to evaluate the improvement of the classification accuracies. Approximately 50% of the ground truth parcels identified in the field per crop were randomly chosen to train the classifiers, while the rest was used to validate the classification results (Table 4). For the classification, only 4 crop classes were considered: maize, soybean, pasture and bean. Four other crop classes (sunflower, millet, cabbage and potato) were excluded due to their limited number of ground truth parcels. A confusion matrix was used to compute the overall accuracy (_i.e._, the correctly-classified sample units) and the producer's and user's accuracies. The producer's and user's accuracies represent the accuracy of an individual category.