## 2 Materials and Methods
### Classification Using Artificial Neural Networks  
A multi-layer perceptron neural network (MLPNN) was used for the analysis. The MLPNN is a neural network for performing varied detection and classification tasks. MLPNN has features such as the ability to learn and generalize, a smaller training data requirement, fast operation, and easy implementation. For these reasons, it is one of the neural network models most widely used [25]. It organizes the processing units, neurons, in layers with feedforward connections only between consecutive layers. Therefore, the general scheme includes an input layer, zero or more hidden layers, and an output layer (see Figure 1). The MLPNN training process was performed using a back-propagation technique in a supervised learning scheme. For the neural transfer functions,a hyperbolic tangent sigmoid function for the hidden layers and a normalized exponential function for the output layer were used. The following approach was applied for the optimization of the MLPNN performance:  
* **Data partition. ** Data partitioning can be used to determine the accuracy of a model's estimates of new data. For this work, we chose a 10-fold repeated cross-validation method. This subtype of cross-validation method randomly breaks the dataset into 10 subsets, which are sequentially used as test sets, while the other nine are used for training. This cross-validation method was repeated 50 times to obtain the information necessary to perform a statistically significant evaluation. * **Architecture selection. ** The number of neurons, layers, and their connections determine the architecture of an ANN. There is no general rule in choosing the best architecture, and optimization is based on testing several architectures until finding one that might offer satisfactory results [25]. Several architectures of the ANN with one and two hidden layers were tested to choose the best one. We evaluated architectures of 3, 8, 12, and 15 neurons for one-layer examples and architectures of {5 3}, {8 5}, {10 8}, and {12 10} neurons for two-layer examples. The optimization algorithm used to train these ANNs is a variation of the gradient descent known as scaled conjugate gradient backpropagation [38]. The results were compared using an analysis of variance (ANOVA) and [PERSON]'s honest significance test [39], and a \(p\)-value of \(<\)0.01 was used to determine whether there were statistically significant differences between the proposed architectures. * **Cut-off value selection. ** For a given cut-off value or decision threshold, each patient was classified in one of the diagnostic groups by comparing the measurement to this cut-off value. Choosing an appropriate decision threshold is of paramount importance in using a test effectively. There are various methods to determine the optimal test cut-off value, mostly based on a receiver operating characteristic (ROC) analysis. The ROC curve offers a graphical illustration of the true positive rate (sensitivity) against the false positive rate (1-specificity) for all possible cut-off values. Thus, each point on an ROC curve corresponds to a cut-off value and is associated with a test sensitivity and specificity. Sensitivity is the number of correctly detected positive patterns/total number of actual positive patterns. A positive pattern in this context indicates an MCI patient with depression. On the other hand, specificity is the number of correctly detected negative patterns/total number of actual negative patterns. A negative pattern in this context indicates an MCI patient without depression. Locating the best cut-off point requires a compromise between both measures. One of the most common criteria, and the one chosen in this work, is the point on an ROC curve with the best trade-off between specificity and sensitivity, trying to maximize both indices. * **Performance analysis. *
* The following statistical parameters were computed to evaluate the MLPNN classification performance:
* Number of correctly classified patterns/total number of patterns.