## 2 Processing of HS-SPME-GC-MS Data on Wine Volatiles by Multivariate Statistics
### Artificial Neural Networks  
A further family of techniques for the statistical analysis of multivariate data are the Artificial Neural Networks (ANNs). ANNs are one of the most flexible and performing techniques within the Machine Learning (ML) paradigm. The name of this type of techniques derives from the structure of the algorithm itself, which was originally designed to imitate the learning and operational model of neurons within the brain. ANNs consist of a complex structure of interconnected units that are called artificial neurons. The most widespread neural network models considered in the framework of wine data analysis are the feed-forward ANNs. In this case, single neurons are organized and structured in different layers: an input layer, one or more hidden layers, and an output layer. Typically, each neuron of each intermediate layer is connected with each neuron of the previous layer and each neuron of the next layer. This kind of ANN is called a fully connected network. The individual neurons of each layer operate in parallel and in a very simple way through a function, called transfer function, which the neuron applies to a linear combination of the outputs from the neurons of the previous layer. The weights of the linear combinations determine the functioning of the network itself and are the free parameters that are optimized during the training phase. For neurons belonging to the hidden layers, the transfer function is generally non-linear, typically a sigmoidal function. This type of transfer function allows the network to \"learn\" highly non-linear relationships between the independent input variables and the dependent output variables and even the use of a mix of continuous and categorical independent/input variables. Conversely, the transfer function of the output layer is chosen according to the type of output desired. The dependent/output variables can be continuous (in this case the network can be trained to perform a regression) or categorical (in this case the network can be trained to perform a classification). The design of an ANN depends on several parameters, called hyper-parameters, which must be carefully chosen. Among these, the main ones are the various transfer functions in the different layers, the number of hidden layers and the number of neurons that constitute them and various parameters linked to the specific optimization algorithm used. Generally, the regression or pattern recognition models constituted by neural networks have a high number of free parameters to optimize. This aspect necessarily requires a number of available samples greater than the number of independent variables used. To avoid overfitting phenomena, it is also necessary to carry out an accurate model validation. This validation can be carried out directly during the training phase by imposing an early stop when performance on a validation dataset tends to deteriorate. Over the last 20 years, ANNs have found application in the wine studies for various purposes, including authenticity and traceability assessment [38; 77; 78], discrimination between treatments [79], and wines [80]. As regards the use of VOCs' data as an input for training the networks, 35 volatile compounds were used by [PERSON] et al. [35] as input to a Self-Organizing Map to obtain clusters related to wines' varietal origin and vintage. [PERSON] and co-workers [81] demonstrated the possibility to use them for the classification of white varietal wines. In particular, they employed ANNs to classify Slovak white wines of different variety, year of production and from different producers by using, as independent variables, volatile species analyzed by the GC-MS technique. [PERSON] et al. [68] employed MultiLayer Perceptrons Neural Networks (MLP-NN), together with PCA and LDA, as chemometrics tools to differentiate Spanish white wines according to their geographical origin.