## 3 Popular ANN Architectures Employed for Time Series Forecasting Purposes
### Self-Organizing Maps
#### 3.5.2 Application of Self-Organizing Maps to Time Series Forecasting  
If SOMs are mainly employed to solve unsupervised classification problems, how can they be applied to time series forecasting tasks, which in essence are, as we saw in Section 2.2, function approximation (regression) problems? A simple approach to the univariate time series case is as follows: as training examples for our SOM model, we can use vectors of the form \(\vec{x}=(y_{t+1},y_{t},y_{t-1},\ldots,y_{t-d+1})\), where the first component corresponds to the one-step-ahead target output in our basic FFNN model discussed in Section 3.1. The rest of the components in \(\vec{x}\) correspond to the autoregressive inputs also employed by our FFNN model. Thus, any single row in Table 1, which corresponds to a training example for FFNN models, also serves as a training example for SOM models. The computational layer in our SOM model for univariate time series consists of a one-dimensional lattice of neurons. When forecasting, our SOM model utilizes all of the components from input vector \(\vec{x}\), except for the first, in a competition process among all neurons in the computational layer, just as described in Section 3.5.1. The winning neuron \(I(\vec{x})\) determines our one-step-ahead forecast value \(\hat{y}_{t+1}\) by simply extracting the first component from weight vector \(\widehat{w}_{I(\vec{x})}\) associated to winning neuron \(I(\vec{x})\), i.e., \(\hat{y}_{t+1}=w_{I(\vec{x}),1}\). Thus, the number of neurons in the computational layer determines how many possible discrete values can assume our one-step-ahead forecast value \(\hat{y}_{t+1}\). One disadvantage to this simple approach is the large prediction error due to the step-like output of our SOM model trying to approximate a \"smooth\" time series. SOMs may require too many neurons if we want to reduce their associated prediction error. This alternative, however, would be accompanied by a prohibitively high computational cost. A more sensible solution to this problem would be using RBFNs in conjunction with SOMs: first, we train a univariate time series SOM model just as described above; then, the resulting SOM weights \(\{\widehat{w}_{j}\}\), which define mapping \(\Phi\), are used to directly build an RBFN with \(N\) Gaussian basis functions and one output unit SOM weights \(w_{j,1}\) would be used as RBFN hidden-to-output weights, while the remaining components in vector \(\widehat{w}_{j}\) would play the role of the RBF center for the \(j\)th hidden unit. No further RBFN training is required, although we still need to determine the \(\sigma_{j}\) parameters for each radial basis function in the network; refer to Section 3.2 for more details on RBFNs. Thus, a reduction in prediction error is achieved, at least in places where there are not extreme values in the time series. In these particular locations where extreme values occur, prediction errors are still high for both SOM and SOM-RBFN models. For more details, see [PERSON] (2018), where a comprehensive survey on SOMs applied to time series prediction can also be found. Relatively recent work on model refinements based on the classical SOM and applied to time series prediction can be found in [PERSON] (2018) and [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON] (2018). In Section 4.4, we summarize the work of [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], et al. (2018), where a double SOM model is proposed to generate long-term time series trend predictions.