is not reversible, meaning the GAF no longer allows for a unique reconstruction of the time series. This leads to some loss of information after the encoding has been applied. However, since there is often only moderate overlap in the inverse space, the input can be roughly approximated [@wang2015encoding].

**Proposed modification:** In our study, we propose to scale the training samples based on the full training dataset in order to keep the relationships and differences between the samples. Therefore, we propose to define $\mathrm{UB}$ and $\mathrm{LB}$ based on the training set distribution. If in the test set, a sample contains values exceeding these bounds, we propose to clip the values to the bound.

Markov Transition Field (MTF)
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The Markov Transisition Field [@wang2015encoding], consists of building the matrix of probabilities to observe the change of value between any pair of points in the time series. First, the time series is discretized. Then, the transitions $w$ from one bin to another are counted and normalised over every two consecutive data-points in the whole training set. Last, the MTF matrix contains for every pair of points in the time series the transition probability between the two bins the points belong to.

Assuming 