\\
                      w_{ij | X_N \in q_i, X_1 \in q_j} & \cdots & w_{ij | X_N \in q_i, X_N \in q_j}
                     \end{pmatrix}
                     }}}$$

This transformation of the time series is non reversible, meaning that there is a substantial information loss. In particular, the discretization of the time series plays a crucial role in the amount of information kept or lost by the transformation. A large number of bins might lead to sparsity in the image, while small numbers of bins might lead to substantial information loss [@wang2015encoding].

**Proposed modification:** In the original formulation of the MTF, [@wang2015encoding] proposed to partition the range of values into a number of equi-sized segments. Since in many datasets, the distribution of values tends to follow long tailed distributions, choosing the optimal number and width of bins becomes a challenging step requiring manual tuning. A large bin width would aggregate most values into the bins the closest to the mean, while a small bin width would lead to sparsity in the extreme bins.

To overcome this high dependency on the optimal parameter setting, we propose to extend the original formulation of the bin choice and assignments and to use instead the Symbolic Aggregate approXimation (SAX) algorithm 