a discretization of the time series based on $Q+1$ bin edges, that is, $Q$ bins $q_i$, the transitions are computed over every two consecutive points in the training set as $$\forall (i,j)\in \llbracket 1,Q+1\rrbracket,\quad \widehat{w}_{ij} = \text{number of transitions } q_i \rightarrow q_j$$ $$\forall (i,j)\in \llbracket 1,Q+1\rrbracket,\quad w_{ij} = \frac{\widehat{w}_{ij}}{\sum_j \widehat{w}_{ij}}$$ $W =(w_{ij})$ is the Markov Transition matrix, which at this stage does not capture any temporal relations. The final $N\times N$ matrix, called Markov Transition Field, is computed as follows: $${    \setlength{\eqhsize}{\minof{\widthof{\mbox{\ensuremath{               MTF =   \begin{pmatrix}
                      w_{ij | X_1 \in q_i, X_1 \in q_j}  & \cdots & w_{ij | X_1 \in q_i, X_N \in q_j}\\
                      w_{ij | X_2 \in q_i, X_1 \in q_j} & \cdots & w_{ij | X_2 \in q_i, X_N \in q_j} \\
                      \vdots  & \ddots & \vdots  \\
                      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}
                     }}}}{\linewidth}}
    \resizebox{\eqhsize}{!}{\ensuremath{               MTF =   \begin{pmatrix}
                      w_{ij | X_1 \in q_i, X_1 \in q_j}  & \cdots & w_{ij | X_1 \in q_i, X_N \in q_j}\\
                      w_{ij | X_2 \in q_i, X_1 \in q_j} & \cdots & w_{ij | X_2 \in q_i, X_N \in q_j} \\
                      \vdots  & \ddots & \vdots  