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Table 1 Summary of notation

From: ABBA: adaptive Brownian bridge-based symbolic aggregation of time series

Original time series:\(T = [t_0, t_1, \ldots , t_N] \in \mathbb {R}^{N+1}\)
After compression:\([(\texttt {len}_1, \texttt {inc}_1), (\texttt {len}_2, \texttt {inc}_2), \ldots , (\texttt {len}_n, \texttt {inc}_n)] \in \mathbb {R}^{2 \times n}\)
After digitization:\(S=[s_1, s_2, \ldots , s_n] \in \mathbb {A}^n\) with \(\mathbb {A} = \{ a_1, a_2, \ldots , a_k \}\)
After inverse-digitization:\([(\widetilde{\texttt {len}}_1, \widetilde{\texttt {inc}}_1), (\widetilde{\texttt {len}}_2, \widetilde{\texttt {inc}}_2), \ldots , (\widetilde{\texttt {len}}_n, \widetilde{\texttt {inc}}_n)] \in \mathbb {R}^{2 \times n}\)
After quantization:\([(\widehat{\texttt {len}}_1, \widehat{\texttt {inc}}_1), (\widehat{\texttt {len}}_2, \widehat{\texttt {inc}}_2), \ldots , (\widehat{\texttt {len}}_n, \widehat{\texttt {inc}}_n)] \in \mathbb {R}^{2 \times n}\)
After inverse-compression:\(\widehat{T} = [\widehat{t}_0, \widehat{t}_1, \ldots , \widehat{t}_N] \in \mathbb {R}^{N+1}\)