Table 1.

Table of statistical parameters defining classes in the synthetic data. The base multivariate time series follow a normal distribution where $A_n\sim N\left({\mathrm{\mu }}_0,{\sigma }_0\right)({\mathrm{\mu }}_0=0.5$ and ${\sigma }_0=0.1$). Each pair of $\mathrm{\mu }$ and s shown in the table represents one feature pattern. For example, the positive class in simulation A, the feature $k_{s_1}$ and $k_{s_1+1}\left(k_2\right.$ and $\left.k_3\right)$ follows the normal distribution with $\mathrm{\mu }={\mathrm{\mu }}_1$ and $\sigma ={\sigma }_0$ in selected five consecutive time points. All other features except $k_{s_1}$ and $k_{s_1+1}$ in entire T as well as $k_{s_1}$ and $k_{s_1+1}$ in time points except selected five consecutive time points follow the base distribution if no other parameters specified. For better visualized evaluation, the selected five consecutive time points (refer as time blocks below) starts at $\mathrm{T}=0$ for $A_0,\mathrm{T}=1$ for $A_1$, and so on. Such pattern applied to all the simulations except the second pattern of positive class in simulation F, which the second pattern starts in reverse order (start at $\mathrm{T}=\mathrm{T}-5$ for $A_0,\mathrm{T}=\mathrm{T}-6$ for $A_1$, and so on). All index used in the table is 0-indexing.

	Negative Class	Positive Class
S-A	-	${\mathrm{\mu }}_1=1,{\mathrm{s}}_1=2$
S-B	-	${\mathrm{\mu }}_2=0.2,{\mathrm{s}}_1=2$
S-C	-	$$\begin{gathered} {\mathrm{\mu }}_1=1,{\mathrm{s}}_1=2 \\ {\mathrm{\mu }}_{\mathrm{balance}}=0.4,{\mathrm{s}}_1=2 \end{gathered}$$
S-D	${\mathrm{\mu }}_2=0.2,{\mathrm{s}}_1=2$	${\mathrm{\mu }}_2=0.8,{\mathrm{s}}_2=8$
S-E	${\mathrm{\mu }}_1=1,{\mathrm{s}}_2=8$	${\mathrm{\mu }}_1=1,{\mathrm{s}}_1=2$
S-F	-	${\mathrm{\mu }}_1=1,{\mathrm{s}}_1=2$ ${\mathrm{\mu }}_1=1,{\mathrm{s}}_2=8$
Base Distribution: ${\mathrm{\mu }}_0=0.5,{\mathrm{\sigma }}_0=0.1$