Metric | Range | Parameters fixed ad hoc and Assumptions |
---|---|---|
\(Prox = K_{\delta }^{+}/T\) | [0, 1] | i) δ: distance threshold, ii) K : kernel |
\(Cs = \frac { D_{chance} - \left (\sum _{t=1}^{T} d_{t}^{A,B} \right)/T}{D_{chance} + \left (\sum _{t=1}^{T} d_{t}^{A,B} \right)/T} \) | ]−1,1] | Dchance definition |
\(HAI = \frac {K_{\delta }^{+}}{K_{\delta }^{+} + (n_{A0} + n_{0B})/2}\) | [0,1] | i) Reference area, ii) δ: distance threshold |
\(L_{ixn}T = \text {logistic}\left (\ln {\left (\frac {n_{AB}/p_{AB} + n_{00}/p_{00}}{n_{A0}/p_{A0} + n_{0B}/p_{0B} }\right)}\right)\) | [0, 1] | Reference area; |
\(jPPA = \frac {S\left \{ \bigcup \limits _{t=1}^{T-1} \left (E_{\phi ^{A}}\left (X_{t}^{A},X_{t+1}^{A}\right) \cap E_{\phi ^{B}}\left (X_{t}^{B},X_{t+1}^{B}\right) \right) \right \}}{S\left \{ \bigcup \limits _{t=1}^{T-1} \left (E_{\phi ^{A}}\left (X_{t}^{A},X_{t+1}^{A}\right) \cup E_{\phi ^{B}}\left (X_{t}^{B},X_{t+1}^{B}\right) \right) \right \}}\) | [0, 1] | i) Every zone within ellipse has same odd of being transited, ii) Ï•: maximum velocity |
\(CSEM = \frac {\max \left \{m; N_{m} >0\right \} }{T-1}\) | [0, 1] | distance threshold |
\(r_{V} = \frac {\sum _{t=1}^{T}\left (V^{A}_{t} - \bar {V}^{A}\right)\left (V^{B}_{t} - \bar {V}^{B}\right)}{\sqrt {\sum _{t=1}^{T}\left (V^{A}_{t} - \bar {V}^{A}\right)^{2}}\sqrt {\sum _{t=1}^{T}\left (V^{B}_{t} - \bar {V}^{B}\right)^{2}}}\) | [-1, 1] | Â |
\(DI_{d} = \left (\sum _{t=1}^{T-1} \left [1 - \left (\frac {\mid d_{t,t+1}^{A}-d_{t,t+1}^{B}\mid }{d_{t,t+1}^{A}+d_{t,t+1}^{B}}\right)^{\beta }\right ]\right)/(T-1)\) | [0, 1] | β: scaling parameter |
\(DI_{\theta } = \left (\sum _{t=1}^{T-1} \cos \left (\theta _{t,t+1}^{A} - \theta _{t,t+1}^{B}\right)\right)/(T-1)\) | [-1, 1] | Â |
\(DI = \frac {\sum _{t=1}^{T-1} \cos (\theta _{t,t+1}^{A} - \theta _{t,t+1}^{B})\left [1 - \left (\frac {\mid d_{t,t+1}^{A}-d_{t,t+1}^{B}\mid }{d_{t,t+1}^{A}+d_{t,t+1}^{B}}\right)^{\beta }\right ]}{T-1}\) | [-1, 1] | Â |
 |  | β: scaling parameter |