A Framework for Bus Trajectory Extraction and Missing Data Recovery for Data Sampled from the Internet

. 2017 Feb 10;17(2):342. doi: 10.3390/s17020342

Algorithm 1 F-FCM clustering algorithm.

Input:

G^{(m, l)}

;

Output:

U^{F - F C M}

(the partition matrix),

V^{F - F C M}

(the prototypes set),

J_{a}^{F - F C M}

(the objective function);

Process:

(a1) get $c_{0}$ by Equation (9);
(a2) set α and get c by Equation (10);
(a3) generate the clustering feature X by Equation (5);
(a4) initiate the prototypes set $V^{(0)}$ by Equation (11), get $U^{(0)}$ by Equation (4), get $J_{a}^{(0)} ≜ J_{a} (U^{(0)}, V^{(0)})$ with Equation (1);
(a5) set the maximum FCM iteration $K_{\max}$ , error tolerance δ and execute the following iterative loop:
for i← 1 to $K_{\max}$ do
get $V^{(i)}$ by $U^{(i - 1)}$ with Equation (3);
get $U^{(i)}$ by $V^{(i)}$ with Equation (4);
get $J_{a}^{(i)}$ by Equation (1);
if $| J_{a}^{(i)} - J_{a}^{(i - 1)} | < δ$ then
break;
end if
end for
(a6) set $U^{F - F C M} = U^{(i)}$ , $V^{F - F C M} = V^{(i)}$ , $J_{a}^{F - F C M} = J_{a}^{(i)}$ for the last iteration i in Step (a5).