Complete trajectory reconstruction from sparse mobile phone data

Chen, Guangshuo; Viana, Aline Carneiro; Fiore, Marco; Sarraute, Carlos

doi:10.1140/epjds/s13688-019-0206-8

EPJ Data Science

Table 2 Empirical fittings of the completeness of trajectories. Fitting quality of six standard long-tailed distributions to the empirical PDF of trajectory completeness, in terms of \(R^{2}\) and \(D_{\mathrm{KS}}\). Rows refer to different combinations of observation period \(\mathcal{T}\) and time resolution τ. Best-fit \(R^{2}\) and \(D_{\mathrm{KS}}\) are highlighted in bold

From: Complete trajectory reconstruction from sparse mobile phone data

Duration \(\mathcal{T}\)	Resolution τ	Weibull		Lognormal		Gamma		Pareto		Levy		Power law
Duration \(\mathcal{T}\)	Resolution τ	\(D_{\mathrm{KS}}\)	\(R^{2}\)	\(D_{\mathrm{KS}}\)	\(R^{2}\)	\(D_{\mathrm{KS}}\)	\(R^{2}\)	\(D_{\mathrm{KS}}\)	\(R^{2}\)	\(D_{\mathrm{KS}}\)	\(R^{2}\)	\(D_{\mathrm{KS}}\)	\(R^{2}\)
7 d	15 min	0.0334	0.9990	0.0318	0.9973	0.3710	0.4679	0.0495	0.9969	0.2509	0.8046	0.3538	0.5031
	30 min	0.0302	0.9993	0.0345	0.9967	0.0548	0.9962	0.1716	0.8973	0.2649	0.7848	0.3587	0.4894
	60 min	0.0278	0.9990	0.0372	0.9958	0.0475	0.9977	0.1198	0.9516	0.2888	0.7506	0.4162	0.2041
	120 min	0.0375	0.9972	0.0443	0.9938	0.0629	0.9853	0.1043	0.9768	0.3238	0.6977	0.2456	0.7450
15 d	15 min	0.0264	0.9986	0.0233	0.9984	0.3594	0.5007	0.0627	0.9893	0.2620	0.7853	0.3949	0.4120
	30 min	0.0208	0.9995	0.0264	0.9980	0.0271	0.9991	0.0724	0.9851	0.2765	0.7647	0.3576	0.4975
	60 min	0.0188	0.9997	0.0279	0.9974	0.0257	0.9987	0.0935	0.9719	0.2997	0.7315	0.3176	0.6076
	120 min	0.0254	0.9987	0.0332	0.9961	0.0913	0.9572	0.1880	0.8780	0.3349	0.6792	0.2721	0.7116
30 d	15 min	0.0239	0.9985	0.0207	0.9985	0.3514	0.5261	0.0700	0.9835	0.2619	0.7872	0.3829	0.4365
	30 min	0.0205	0.9992	0.0216	0.9983	0.0203	0.9991	0.1528	0.8976	0.2763	0.7661	0.3912	0.4149
	60 min	0.0149	0.9996	0.0263	0.9975	0.0289	0.9982	0.0895	0.9702	0.3003	0.7346	0.3131	0.6212
	120 min	0.0239	0.9984	0.0315	0.9962	0.0995	0.9479	0.1069	0.9538	0.3337	0.6893	0.3154	0.6176
60 d	15 min	0.0266	0.9980	0.0239	0.9977	0.1990	0.8284	0.0458	0.9934	0.2527	0.8076	0.3850	0.4156
	30 min	0.0233	0.9985	0.0234	0.9976	0.0286	0.9974	0.1944	0.8669	0.2649	0.7903	0.3897	0.4212
	60 min	0.0207	0.9985	0.0264	0.9970	0.0310	0.9980	0.0772	0.9769	0.2883	0.7622	0.3451	0.5635
	120 min	0.0245	0.9975	0.0316	0.9958	0.0754	0.9750	0.0946	0.9617	0.3209	0.7196	0.3491	0.5070
90 d	15 min	0.0298	0.9954	0.0329	0.9954	0.3619	0.5248	0.0322	0.9954	0.2371	0.8390	0.3866	0.4528
	30 min	0.0336	0.9958	0.0335	0.9950	0.0583	0.9864	0.0398	0.9942	0.2487	0.8264	0.3819	0.4774
	60 min	0.0305	0.9960	0.0355	0.9944	0.0454	0.9913	0.0611	0.9843	0.2705	0.8020	0.3231	0.6123
	120 min	0.0369	0.9940	0.0379	0.9932	0.0486	0.9927	0.0760	0.9743	0.2998	0.7687	0.3359	0.5885

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