Impact of Parameters Sample Clauses

Impact of Parameters. ‌ Since the performance may vary for different trajectories, we chose 100 trajec- tories from 100 users, each of which has 500 timestamps, to evaluate the overall performance and the impact of parameters. The default values are ϵ = 1 and δ = 0.01 if not mentioned. The average performances for both datasets are reported in Figures 3.5 (on GeoLife data with popular M), Figure 3.6 (on Ge- oLife data with personal M) and Figure 3.7 (on Gowalla data with popular Size of ∆X vs. s. In Figures 3.5a and 3.6a (Geolife data), size of ∆X shrinks with larger ϵ because the inference result is enhanced by big ϵ. On the other hand, impact of ϵ would be negligible in Gowalla data because one- step transition in Markov model has limited predictability (check-ins are not frequent), as in Figure 3.7a. Size of ∆X vs. δ. Size of ∆X is mainly determined by δ as shown in Figures 3.5d, 3.6d and 3.7d. Note that LM and PIM have similar size of ∆X, meaning the true location is hidden in the similar size of candidates. When δ grows, size of ∆X reduces dramatically because more improbable locations are truncated. However, δ cannot be too large because it preserves nearly no privacy if size of ∆X is close to 1. Thus we use δ = 0.01 by default, which guarantees the sizes of ∆X are larger than 4 in the three settings. Drift Ratio vs. s. Figures 3.5b and 3.7b show that drift ratio declines with larger ϵ, which is easy to understand because larger ϵ provides more accurate release. However, the impact of ϵ is not obvious in Figure 3.6b. The reason is that the size of ∆X is already small as in Figure 3.6d, hence the increase of ϵ does not help much in improving the accuracy of the inference. Drift Ratio vs. δ. Figures 3.5e, 3.6e and 3.7e show that drift ratio rises when δ increases due to reduced ∆X, and PIM is slightly better than LM. However, due to the phenomenon of “lagged catch-up”, we will see next that the accuracy of the released locations was still improved with increasing δ.