Modified Datasets

The following figures show the performance of the proposed and baseline methods on the modified data sets we described earlier. As before, we first show the perfor- mance during the feature selection. Then, in the subsequent graphs, we increase the degree of each adjustment and compare the method’s resulting accuracy. The main purpose of these graphs is to demonstrate the robustness of the proposed method under unfavorable environmental circumstances.

Performance during feature selection

Figure 5.17 shows the progression of performance for location A while using the feature selection algorithm for both the unadjusted data set and the data sets af- ter adjustment 1 (50% of probes removed by decreasing frequency), adjustment 2 (50% of samples removed) and adjustment 3 (50% of probes removed probabilisti- cally). The figure shows that the proposed method performs better than the base- line method on each of the data sets, and that each of the adjustments decreases the performance slightly for both methods.

1 2 3 4 5 6 7 8 9 10 11 12 0 0.005 .1 00..152 0.25 0.3 0.35 0.4

Number of features added

Coefficient

of

determination

Baseline without adjustments Baseline after adjustment 1 Baseline after adjustment 2 Baseline after adjustment 3 Proposed without adjustments

Proposed after adjustment 1 Proposed after adjustment 2 Proposed after adjustment 3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 0.005 .1 00.15 .2 0.25 0.3 00.35 .4

Number of features added

Coefficient

of

determination

Baseline without adjustments Baseline after adjustment 1 Baseline after adjustment 2 Baseline after adjustment 3 Proposed without adjustments

Proposed after adjustment 1 Proposed after adjustment 2 Proposed after adjustment 3

Figure 5.18:Progression of performance for loca on B a er data set adjustments

Figures 5.18 and 5.19 show the same data, but for location B and C. For these loca- tions also, the proposed method performs better than the baseline method, and both perform worse after the data set adjustments. It is also clear that adjustment 2 has the largest negative impact of the three adjustments for the proposed method, but not in each location for the baseline method.

1 2 3 4 5 6 7 8 9 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Number of features added

Coefficient

of

determination

Baseline without adjustments Baseline after adjustment 1 Baseline after adjustment 2 Baseline after adjustment 3 Proposed without adjustments

Proposed after adjustment 1 Proposed after adjustment 2 Proposed after adjustment 3

Final performance for different degrees of adjustment

The next three figures show the final performance of the proposed method, which is the accuracy of the regressor after the feature selection algorithm has completed. Each figure shows this performance for different degrees of one of the three adjust- ment types, for each of the locations. For example, figure 5.20 shows the proposed and baseline performances when 0% (unadjusted), 50%, 75%, etc. of the probes have been removed by decreasing frequency. As expected, the proposed method performs better than the baseline in every case. Also, higher degrees of the adjust- ment decrease performance of both methods in nearly every case. Secondly, the performance decreases more quickly at the last degrees of adjustment for location A and C than for location B. This may be caused by the fact that these locations have fewer visitors than location B, so removing over 95% of the probes may make it impossible to find any meaningful overlapping visits.

0% 50% 75% 87.5% 93.75% 96.875% −0.7 −−−00.65.6 0.55 −0.5 −−−000.45.4 .35 −0.3 −−−00.25.2 0.15 −0.1 −0.050 00.005.1 .15 0.2 000.25.3 .35 0.4

Percentage of probes removed by decreasing frequency

Coefficient

of

determination

Baseline for location A Baseline for location B Baseline for location C Proposed for location A Proposed for location B Proposed for location C

0% 50% 75% 87.5% −0.5 −−−00.45.4 0.35 −0.3 −−−00.25.2 0.15 −0.1 −0.050 0.005.1 00..152 00.25.3 00..354

Percentage of samples removed

Coefficient

of

determination

Baseline for location A Baseline for location B Baseline for location C Proposed for location A Proposed for location B Proposed for location C

Figure 5.21:Final performance for different degrees of adjustment 2

The performances for different degrees of adjustment 2 and 3 are shown in figures 5.21 and 5.22. The general observations as those for figure 5.20 hold. Each of the fig- ures shows that a large amount of input data can be removed before the proposed method performs worse than the baseline method on the unadjusted data. This suggests that the proposed method would also work well in locations with negative external circumstances such as noise.

0% 50% 75% 87.5% 93.75% 96.875% −0.5 −−−00.45.4 0.35 −0.3 −−−00.25.2 0.15 −0.1 −0.050 0.005.1 00..152 00.25.3 00..354

Percentage of probes removed randomly

Coefficient

of

determination

Baseline for location A Baseline for location B Baseline for location C Proposed for location A Proposed for location B Proposed for location C

Figure 5.22:Final performance for different degrees of adjustment 3

From these graphs, we can conclude that the proposed method continues to do well even in very unfavorable circumstances, as simulated by the data set adjust- ments. In each examined case, the proposed method continues to outperform the baseline method. Specifically, the proposed method has an accuracy similar to the unadjusted data set when 75% of probes are removed (either by decreasing fre- quency or probabilistically), and its performance decreases to a slower degree than that of the baseline method. From this, we conclude that the proposed method is more robust than the baseline.

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