# Indoor Localization Using Semi-Supervised Manifold Alignment with Dimension Expansion
## 4 Testing Results
### Experimental Results  
In this section, we will continue to examine the performance of the proposed approach in the real indoor environment with the same layout in Figure 2. We set that the ratio of calibrated fingerprints ranges from 30% to 100%, the number of RSS samples at each RP ranges from 10 to 150 and the augmentation dimension ranges from \(m\) to \(5m\), where \(m\) is the number of APs. The CDFs of errors by using the proposed approach under different ratios between the number of calibrated and labeled locations are shown in Figure 4a, from which we can find that the localization accuracy also increases as the ratio increases.  
Figure 4b shows the CDFs of errors by using the proposed approach under different numbers of RSS measurements collected at each calibrated location. As expected, a larger number of collected RSS measurements results in a higher localization accuracy, which is in accordance with the previous discussion. The CDFs of errors by the proposed approach under different augmentation dimensions are shown in Figure 4c. As can be seen from this figure, the localization performance deteriorates with the increase of augmentation dimension. Meanwhile, as for the augmentation corresponding to the physical coordinates, we also explore the localization performance with random replication with which the replicated value is selected randomly from the initial two-dimensional physical coordinate. Figure 4d shows the localization errors under different replications for the physical coordinates augmentation. Each running time relates to a specific replication, and the corresponding CDFs of the mean and standard deviation of errors are shown in Figure 4e. From these figures, we can find that more than 80% mean errors are smaller than 3 m, and meanwhile, the localization accuracy can be well guaranteed under most of the replications for the physical coordinates augmentation.  
Figure 4f compares the CDFs of errors of the target by using the proposed and other four popular approaches, i.e., WKNN, Bayesian, kernel and the conventional manifold alignment without transformation matrices [28]. From this figure, we can find that the proposed approach outperforms the other four in localization accuracy, which demonstrates the significant benefit provided by the dimension expansion to the manifold alignment for indoor localization. In addition, the mean and standard deviation of errors are also illustrated in Table 2, from which we can find that both the smallest mean and standard deviation of errors, i.e., 2.4 m and 1.1 m, are achieved by the proposed approach. Furthermore, Figure 5 shows the mean of errors under different numbers of RSS samples at each RP and the ratios of calibrated fingerprints, from which we can find that the proposed approach achieves good localization performance especially under the small number of RSS samples at each RP and low ratios of calibrated fingerprints.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Approaches** & **Mean of Errors (m)** & **Standard Deviation of Errors (m)** \\ \hline The proposed & 2.4 & 1.1 \\ WKNN & 5.6 & 1.5 \\ Bayesian & 4.1 & 1.3 \\ Kernel & 3.8 & 1.2 \\ Manifold alignment & 3.4 & 1.2 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Mean and standard deviation of errors by different approaches.  
Figure 4: Parameter discussion in the actual environment. (**a**) CDFs of errors under different numbers of calibrated locations; (**b**) CDFs of errors under different numbers of RSS measurements; (**c**) CDFs of errors under different augmentation dimensions; (**d**) localization errors under different replications for physical coordinates augmentation; (**e**) CDFs of mean and standard deviation of errors; (**f**) CDFs of errors by different approaches.