# Enhancing Indoor Localization with Room-to-Room Transition Time: A Multi-Dataset Study
## 4 Experimental Results and Discussions
The results indicate a consistent improvement in accuracy when incorporating room-to-room transition time features, with Wi-Fi + room-to-room transition time outperforming Wi-Fi across all the algorithm groups. The SVM algorithm showed high performance on all three datasets, with values of 89.6, 89.5, and 90.5%, respectively. Medium Gaussian SVM achieved the highest performance, with accuracy peaking at 90.5% on Dataset 3. Neural Networks and k-NN also showed substantial improvements when contextual data were added, though Neural Networks underperformed slightly on Dataset 1. Overall, across all the datasets, the Wide Neural Network method demonstrated the most significant performance improvement when transitioning from Wi-Fi to Wi-Fi + room-to-room transition time (Wi-Fi + RR). Tables 8-10 provide an overview, according to the experimental results, of the performance metrics (Precision, Recall, and F1 score) for Wi-Fi and Wi-Fi + room-to-room transition time (Wi-Fi + RR) for the various ML algorithms on the three datasets. Table 8 shows consistent performance improvements across all the methods, with algorithms like Medium Gaussian SVM and Ensemble Bagged Trees achieving near-optimal Precision and Recall on the Wi-Fi + RR dataset. Similarly, Table 9 demonstrates that most of the algorithms achieved performance above 90% for Precision, Recall, and F1 score on the Wi-Fi + RR dataset. Specifically, the Wide Neural Network model exhibited notable improvements, with a 3.33% increase in Precision, 12.45% in Recall, and 11.51% in F1 score when using the enriched feature set. Consistent with the results observed for the other datasets, incorporating room-to-room transition time information enhanced performance across all the algorithms in Table 10. Notably, the Wide Neural Network method demonstrated  
The complexity values presented in Table 11 reveal the computational trade-offs among the different ML algorithms, in terms of training and testing costs. Evaluating these complexities helped to determine the suitability of each approach, based on dataset size, real-time performance needs, and resource availability. When we discuss the complexities of the algorithms through the Dataset 2 samples, the _Fine Tree_ algorithm, despite having high training complexity (\(O(F\cdot N^{2}\cdot\log N)\approx O(63\cdot 2700^{2}\cdot\log(2700))\approx O (2.99\cdot 10^{8})\)), demonstrated faster testing with lower complexity (\(O(N)\approx O(2700)\)), resulting in significant performance improvement for Wi-Fi + RR. _Efficient Logistic Regression_ had low training complexity (\(O(I\cdot F\cdot N)\approx O(100\cdot 63\cdot 2700)\approx O(1.7\cdot 10^{7})\)) and extremely low testing complexity (\(O(F)\approx O(63)\)), making it a highly efficient algorithm. While it performed well in Recall improvements on Wi-Fi + RR, its overall accuracy gain was relatively modest, due to its linear nature. _Weighted k-NN_, _Coarse k-NN_, and _Cosine k-NN_, although they did not have explicit training complexity (lazy learning), exhibited high testing complexity, due to their reliance on pairwise distance calculations. Specifically, _Weighted k-NN_ and _Coarse k-NN_ required \(O(N\cdot F+k\cdot\log k)\approx O(2700\cdot 63+5\cdot\log(5))\approx O (1.7\cdot 10^{5})\), while _Cosine k-NN_ had slightly lower but still significant complexity of \(O(N\cdot F)\approx O(2700\cdot 63)\). These models required higher computational power during inference, making them less practical for real-time applications, despite their strong accuracy improvements with Wi-Fi + RR. _Linear SVM_ exhibited high training complexity (\(O(\max(N,F)\cdot\min(N,F)\cdot I)\approx O(2700\cdot 63\cdot 100)\approx O (1.7\cdot 10^{7})\)), but its testing complexity remained moderate (\(O(F\cdot M)\approx O(63\cdot M)\)). It showed moderate improvement in accuracy with Wi-Fi + RR, making it a reasonable choice when balancing accuracy and efficiency.