## 4 Experiments and Results Analysis
### Comparison of Preprocessing Methods  
To verify the effectiveness of the improved denoising algorithm, we apply A-DBSCAN denoising to 180 subcarriers, calculate the variance of each subcarrier after denoising, and compare it with the variance of the original data and the variance after standard DBSCAN denoising. As Figure 8 shows, after executing the A-DBSCAN algorithm for denoising, the variance of the CSI subcarriers is significantly reduced. The dashed line in Figure 8 represents the average variance of the 180 subcarriers, where A-DBSCAN is 1.343, outperforming the standard DBSCAN's 1.450 and the original data's 1.531, proving that the A-DBSCAN algorithm can effectively remove the noise from the original CSI amplitude. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Specifications** & **Transmitter** & **Receiver** \\ \hline Network Standard & IEEE 802.11 b/g/n \\ Maximum Transmission Rate & 300 Mbps \\ Operating Band & 2.4 GHz \\ Number of Antennas & 4 & 3 \\ MIMO Mode & 2 \(\times\) 2 MIMO & 2 \(\times\) 3 MIMO \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Configuration parameters of experimental equipment. Figure 7: Experimental layout. (**a**) Scenario 1; (**b**) Scenario 2. We take the noise-reduced CSI amplitude as input and use AE for dimensionality reduction. In our tests, the error from the 20-dimensional features extracted by AE was only 0.15%. This result shows that the extracted low-dimensional features already contain most of the relevant information. Therefore, we choose 20-dimensional data to construct fingerprints. To assess the performance of our dimensionality reduction technique, we juxtaposed it with two well-established methods, PCA and KPCA. We subjected the CSI amplitude data, gathered during the offline phase, to each of these three methods. Using the dimensionally reduced feature sets combined with the coordinates of reference points, we formulated position fingerprints \(F_{i}=\{(P_{i},(x_{i},y_{i})\}\), where \(P=\big{\{}p_{1},\cdots,p_{j}\big{\}}\) stand for the reduced feature sets with components, while \((x_{i},y_{i})\) signifies the position label. We used these fingerprints to create a database. Subsequently, data procured during the online phase were processed similarly, with positioning executed using the KNN algorithm. Table 2 provides the parameter settings for the three dimensionality reduction methods used in the experiments of this paper. Figure 9 shows the positioning results from which we observe that the root-mean-square error (RMSE) for the KNN algorithm is consistently highest when using data without dimensionality reduction, regardless of the chosen value for \(K\). Specifically, when K = 3 (where the KNN algorithm performs optimally), the RMSE value for the unprocessed data is 1.95 m. For data processed with the three dimensionality reduction techniques, the values are 1.73 m, 1.65 m, and 1.81 m, respectively. This demonstrates that using dimensionality-reduced data provides better positioning accuracy compared to the direct use of raw data. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Reduction Algorithms** & **Parameters** & **Value** \\ \hline \multirow{5}{*}{AE} & Coding dimension & 20 \\  & Iterations & 200 \\  & Activation functions (encoding and & \\  & decoding layers) & tanh \\  & Adam optimizer learning rate & 0.01 \\  & Loss function & MSE \\  & Variance explained/number of & 99\%/74 \\  & principal components & \\  & Kernel function & RBF \\  & Variance explained/number of & 99\%/110 \\  & principal components & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters chosen for the three dimensionality reduction algorithms. Figure 8: Variance of each subcarrier after noise reduction. Theoretically, CSI data are understood to exhibit a high degree of nonlinearity, suggesting that nonlinear dimensionality reduction methods might offer better results. Yet, according to this study's outcomes, the KPCA algorithm consistently underperforms compared to PCA, both in dimensionality reduction and positioning phases.