# Audio Fingerprint Extraction Based on Locally Linear Embedding for Audio Retrieval System
## 4 Experimental Results and Analysis
### Results and Analysis
#### 4.2.2 Dimensionality Reduction in a Single Group  
In order to verify the maximum dimensionality reduction that LLE can achieve, this paper increases the number of reduced dimension step by step on the single sub-region group. The increasing is implemented until the group has no space for further reduction or its retrieval performance cannot be accepted by the actual situation. However, since the construction of the fingerprint in the extended group is a combination of multiple sub-region energies, this group is not included in the consideration of dimensionality reduction in the paper. First, Table 3 shows the retrieval results of different reduction of horizontal group.  
In the case that the reduced dimension is set to 4 in the horizontal group, the method can still maintain high recall and precision rate (Table 3). The original dimension of fingerprint in the horizontal group is 7 and the reduced dimension is raised from 1 to 4. It can be seen that the reduction proportion is more than 50% in the horizontal group and 20% in the overall fingerprint (22 dimensions). Similar results are obtained in other groups.  
The original fingerprint dimensions in each group are different, so the maximum reduction are also different. The reduction of the three groups shown in Table 4 reached a proportion 50% of group and about 10% of the overall fingerprint. The result is mainly limited by the original fingerprint dimension. The original fingerprint dimension in the horizontal group is quite large (seven dimensions), while the other groups have no reduction space as large as that in the horizontal group, making the overall dimensionality reduction lower than that in the horizontal area.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Reduced** & \multirow{2}{*}{**Group**} & \multirow{2}{*}{**Optimal \(K\)**} & **Proportion of** & **Proportion of** & \multirow{2}{*}{**Recall (\%)**} & **Precision** \\
**Dimension** & & & **of Group** & **Fingerprint** & & **(\%)** \\ \hline
1 & Vertical & 5 & 1/3 & 1/22 & 99.2 & 98.0 \\
2 & Vertical & 5 & 2/3 & 2/22 & 98.1 & 96.5 \\
1 & Central & 5 & 1/4 & 1/22 & 99.3 & 98.9 \\
2 & Central & 5 & 2/4 & 2/22 & 98.5 & 97.6 \\
1 & Marginal & 6 & 1/4 & 1/22 & 99.1 & 97.8 \\
2 & Marginal & 4 & 2/4 & 2/22 & 97.4 & 94.2 \\ \hline \hline \end{tabular}
\end{table}
Table 4: None horizontal dimensionality reduction results.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**\(K\) Value** & **Recall (\%)** & **Precision (\%)** \\ \hline
3 & 99.6 & 98.6 \\
4 & 97.2 & 95.4 \\
5 & 93.3 & 89.3 \\
6 & 89.1 & 85.4 \\
7 & 82.6 & 76.5 \\
8 & 75.2 & 70.8 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The retrieval result of different \(K\) (reduced dimension of horizontal group = 1).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Reduced** & \multirow{2}{*}{**Optimal \(K\)**} & **Proportion of** & **Proportion of** & \multirow{2}{*}{**Recall (\%)**} & **Precision (\%)** \\
2 & 3 & 2/7 & 2/22 & 99.4 & 98.4 \\
3 & 5 & 3/7 & 3/22 & 99.0 & 98.2 \\
4 & 5 & 4/7 & 4/22 & 98.8 & 97.9 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Horizontal dimensionality reduction results.