## 3 Experiments and Discussions
### Algorithm Performance with Changes in Labeled Data Proportion  
For semi-supervised algorithms, one of the best evaluation perspectives is the ability of the algorithm to maintain its effectiveness as the proportion of labeled data varies. According to our analysis, the proposed approach effectively captures the intrinsic manifold relationship within the original data in the frequency domain, thereby achieving accurate mapping in low-dimensional space. Different from the supervised classification techniques, despite relying on only a small amount of labeled data, the algorithm can still accurately classify samples based on precise low-dimensional mapping relationships. In this section, experiments are conducted to compare the performance variation of our FMDR with comparison algorithms under varying proportions of labeled data. Specifically, six levels of labeled data proportions are set from small to large: 5%, 10%, 15%, 20%, 25% and 30%. In the semi-supervised classification experiments conducted on four datasets, the accuracy variations of FMDR and the comparative algorithms are recorded in Table 3.  
Achieving high accuracy with very few labeled datasets presents a challenge for all semi-supervised algorithms. All accuracies decrease due to the insufficient information, with some algorithms even becoming ineffective. However, FMDR demonstrates an advantage in accuracy even with a smaller proportion of labeled data. Despite having only 5% of labeled data, FMDR achieves the highest accuracy in four datasets, with values of 52.50%, 74.80%, 52.00% and 53.93%, respectively. As the proportion of labeled data increases, the accuracy of FMDR also improves. In the AR dataset, with labeled data comprising 10%, FMDR achieved an accuracy of 92.61%, marking a significant increase of 17.84% compared to when only 5% of the data were labeled. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **Acc** & **Pre** & **Rec** & **F1** \\ \hline FMDR & 2.34 & 3.27 & 3.43 & 2.87 \\ KNN & 4.24 & 5.63 & 6.02 & 3.50 \\ Kmeans & 3.62 & 3.53 & 3.69 & 3.77 \\ ATNMTF & 5.22 & 5.89 & 7.34 & 5.35 \\ LE & 3.55 & 4.17 & 4.53 & 2.95 \\ NMF & 4.32 & 5.37 & 5.13 & 3.06 \\ RPCA & 3.94 & 4.55 & 4.58 & 3.26 \\ DANMF & 3.02 & 4.21 & 4.88 & 3.23 \\ \hline \hline \end{tabular} The highest values are emphasized in bold font.  
\end{table} 
Table 2: Standard deviations of 100 repeated trials in the AR dataset. The performances of all algorithms are improved when the labeled data increase. FMDR still maintains its superiority with a higher improvement effect. To visually observe the trends of each algorithm's changes, a set of line charts are plotted in Figure 7. The red solid line represents FMDR, while other algorithms are represented by different colors of dashed lines. As the figure shows, FMDR consistently maintains its leading advantage at all four indicators as the proportion of labeled data varies. In summary, FMDR accurately describes the manifold relationships between samples through frequency domain correlationships, enabling precise recognition and classification of samples. Moreover, FMDR demonstrates robustness to labeled data, achieving optimal classification accuracy both when labeled data are scarce and when they are sufficient.