# Laplacian Eigenmaps Dimensionality Reduction Based on Clustering-Adjusted Similarity
## 4 Results
### Results on Different Datasets
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **FMI** & **F-measure** & **PU** \\ \hline \multicolumn{4}{c}{Msplice} \\ \hline LE-CAS & **0.6133 \(\pm\) 0.0124** & **0.5425 \(\pm\) 0.0302** & **0.7284 \(\pm\) 0.0638** \\ LE & 0.3247 \(\pm\) 0.0233 & 0.1871 \(\pm\) 0.0292 & 0.4914 \(\pm\) 0.0647 \\ S-LE & 0.5552 \(\pm\) 0.0296 & 0.2956 \(\pm\) 0.0239 & 0.5324 \(\pm\) 0.0734 \\ GGELE & 0.4925 \(\pm\) 0.0334 & 0.4025 \(\pm\) 0.0108 & 0.6354 \(\pm\) 0.0619 \\ SCPLE & 0.5852 \(\pm\) 0.0190 & 0.3928 \(\pm\) 0.0099 & 0.6203 \(\pm\) 0.0594 \\ \hline \multicolumn{4}{c}{W1a} \\ \hline LE-CAS & **0.9285 \(\pm\) 0.0514** & **0.4691 \(\pm\) 0.0375** & **0.9608 \(\pm\) 0.0461** \\ LE & 0.6429 \(\pm\) 0.0285 & 0.2488 \(\pm\) 0.0215 & 0.6541 \(\pm\) 0.0427 \\ S-LE & 0.7042 \(\pm\) 0.0342 & 0.3158 \(\pm\) 0.0261 & 0.7028 \(\pm\) 0.0395 \\ GGELE & 0.8731 \(\pm\) 0.0427 & 0.4021 \(\pm\) 0.0125 & 0.7936 \(\pm\) 0.0409 \\ SCPLE & 0.8392 \(\pm\) 0.0307 & 0.4210 \(\pm\) 0.0325 & 0.8333 \(\pm\) 0.0326 \\ \hline \multicolumn{4}{c}{Soccer-sub1} \\ \hline LE-CAS & **0.4268 \(\pm\) 0.0014** & **0.3172 \(\pm\) 0.0025** & **0.4774 \(\pm\) 0.0259** \\ LE & 0.1242 \(\pm\) 0.0062 & 0.1573 \(\pm\) 0.0029 & 0.2358 \(\pm\) 0.0291 \\ S-LE & 0.1995 \(\pm\) 0.0051 & 0.2319 \(\pm\) 0.0015 & 0.2936 \(\pm\) 0.0245 \\ GGELE & 0.2452 \(\pm\) 0.0024 & 0.2906 \(\pm\) 0.0015 & 0.3534 \(\pm\) 0.0208 \\ SCPLE & 0.3052 \(\pm\) 0.0099 & **0.3173 \(\pm\) 0.0024** & 0.3726 \(\pm\) 0.0213 \\ \hline \multicolumn{4}{c}{Medelon} \\ \hline LE-CAS & **0.6967 \(\pm\) 0.0416** & **0.3024 \(\pm\) 0.0252** & **0.7804 \(\pm\) 0.1860** \\ LE & 0.5852 \(\pm\) 0.0437 & 0.1921 \(\pm\) 0.0207 & 0.5046 \(\pm\) 0.1643 \\ S-LE & 0.6082 \(\pm\) 0.0367 & 0.2235 \(\pm\) 0.0200 & 0.5478 \(\pm\) 0.1302 \\ GGELE & 0.6552 \(\pm\) 0.0345 & **0.3023 \(\pm\) 0.0132** & 0.6532 \(\pm\) 0.1033 \\ SCPLE & **0.6923 \(\pm\) 0.0570** & 0.3008 \(\pm\) 0.0219 & 0.6378 \(\pm\) 0.1126 \\ \hline \multicolumn{4}{c}{FG-NET} \\ \hline LE-CAS & **0.6515 \(\pm\) 0.0200** & **0.5042 \(\pm\) 0.0016** & **0.7520 \(\pm\) 0.0619** \\ LE & 0.4952 \(\pm\) 0.0138 & 0.3895 \(\pm\) 0.0021 & 0.5923 \(\pm\) 0.0573 \\ S-LE & 0.4652 \(\pm\) 0.0207 & 0.4014 \(\pm\) 0.0015 & 0.6752 \(\pm\) 0.0592 \\ GGELE & 0.5558 \(\pm\) 0.0169 & 0.4977 \(\pm\) 0.0020 & 0.6936 \(\pm\) 0.0499 \\ SCPLE & 0.5874 \(\pm\) 0.0245 & **0.5044 \(\pm\) 0.0021** & 0.7233 \(\pm\) 0.0601 \\ \hline \multicolumn{4}{c}{ORL} \\ \hline LE-CAS & **0.5635 \(\pm\) 0.0452** & **0.3388 \(\pm\) 0.0092** & **0.6710 \(\pm\) 0.0229** \\ LE & 0.1398 \(\pm\) 0.0226 & 0.1247 \(\pm\) 0.0084 & 0.4215 \(\pm\) 0.0198 \\ S-LE & 0.2635 \(\pm\) 0.0356 & 0.1964 \(\pm\) 0.0078 & 0.5024 \(\pm\) 0.0099 \\ GGELE & 0.4545 \(\pm\) 0.0279 & 0.2311 \(\pm\) 0.0065 & 0.5924 \(\pm\) 0.0187 \\ SCPLE & 0.4933 \(\pm\) 0.0281 & 0.2295 \(\pm\) 0.0081 & 0.6011 \(\pm\) 0.0125 \\ \hline \end{tabular}
\end{table} 
Table 2: Results (average \(\pm\) std) of comparing methods on different datasets (Msplice, W1a, Soccer-sub1, Medelon, FG-NET, ORL, Musk, CNAE-9, SECOM, DrivFace). The target dimensionality \(c\) is set to 10. The best (or comparable to the best) results are in **boldface**. After detailed observations of the results on different datasets, we found that the FMI results on several datasets are much lower than others (Look at the FMI values on dataset soccer-sub1, ORL, DrivFace). Since FMI is an evaluation index which measures the consistency between the clustering results and the real labels as we mentioned before, there are good reasons to believe that clustering occur in these datasets are not so perfect, which means that the clusters identified by the clustering method we used in LE-CAS (kernel _k_-means) are not well suitable for the true decision boundaries. Fortunately, even though the clusters we obtained are not so satisfied, the performance of the LE-CAS is still better than the performance of GGLE, S-LE, SCPLE and LE, we can still get relatively good results.