# A Hierarchical Multi-Label Classification Algorithm for Gene Function Prediction
## The Proposed Algorithm
### Experiment Results and Analysis
#### 3.3.2 Experiments on Eight Data Sets
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & **Method** & \(hPre^{M}\) & \(hRec^{M}\) & \(hF^{M}_{1}\) \\ \hline D1 & TPR & 0.366 & 0.548 & 0.380 \\ D1 & CLUS-HMC & 0.514 & 0.362 & 0.352 \\ D1 & Proposed & 0.347 & 0.633 & **0.405** \\ D2 & TPR & 0.385 & 0.441 & 0.346 \\ D2 & CLUS-HMC & 0.468 & 0.392 & 0.347 \\ D2 & Proposed & 0.347 & 0.598 & **0.385** \\ D3 & TPR & 0.445 & 0.544 & 0.432 \\ D3 & CLUS-HMC & 0.525 & 0.423 & 0.396 \\ D3 & Proposed & 0.419 & 0.643 & **0.457** \\ D4 & TPR & 0.406 & 0.514 & 0.389 \\ D4 & CLUS-HMC & 0.518 & 0.408 & 0.379 \\ D4 & Proposed & 0.368 & 0.625 & **0.413** \\ D5 & TPR & 0.370 & 0.544 & 0.381 \\ D5 & CLUS-HMC & 0.505 & 0.379 & 0.360 \\ D5 & Proposed & 0.344 & 0.665 & **0.403** \\ D6 & TPR & 0.360 & 0.521 & 0.365 \\ D6 & CLUS-HMC & 0.554 & 0.335 & 0.350 \\ D6 & Proposed & 0.324 & 0.674 & **0.390** \\ D7 & TPR & 0.373 & 0.491 & 0.371 \\ D7 & CLUS-HMC & 0.481 & 0.379 & 0.344 \\ D7 & Proposed & 0.344 & 0.629 & **0.397** \\ D8 & TPR & 0.393 & 0.536 & 0.400 \\ D8 & CLUS-HMC & 0.501 & 0.438 & 0.395 \\ D8 & Proposed & 0.371 & 0.626 & **0.418** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The macro-averaged version of experimental results on eight data sets. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & **Method** & \(hPre^{\mu}\) & \(hRec^{\mu}\) & \(hF^{\mu}_{1}\) \\ \hline D1 & TPR & 0.348 & 0.518 & 0.416 \\ D1 & CLUS-HMC & 0.449 & 0.306 & 0.364 \\ D1 & Proposed & 0.333 & 0.627 & **0.435** \\ D2 & TPR & 0.360 & 0.397 & 0.377 \\ D2 & CLUS-HMC & 0.402 & 0.335 & 0.365 \\ D2 & Proposed & 0.331 & 0.533 & **0.408** \\ D3 & TPR & 0.434 & 0.515 & 0.471 \\ D3 & CLUS-HMC & 0.476 & 0.387 & 0.427 \\ D3 & Proposed & 0.396 & 0.663 & **0.496** \\ D4 & TPR & 0.385 & 0.477 & 0.426 \\ D4 & CLUS-HMC & 0.453 & 0.355 & 0.398 \\ D4 & Proposed & 0.358 & 0.585 & **0.444** \\ D5 & TPR & 0.359 & 0.519 & **0.425** \\ D5 & CLUS-HMC & 0.442 & 0.322 & 0.373 \\ D5 & Proposed & 0.333 & 0.623 & **0.434** \\ D6 & TPR & 0.331 & 0.483 & 0.393 \\ D6 & CLUS-HMC & 0.487 & 0.270 & 0.348 \\ D6 & Proposed & 0.314 & 0.606 & **0.413** \\ D7 & TPR & 0.366 & 0.423 & 0.393 \\ D7 & CLUS-HMC & 0.418 & 0.331 & 0.369 \\ D7 & Proposed & 0.339 & 0.541 & **0.417** \\ D8 & TPR & 0.388 & 0.509 & 0.441 \\ D8 & CLUS-HMC & 0.444 & 0.390 & 0.415 \\ D8 & Proposed & 0.372 & 0.577 & **0.454** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The micro-averaged version of experimental results on eight data sets. In the ideal world, we expect both hierarchical precision and hierarchical recall to have higher values to show better performance. However, typically, precision and recall are inversely related. As one increasing leads to the other falling, the hierarchical F-measure is proposed to balance these two metrics. In this paper, the hierarchical F-measure is used to evaluate the performance of each algorithms, and the algorithm that has the highest value of F-measure shows the best performance. The other two values of precision and recall are also listed in the tables as details of the F-measure, and for whoever is interested in these values. According to these tables, we can come to a conclusion that the proposed HMC algorithm performs significantly better than the other two algorithms in terms of both micro-averaged and macro-averaged metrics on all eight data sets.