# 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  
This algorithm is designed to tackle the HMC problem for solving the gene function prediction task based on GO. To present the performance of this algorithm, it is also necessary to compare with other state-of-the-art algorithms. Due to the complexity of the HMC problem with DAG structure, only a few algorithms have been proposed by others. The TPR ensemble method and the CLUS-HMC method are two typical state-of-the-art algorithms used for gene function prediction. The TPR ensemble method is the representation of the algorithms that belongs to the local approach. It has better performance than other local algorithms such as the flat ensemble method and the hierarchical top-down method. As a representative of global algorithms, the CLUS-HMC method outperforms the HLCS-Multi algorithm, the HLCS-DAG algorithm and the HMC-LMLP algorithm. Thus, these two algorithms are selected to be compared with the proposed HMC algorithm. For consistency, we used the same data sets and the same evaluation scheme for each algorithm we tested. The details of these two methods are listed below. The TPR ensemble method: this method integrates the predictions of base classifiers with the positive results that come from the classifiers at the lower level, together with the negative results that are given by the higher level classifiers [18]. The TPR ensemble method contains two steps. In the bottom-up step, the positive predictions are moved towards the parent nodes and gradually towards the ancestor nodes. In the top-down step, negative predictions are propagated to the children nodes and the descendant nodes of each node, aiming to ensure the consistency of the final results and also give more precise predictions [17]. CLUS-HMC [13]: this method belongs to the global approach, and it predicts all class labels at the same time by inducing a single decision tree. The predictive clustering tree framework is used in this algorithm. The hierarchy structure is considered by modifying different weights to the labels according to the level, and the DAG can also be solved by this method. The level parameter is selected through the cross validation, and the weighted Euclidean distances are designed for the variance reduction. We computed both the micro-averaged version and macro-averaged version of \(hPre\), \(hRec\) and \(hF_{1}\) to appraise the performance of the proposed algorithm. In Table 3, the micro-averaged version \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**GO ID** & **Original _Prec_** & **Original _Rec_** & **Original \(F_{1}\)** & **Improved _Prec_** & **Improved _Rec_** & **Improved \(F_{1}\)** \\ \hline GO:0065007 & NaN & 0 & NaN & 0.408 & 0.454 & **0.430** \\ GO:0016043 & NaN & 0 & NaN & 0.486 & 0.539 & **0.511** \\ GO:0044710 & 0.577 & 0.121 & 0.206 & 0.478 & 0.433 & **0.455** \\ GO:000696 & NaN & 0 & NaN & 0.358 & 0.775 & **0.490** \\ GO:0044249 & 0.552 & 0.181 & 0.272 & 0.440 & 0.630 & **0.518** \\ GO:0046483 & NaN & 0 & NaN & 0.437 & 0.699 & **0.538** \\ GO:1901360 & 0.750 & 0.013 & 0.025 & 0.448 & 0.734 & **0.557** \\ GO:1901564 & 0.591 & 0.050 & 0.092 & 0.373 & 0.431 & **0.400** \\ GO:0009059 & 0.472 & 0.045 & 0.082 & 0.384 & 0.451 & **0.415** \\ GO:0019538 & 0.520 & 0.040 & 0.073 & 0.352 & 0.489 & **0.410** \\ GO:0044271 & 0.500 & 0.011 & 0.021 & 0.344 & 0.603 & **0.438** \\ GO:0034645 & 0.472 & 0.045 & 0.082 & 0.364 & 0.596 & **0.452** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The experimental results for specific classes. values of these algorithms on eight data sets are given. Table 4 compares the different algorithms with the macro-averaged version values.