## 2 Methods
## 4 Discussions

In this research, we have compared the performance of CBDF with five popular machine learning algorithms, CART, RF, SVM, MLP and LR, and evaluated their applications in predicting unbalanced semen concentration results. CART, RF, SVM, MLP and LR are highly accurate classifiers and find great applications in various fields but experiment results on Fertility Dataset have shown that they are overtaken by the proposed CBDF in terms of AUC. Besides CBDF, the performance of CART is the most stable one as AUC scores in all folds is greater than 0.5 but it is much less accurate than CBDF. We notice that MLP, the learning algorithm chosen in [5], gets a perfect classification in fold 1 but its poor performance in other folds demonstrates its instability and makes it an unsatisfactory choice in our research. RF, another ensemble of CART decision trees, is the most similar one to CBDF in performance and could be an alternative when CBDF is not available. In the experiments, we also justify the contributions of deletion of majority Tomek Links instances, clustering of majority samples and weights placed on base learners. Preprocessing data by only removing majority Tomek Links and/or balancing data by only applying SMOTE all obtain lower AUC scores. These observations suggest that both the noise induced by majority samples and the unbalance due to lack of minority data may degrade the performance of the learning algorithms. Various studies have suggested that age [19], sexual abstinence [20], cigarette smoking [21], food intake [22], obesity [23], psychosocial stress [24,25] are all associated with altered semen quality, but conclusions about the extent of the deleterious effects vary widely. In this research, we use CBDF to calculate variables' importance and detect which factors are most relevant to semen concentration. The most important factor related to semen concentration found in this study is \"Age\". We find males particularly those older than 24 have a higher risk of semen concentration problem, which agrees with a previous research [19] stating that aging increases risks of diminished semen quality. However, our finding is inconsistent with a previous review suggesting that increased male age is not associated with sperm concentration [25]. From the Fertility Dataset, accident or serious trauma is also highly related to semen quality. This is probably because serious traumas, particularly spinal cord injuries, cause changes to the seminal plasma constituents, bladder management, and the neurogenic impairment to the ejaculatory function [26]. The next three important factors are \"Season\", \"Sitting\" and \"Fever\". These factors are all temperate-related variables and their importance justifies the fact that sperm are heat-sensitive and cannot endure high temperatures. The increase in environment temperature and the influence on testicular temperature may explain for why semen samples obtained in winter are probably better than semen samples collected in other seasons (one-tailed [PERSON]'s exact test \(p\) value = 0.0952 in this study). Also, sitting too long may cause an elevation of testicular temperature that may result in poor semen quality, which agrees with [27]. In the same way, having high fevers can adversely affect sperm count, motility and morphology, and this result agrees with [28]. Regarding the contribution of alcohol to semen quality, our research results are consistent with previous studies that moderate alcohol consumption (\(\leq\)125 g per week in this study) is unlikely to have negative effects on semen quality [21; 29]. However, when alcohol consumption grows, it might have detrimental effect on semen quality and this findings is also consistent with [30].