# Dynamic Online Label Distribution Feature Selection Based on Label Importance and Label Correlation
## 5 Experimental Data
### Statistical Tests  
Because some of the experimental results were similar, statistical tests were used to evaluate whether there are significant differences in the experimental results. To systematically explore the statistical significance of the comparison algorithms, we used the Friedman test to further analyze the differences between the performance results of the comparison algorithms. This is a highly accepted method of statistically comparing multiple algorithms for significant differences across many datasets [60]. The specific method is as follows: given \(k\) comparison algorithms and \(N\) multi-label datasets, \(R_{j}=\frac{1}{N}\sum_{i=1}^{N}r_{i}^{j}v\) represents the average rank of the \(j\)-th algorithm on all datasets, where \(r_{i}^{j}\) is the rank of algorithm \(j\) on the \(i\)-th dataset. Under the null hypothesis (it is assumed that the classification performance of each algorithm under each evaluation index is equal, that is, the ranks of all algorithms are equal), the Friedman test can be defined as follows:  
\[F_{F}=\frac{(N-1)\chi_{F}^{2}}{N(k-1)-\chi_{F}^{2}},\text{where }\chi_{F}^{2}=\frac{12N}{k(k+1)}\left(\sum_{i=1}^{k}R_{i}^{2}-\frac{k(k+1)^{ 2}}{4}\right) \tag{20}\]  
where \(F_{F}\) follows an \(F\)-distribution with \((k-1)\) and \((k-1)(N-1)\) degrees of freedom. Table 9 summarizes the \(F_{F}\) values and the corresponding critical values of each evaluation index after the Friedman test statistics were calculated [61].  
As Table 10 reveals, for all evaluation indicators with a significance level of \(a=0.10\), the null hypothesis is clearly disproved. Next, we used post hoc tests to further determine the differences in performance of these comparison algorithms. Because our focus was on comparing the proposed method with other algorithms, the Bonferroni-Dunn test was used [62]. The Bonferroni-Dunn test is a method used in multiple comparison problems to control the probability of a Type I error (that is, incorrectly rejecting a hypothesis that is truly null). When conducting multiple statistical tests, the probability of rejecting one or more null hypotheses (i.e., the probability of making a Type I error) increases with the number of tests, even if all of the null hypotheses are true. The Bonferroni-Dunn test reduces the overall risk of this error by reducing the significance level of a single test. The disadvantage of the Bonferroni-Dunn test is that it is relatively conservative and may increase the risk of Type II errors (i.e., incorrectly accepting a false null hypothesis) when the amount of data is large. Therefore, we set the reported corrected P value (the probability of observing the current result or a more extreme result under the premise that the null hypothesis is true) greater than 1 as 1. This was performed to maintain the accuracy of statistical analysis and the legitimacy of probability, and reduce the probability of Type II errors. When the distance between the average ranks exceeds the following critical difference (cd), we consider DLILC-LDL to have the same performance as that of a comparison algorithm.