Table 2 Details of aggregation techniques
From: The stability of different aggregation techniques in ensemble feature selection
Aggregation Technique | Formula | Description |
|---|---|---|
Arithmetic Mean | \(\dfrac{a_1+a_2+\ldots +a_m}{m}\) | Calculates the average across importance scores and uses it to determine final aggregated score [36] |
Geometric Mean | \(\root m \of { a_1 a_2 \ldots a_m}\) | Calculates the geometric average across importance scores and uses it to determine final aggregated score [36] |
L2 Norm | \(\sqrt{a_1^2 +a_2^2 +\ldots +a_m^2}\) | Views the importance scores as an n-dimensional vector and calculates the Euclidean norm for that vector [36] |
Stuart | \(\begin{array}{c} {\text {Pr}}[X \le \rho ]=\\ 1- {\text {Pr}}[\hat{r}_{(1)} \le 1-\beta _{m, m}^{-1}(\rho )\\ , \ldots , \hat{r}_{(m)} \le 1-\beta _{m, 1}^{-1}(\rho )] \end{array}\) | Compares obtained rank vectors to a baseline of randomly ranked features then assigns the features significance scores using the beta distribution [26] |
RRA | \(\begin{array}{c} \rho (r)=\min _{k-1} \beta _{k, m}(r), \\ \beta _{k,m}(x):=\\ \sum _{\ell =k}^{m}\left( {\begin{array}{c}\ell \\ m\end{array}}\right) x^{\ell }(1-x)^{m-\ell } \end{array}\) | Similar to Stuart, but achieves efficiency & precision trade-off by using Bonferroni corrections [27] |