Most feature selection methods identify only a single solution. This is acceptable for predictive purposes, but is not sufficient for knowledge discovery if multiple solutions exist. We propose a strategy to extend a class of greedy methods to efficiently identify multiple solutions, and show under which conditions it identifies all solutions. We also introduce a taxonomy of features that takes the existence of multiple solutions into account. Furthermore, we explore different definitions of statistical equivalence of solutions, as well as methods for testing equivalence. A novel algorithm for compactly representing and visualizing multiple solutions is also introduced. In experiments we show that (a) the proposed algorithm is significantly more computationally efficient than the TIE* algorithm, the only alternative approach with similar theoretical guarantees, while identifying similar solutions to it, and (b) that the identified solutions have similar predictive performance.

大多数特征选择方法仅识别单个解决方案。这对于预测目的是可以接受的，但如果存在多个解决方案，则不足以用于知识发现。我们提出了一种策略来扩展一类贪婪方法以有效识别多个解决方案，并显示它在哪些条件下识别所有解决方案。我们还介绍了一种特征分类法，该分类法考虑了多个解决方案的存在。此外，我们探索了解决方案统计等效性的不同定义，以及测试等效性的方法。还介绍了一种用于紧凑地表示和可视化多个解决方案的新算法。在实验中，我们表明 (a) 所提出的算法比 TIE* 算法的计算效率明显更高，