U型代价函数的分枝定界特征选择算法
A branch-and-bound feature selection algorithm for U-shaped cost functions
摘要：
本文提出了一个具有下列特征的组合优化问题的公式：（1）搜索空间是布尔格结构的有限集的幂集;（2）当应用于任意格链时，代价函数形成U形曲线。该公式适用于模式识别背景下的特征选择。已知的解决这个问题的方法是分支定界算法和启发式算法，它们部分地探索搜索空间。分支定界算法等价于全搜索，而启发式算法则不是。本文提出了一种分枝定界算法，它通过探索搜索空间的格结构和U形链曲线而不同于其他已知算法。本文的主要贡献是该算法的架构，是基于表示和探索的搜索空间的新格属性证明这里。几个实验，众所周知的公共数据，表明该方法的优越性SFFS，这是一个流行的启发式，在很短的计算时间内给出了良好的结果。在所有的实验中，所提出的方法得到了更好的或相同的结果在相似的或更小的计算时间。
英文摘要：
This paper presents the formulation of a combinatorial optimization problem with the following characteristics: i.the search space is the power set of a finite set structured as a Boolean lattice; ii.the cost function forms a U-shaped curve when applied to any lattice chain. This formulation applies for feature selection in the context of pattern recognition. The known approaches for this problem are branch-and-bound algorithms and heuristics, that explore partially the search space. Branch-and-bound algorithms are equivalent to the full search, while heuristics are not. This paper presents a branch-and-bound algorithm that differs from the others known by exploring the lattice structure and the U-shaped chain curves of the search space. The main contribution of this paper is the architecture of this algorithm that is based on the representation and exploration of the search space by new lattice properties proven here. Several experiments, with well known public data, indicate the superiority of the proposed method to SFFS, which is a popular heuristic that gives good results in very short computational time. In all experiments, the proposed method got better or equal results in similar or even smaller computational time.
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