[Sequence Alignment Methods] Smith–Waterman algorithm

Smith–Waterman algorithm

首先需要澄清一个事实，Smith–Waterman algorithm是求两个序列的最佳subsequence匹配，与之对应的算法但是求两个序列整体匹配的算法是Needleman-Wusch algorithm，即

　　Smith–Waterman algorithm：Local

　　Needleman-Wusch algorithm: Global

Needleman-Wusch algorithm与longest common subsequence (LCS)很相似，最大差别在于它给LCS中增、减、替换等操作赋予了不同的负权值，甚至不同的匹配对(a,a),(b,b)也有不同的正权值。可以这么说，Needleman-Wusch algorithm是改进的LCS算法。主要解决如下谁最优的问题：

首先，Needleman-Wusch algorithm需要一个Score Matrix（可以看成是一个离散的损失函数），用来表示不同匹配对的权值。

类似LCS，用动态规划求解，状态转移方程如下：

以上为Needleman-Wusch algorithm的步骤，计算局部的Smith–Waterman algorithm只需找到最大的M[i][j]，然后回溯即可，

时间： 2024-10-15 03:37:10

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