Spearman’s correlation介绍
斯皮尔曼等级相关(Spearman’s correlation coefficient for ranked data)主要用于解决名称数据和顺序数据相关的问题。适用于两列变量,而且具有等级变量性质具有线性关系的资料。由英国心理学家、统计学家斯皮尔曼根据积差相关的概念推导而来,一些人把斯皮尔曼等级相关看做积差相关的特殊形式。
公式如下:
Pytorch实现
矩阵运算实现,运行简便快捷,变量名字可自行替换。输入logits即可
def compute_rank_correlation(att, grad_att):
"""
Function that measures Spearman’s correlation coefficient between target logits and output logits:
att: [n, m]
grad_att: [n, m]
"""
def _rank_correlation_(att_map, att_gd):
n = torch.tensor(att_map.shape[1])
upper = 6 * torch.sum((att_gd - att_map).pow(2), dim=1)
down = n * (n.pow(2) - 1.0)
return (1.0 - (upper / down)).mean(dim=-1)
att = att.sort(dim=1)[1]
grad_att = grad_att.sort(dim=1)[1]
correlation = _rank_correlation_(att.float(), grad_att.float())
return correlation
Numpy实现
这里调用函数前,请保证输入的maps都已经转成了rank的形式
def rank_correlation(att_map, att_gd):
"""
Function that measures Spearman’s correlation coefficient between target and output:
"""
n = att_map.shape[1]
upper = 6 *np.sum(np.square(att_gd - att_map), axis=-1)
down = n*(np.square(n)-1)
return np.mean(1 - (upper/down))