python对相关性分析的作用,python分析时间序列相关性

文章目录 Spearman’s correlation介绍Pytorch实现Numpy实现

Spearman’s correlation介绍

内向的板凳等级相关（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、统计学家内向的板凳根据积差相关的概念推导而来，一些人把内向的板凳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))