问题描述
我有一个形状为（batch_size，number_maps，x_val，y_val）的火炬张量。张量通过S型函数进行归一化，因此在[0,1]范围内。我想找到每个贴图的协方差，所以我想要一个具有形状的张量（batch_size，number_maps，2、2）。据我所知，没有numpy中的torch.cov()函数。如何在不将其转换为numpy的情况下有效地计算协方差？
编辑：
def get_covariance(tensor):
bn,nk,w,h = tensor.shape
tensor_reshape = tensor.reshape(bn,2,-1)
x = tensor_reshape[:,:,:]
y = tensor_reshape[:,1,:]
mean_x = torch.mean(x,dim=2).unsqueeze(-1)
mean_y = torch.mean(y,dim=2).unsqueeze(-1)
xx = torch.sum((x - mean_x) * (x - mean_x),dim=2).unsqueeze(-1) / (h*w - 1)
xy = torch.sum((x - mean_x) * (y - mean_y),dim=2).unsqueeze(-1) / (h*w - 1)
yx = xy
yy = torch.sum((y - mean_y) * (y - mean_y),dim=2).unsqueeze(-1) / (h*w - 1)
cov = torch.cat((xx,xy,yx,yy),dim=2)
cov = cov.reshape(bn,2)
return cov
我现在尝试了以下操作，但是我很确定这是不正确的。
解决方法
您可以尝试在Github上建议的功能：
def cov(x,rowvar=False,bias=False,ddof=None,aweights=None):
"""Estimates covariance matrix like numpy.cov"""
# ensure at least 2D
if x.dim() == 1:
x = x.view(-1,1)
# treat each column as a data point,each row as a variable
if rowvar and x.shape[0] != 1:
x = x.t()
if ddof is None:
if bias == 0:
ddof = 1
else:
ddof = 0
w = aweights
if w is not None:
if not torch.is_tensor(w):
w = torch.tensor(w,dtype=torch.float)
w_sum = torch.sum(w)
avg = torch.sum(x * (w/w_sum)[:,None],0)
else:
avg = torch.mean(x,0)
# Determine the normalization
if w is None:
fact = x.shape[0] - ddof
elif ddof == 0:
fact = w_sum
elif aweights is None:
fact = w_sum - ddof
else:
fact = w_sum - ddof * torch.sum(w * w) / w_sum
xm = x.sub(avg.expand_as(x))
if w is None:
X_T = xm.t()
else:
X_T = torch.mm(torch.diag(w),xm).t()
c = torch.mm(X_T,xm)
c = c / fact
return c.squeeze()