Cross-Correlation

I was studying STAT206 and this word came up in my mind, and I thought it was just Correlation, but maybe not.

In Signal Processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other.

1D Cross-Correlation $y[n]={\sum }_{k}x[n+k]\cdot h[k]$

2D Convolution $y[i,j]={\sum }_m{\sum }_{n}x[i-m,j-n]\cdot h[m,n]$

In deep learning, since the kernel weights are learned, CNNs just use cross-correlation — flipping isn’t necessary because the network can learn flipped patterns if needed.

• I did not fully understand this https://chatgpt.com/share/6817c0d8-d760-8002-9eab-a5b9ccd8760b