Vector Convolution is a special operation for vector. In this tutorial, we will use some simple examples to illustrate it for deep learning beginners.
What is vector convolution?
As to n dimension vector A and B
A = [a0, a1, a2, …, an-1]
B = [b0, b1, b2, …, bn-1]
The convolution of f(A,B) is C:
C = [c0, c1, …, c2n-2]
where
From the equation above, we can find:
- The dimension of vector A and B must be the same.
- The dimension of result C is 2n-1
We can understand the vector C as following:
Here is an example.
A = [1,2,3,4] B = [2,3,4,5]
Here vector A and B is 4 dimension. It means the dimension of convolutional C is 2 * 4 – 1 = 7.
A * BT =
[2, 3, 4, 5 4, 6, 8, 10 6, 9, 12, 15 8, 12, 16, 20]
c0 = 2
c1 = 3 + 4 = 7
c2 = 4 + 6 + 6 = 16
c3 = 5 + 8 + 9 + 8 = 30
c4 = 10 + 12 + 12 = 34
c5 = 15 + 16 = 31
c6 = 20
It menas C is:
[2,7,16,30,34,31,20]