Convolution only works on data that is spatially related, meaning data points that are close to each other are more related than data points that are far apart.

Convolution only works on data that is spatially related, meaning data points that are close to each other are more related than data points that are far apart. It doesn't give meaningful results on data like spreadsheets where columns or rows can be rearranged without corrupting the underlying information. If by non-image data you mean something like audio, then yes it could probably work.