1D Convolution in Neural Networks I understand how convolution works but I don't get how 1D convolutions are applied to 2D data.

In this example you can see a 2D convolution in a 2D data.
But how it would be if was a 1D convolution?
Just a 1D kernel sliding in the same way? And if the stride was 2? 
Thank you!
 A: Let $x_1, …,x_n $ be a sequence of vectors (e.g., word vectors). Applying a convolutional layer is equivalent to applying the same weight matrices to all n-grams, where $n$ is the height of your filter. E.g., if $n=3$, you can visualize it as follows:

For a slightly more mathematical explanation, you can check out 
Ji Young Lee, Franck Dernoncourt. "Sequential Short-Text Classification with Recurrent and Convolutional Neural Networks". NAACL 2016. section 2.1.2:

A: 1D convolutions are used in convolutional networks for down sampling and up sampling in the filter dimension. Convolutional networks build up these filter maps as you go through the network, you can really think of them as a 3rd dimension. The usual base case of the filter map dimension is a size of 3, since we will often have RGB images going through our network. 
These 1D convolutions can be useful for down sampling, performing some operation, then up sampling back to the same dimension. This is quite useful for performance reasons.
To really intuitively understand I'd suggest reading: 
Network-in-network - http://arxiv.org/abs/1312.4400
Going deeper with convolutions - https://www.google.com/url?sa=t&source=web&rct=j&url=http://www.cs.unc.edu/~wliu/papers/GoogLeNet.pdf&ved=0ahUKEwi89oeuxqnLAhXhuIMKHZrTCe0QFggkMAE&usg=AFQjCNGCEEnUgrgCn-rrECNQ72wI3PH1Qw&sig2=VhjfaMvuskNIDVKhFfNiqQ
