Why do row normalization instead of column normalization？ about pygcn HOT 2 OPEN

This depends on how you arrange the data. e.g. data matrix D, D could be arranged as [# of data, data dimension], and D^T is [data dimension, # of data]. So, some do row normalization, and some use column normalization.

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I was wondering the same thing when I first studied graph neural networks. I believe this is mainly due to the dataset's inputs. Cora uses one-hot bag-of-words as input features. Therefore the input features are very sparse and only have 1 and 0. The first linear layer will effectively act like an embedding layer nn.Embedding(), learn an embedding vector for each word in the one-hot input features. Without row normalization, effectively it is a sum of embeddings, thus the magnitude (after the first layer) can vary widely among the samples. With row normalization, effectively it is an average of embeddings, therefore preserving the magnitude among the samples. I have tried training a GCN model on Cora without row-normalization, and it performs poorly.

Hope it helps. I do realize this kind of thing is rarely mentioned anywhere, so I hope this is a logical explanation.

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