There are some field-specific reasons to do it as well. In text analysis, it is quite common to represent a text with the histogram of the words it contains. Starting from the count of words to the histogram is just raw standardization.

And the computational reason. If you are working with a sparse matrix, you cannot center and scale the data column by column easily. If you embed it in a dense matrix, the data can become too large to fit in memory. However, the scaling row by row does not affect the total amount of memory needed.

There are some field-specific reasons to perform row normalization. In text analysis, it is quite common to represent a text with the histogram of the words it contains. Starting from the count of words for each line, raw standardization turns it into an histogram.

And the computational reason. If you are working with a sparse matrix, you cannot center and scale the data column by column easily. If you embed it in a dense matrix, the data can become too large to fit in memory. However, the scaling row by row does not affect the total amount of memory needed.