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Suppose I have a matrix compose of row as each observation, column as each property and I want to calculate the distance between each observation.

In this case I think I should normalize each column, instead of row, to a unit vector? I think that would make more sense since each column can have different unit. In contrast if I normalize it by rows to unit vectors, it will be dominated by the property that has larger average value.

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I think he is asking about feature normalization.

A good discussion already on stats.se: How and why do normalization and feature scaling work?

Also look at Prof. Ng.'s online course: week 2

In case you read Chinese, (I guessed from your username, apologies if you do not.)

read about a good blog post that have some study notes on that part of Prof. Ng.'s lecture.

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