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By scaling features, we can prevent one feature from dominating the decisions of a model. For example, say heights (cm), and age (years) are two features in my data. Since range of heights is larger than of years, a trained model could weight importance of heights much more than years. This could result in a poor model in return.

However, say that all of my features are binary, they take a value of either 0 or 1. In such a case, does feature scaling still have any benefits?

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If all you features are binary, then, you don't need to apply normalization on them. Since their values are on the same scale already.

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