I read today about Feature Scaling and that it is essential to make some of the Machine Learning algorithms work efficiently. It was calculated as (x - x min)/(range x). So I wanted to ask -- wouldn't this change the Column space of the matrix? So we're projecting the vector on a different matrix? Why didn't we just divide it by the maximum value of x or Range of x so that the column space does not change? Thanks!
Wouldn't Feature Scaling in Machine Learning change the Column space of the matrix?
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linear-algebra
machine-learning
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1$\dfrac{x_i - x_{\min{}}}{\text{range}(x)}$ gives values between $0$ and $1$, while $\dfrac{x_i}{\text{range}(x)}$ gives values which are equivalent except for the addition of an arbitrary constant. In many machine learning algorithms this may make no difference to the outcome (except possibly some precision issues if the constant is very large) – 2017-01-15
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0@Henry Thanks for the explanation – 2017-01-16
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A min-max scaler ensures that different features are scaled to the same range. A max-abs scaler scales each feature by its maximum absolute value. A standard scaler standardize features by removing the mean and scaling to unit variance. A robust scaler scales features using statistics that are robust to outliers. For more information, have a look at: http://scikit-learn.org/stable/modules/preprocessing.html