Suppose that I have two features: age and income.
I'm told that I need to normalize features before modeling with KNN. What's the difference between scaling to 0 and 1, taking a unit norm, or z score? I've been taught all of these to "normalize" data, but don't know how or why each apply.
RESCALING attribute data to values to scale the range in [0, 1] or [−1, 1] is useful for the optimization algorithms, such as gradient descent, that are used within machine learning algorithms that weight inputs (e.g. regression and neural networks). Rescaling is also used for algorithms that use distance measurements for example K-Nearest-Neighbors (KNN). Rescaling like this is sometimes called "normalization". MinMaxScaler class in python skikit-learn does this.
NORMALIZING attribute data is used to rescale components of a feature vector to have the complete vector length of 1. This is "scaling by unit length". This usually means dividing each component of the feature vector by the Euclidiean length of the vector but can also be Manhattan or other distance measurements. This pre-processing rescaling method is useful for sparse attribute features and algorithms using distance to learn such as KNN. Python scikit-learn Normalizer class can be used for this.
STANDARDIZING attribute data is also a preprocessing method but it assumes a Gaussian distribution of input features. It "standardizes" to a mean of 0 and a standard deviation of 1. This works better with linear regression, logistic regression and linear discriminate analysis. Python StandardScaler class in scikit-learn works for this.
