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Generally if I want to normalize my data in which direction I should normalize (subtracting mean and dividing by std)?

Lets say I have a data matrix D (dxN, d-dimension of data, N - no of data) where each column represents a feature vector obtained from an image. In that case should I apply a column wise normalization (independently for each image) or should I normalize each feature type independently?

If I am correct, in k-means a column-wise normalization is applied but in SVMs a row-wise normalization is used. Why is that?

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Both types of normalization can be useful. Doing a column-wise normalization on each image can help correct for image illumination or other global image differences. Doing a row-wise normalization is useful to control how much weight is applied to each feature. As an example, you don't want the output of the clustering or the svm to depend on the units of measurement of your features. If one feature is for height and another for weight you don't want the output to differ depending on whether you use feet and pounds or inches and pounds.

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