Calculate inverse document frequency

Question

Im am following this excellent tutorial to get a better grasp on the concept of tv-idf: http://blog.christianperone.com/2011/10/machine-learning-text-feature-extraction-tf-idf-part-ii/

Everything is clear till the final part where this data has to be normalized;

Mtf-idf = [(0,0), (0.41,0.81), (0.41, 0.41), (0,0)]

This should lead to:

Mtf-idf = Mtf-idf/Mtfidf||2 = [(0,0), (0,71, 0.89), (0.71, 0.45), (0,0)]

Could anybody explain to me in plain English what is happening here?

Answer 1

It normalizing row as it said in text , it means sum of squares of rows must be 1 , so :

(0)^2 + (-0.41)^2 + (-0.41)^2 + (0)^2 = 0.34

to normalize the sum these numbers must be 1 so we calculate sqrt(1/0.34) = 1.71 then we multiple this coefficient to all rows ->

0 , -0.41*1.71 = -0.70, -0.41*1.71 = -0.70, 0

for second row -> sqrt(1/0.84)=1.09

0, 1.09*0.81 = -0.88, -0.41*1.09 = -0.45, 0