CODEWITHSUNDEEP
numpylinear-algebraword2vec
Jay Qadan
Jay Qadan

Reputation: 87

How to add magnitude or value to a vector in Python?

I am using this function to calculate distance between 2 vectors a,b, of size 300, word2vec, I get the distance between 'hot' and 'cold' to be equal 1.

How to add this value (1) to a vector, becz i thought simply new_vec=model['hot']+1, but when I do the calc dist(new_vec,model['hot'])=17? 

import numpy
def dist(a,b):
  return numpy.linalg.norm(a-b)


a=model['hot']
c=a+1
dist(a,c)

17

I expected dist(a,c) will give me back 1!

Upvotes: 0

Views: 2038

Answers (1)

nick
nick

Reputation: 1350

You should review what the norm is. In the case of numpy, the default is to use the L-2 norm (a.k.a the Euclidean norm). When you add 1 to a vector, the call is to add 1 to all of the elements in the vector.

>> vec1 = np.random.normal(0,1,size=300)
>> print(vec1[:5])
... [ 1.18469795  0.04074346 -1.77579852  0.23806222  0.81620881]

>> vec2 = vec1 + 1
>> print(vec2[:5])
... [ 2.18469795  1.04074346 -0.77579852  1.23806222  1.81620881]

Now, your call to norm is saying sqrt( (a1-b1)**2 + (a2-b2)**2 + ... + (aN-bN)**2 ) where N is the length of the vector and a is the first vector and b is the second vector (and ai being the ith element in a). Since (a1-b1)**2 == (a2-b2)**2 == ... == (aN-bN)**2 == 1 we expect this sum to produce N which in your case is 300. So sqrt(300) = 17.3 is the expected answer. 

>> print(np.linalg.norm(vec1-vec2))
... 17.320508075688775

To answer the question, "How to add a value to a vector": you have done this correctly. If you'd like to add a value to a specific element then you can do vec2[ix] += value where ix indexes the element that you wish to add. If you want to add a value uniformly across all elements in the vector that will change the norm by 1, then add np.sqrt(1/300).

Also possibly relevant is a more commonly used distance metric for word2vec vectors: the cosine distance which measures the angle between two vectors.

Upvotes: 2

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