

In [8]:

    
import numpy as np
import matplotlib.pylab as plt
import numpy.random as npr
%matplotlib inline

Setting:

We have a set of datapoints $\mathcal{D} = \{x_1,x_2,\dots,x_m \}$.
Some of them we know to be similar $\mathcal{S} = {(x_i,x_j) |



In [41]:

    
from sklearn import datasets
X,Y = datasets.make_moons(100,noise=0.05)









    



/Users/joshuafass/anaconda/lib/python3.4/site-packages/sklearn/datasets/samples_generator.py:612: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
  y = np.hstack([np.zeros(n_samples_in, dtype=np.intp),



In [42]:

    
plt.scatter(X[:,0],X[:,1],c=Y)









    Out[42]:





<matplotlib.collections.PathCollection at 0x111688160>



In [43]:

    
D = X



In [44]:

    
S = set()
S.add(1)
S









    Out[44]:





{1}



In [45]:

    
#S = set()
S = np.zeros((len(X),len(X)))
for i in range(len(X)):
    for j in range(i):
        if Y[i]==Y[j]:
            #S.add((i,j))
            S[i,j] = 1



In [46]:

    
plt.imshow(S,interpolation='none')









    Out[46]:





<matplotlib.image.AxesImage at 0x111744fd0>



In [46]:



In [47]:

    
# learning diagonal metric
def g(A,S,D):
    ''' S given as a matrix?'''
    def d(x,y):
        return np.sqrt((x-y).T.dot(A).dot(x-y))
    
    first_comp = 0
    second_comp = 0
    for i in range(len(S)):
        for j in range(i):
            d_xy = d(D[i],D[j])
            if S[i,j]==1:
                first_comp += d_xy**2
            second_comp += d_xy
    return first_comp - np.log(second_comp)



In [48]:

    
def potential(A):
    return g(np.diag(A),S,D)



In [61]:

    
As = npr.rand(1000,2)*0.5



In [54]:

    
%timeit potential(As[0])









    



10 loops, best of 3: 37.7 ms per loop



In [62]:

    
ps = [potential(A) for A in As]



In [63]:

    
plt.scatter(As[:,0],As[:,1],c=ps,linewidths=0)
plt.colorbar()









    Out[63]:





<matplotlib.colorbar.Colorbar at 0x111e7eba8>



In [64]:

    
np.min(ps),np.max(ps)









    Out[64]:





(16.728475121361406, 1501.296383120022)



In [65]:

    
np.argmin(ps)









    Out[65]:





925



In [66]:

    
As[np.argmin(ps)]









    Out[66]:





array([ 0.00142986,  0.03807666])



In [ ]: