Parabola.ipynb

Kernel: Python 3 (old Anaconda 3)

import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
import seaborn as sns
sns.set()

x = np.linspace(-5, 5)
y = x ** 2
plt.scatter(x, y)
plt.axis('equal');

data = np.column_stack((x, y))
from scipy.spatial.distance import pdist, squareform
d = pdist(data)
d.shape

(1225,)

d = squareform(d)
d

array([[  0.        ,   2.00955668,   3.93625449, ...,  10.36005956,
          9.99783404,  10.        ],
       [  2.00955668,   0.        ,   1.92670729, ...,   9.58125762,
          9.59183673,   9.99783404],
       [  3.93625449,   1.92670729,   0.        , ...,   9.18367347,
          9.58125762,  10.36005956],
       ..., 
       [ 10.36005956,   9.58125762,   9.18367347, ...,   0.        ,
          1.92670729,   3.93625449],
       [  9.99783404,   9.59183673,   9.58125762, ...,   1.92670729,
          0.        ,   2.00955668],
       [ 10.        ,   9.99783404,  10.36005956, ...,   3.93625449,
          2.00955668,   0.        ]])

from sklearn.manifold import MDS
model = MDS(n_components=2, dissimilarity='precomputed')
out = model.fit_transform(d)
plt.scatter(out[:, 0], out[:, 1])
plt.axis('equal');

d = squareform(pdist(data, metric='cityblock'))
model = MDS(n_components=2, dissimilarity='precomputed')
out = model.fit_transform(d)
plt.scatter(out[:, 0], out[:, 1])
plt.axis('equal');