[PYTHON] Laplacian eigenmaps with Scikit-learn (personal notes)

References

• [Machine learning learned from illustrations, focusing on discriminative model learning by least squares (KS Information Science Specialized Book)](href = "http://www.amazon.co.jp/gp/product/4061538217/ref=as_li_qf_sp_asin_tl" ? ie = UTF8 & camp = 247 & creative = 1211 & creativeASIN = 4061538217 & linkCode = as2 & tag = shimashimao06-22 ") <img src =" http://ir-jp.amazon-adsystem.com/e/ir?t=shimashimao06-22&l=as2&o=9&a = 4061538217 "width =" 1 "height =" 1 "border =" 0 "alt =" "style =" border: none! Important; margin: 0px! Important; "/>
• scikit-learn official: 2.2. Manifold learning
• scikit-learn official: sklearn.manifold.SpectralEmbedding
• scikit-learn official-example: sklearn.manifold.SpectralEmbedding

Reference code

Embed a roll cake in a two-dimensional subspace.

python

# codeing: utf-8

import numpy as np
from numpy.random import uniform
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

from sklearn import manifold

n=1000
k=10

a=np.array(3*np.pi*uniform(0,1,n), dtype=np.float64)
x = np.vstack((a*np.cos(a), 30*uniform(0,1,n), a*np.sin(a)))

fig = plt.figure()
ax = Axes3D(fig)
ax.scatter(x[0,:],x[1,:],x[2,:], c=x[0,:]+x[2,:])
plt.show()

embedder = manifold.SpectralEmbedding(n_components=2, random_state=0, n_neighbors=k,
                                      eigen_solver="arpack")
x_se = embedder.fit_transform(x.T)

plt.scatter(x_se[:,0],x_se[:,1], c=x_se[:,0]+x_se[:,1])
plt.show()

Output result

3D roll cake

2D roll cake