In [1]:
import numpy as np
import pandas as pd
from matplotlib import pyplot as plt
from matplotlib.collections import LineCollection
from sklearn import manifold
from sklearn.metrics import euclidean_distances
from sklearn.decomposition import PCA
n_samples = 20
seed = np.random.RandomState(seed=3)
X_true = seed.randint(0, 20, 2 * n_samples).astype(np.float)
X_true = X_true.reshape((n_samples, 2))
# Center the data
X_true -= X_true.mean()
similarities = euclidean_distances(X_true)
pd.DataFrame(similarities)
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In [2]:
mds = manifold.MDS(n_components=2, max_iter=3000, eps=1e-9, random_state=seed,
dissimilarity="precomputed", n_jobs=1)
pos = mds.fit(similarities).embedding_
nmds = manifold.MDS(n_components=2, metric=False, max_iter=3000, eps=1e-12,
dissimilarity="precomputed", random_state=seed, n_jobs=1,
n_init=1)
npos = nmds.fit_transform(similarities, init=pos)
dissimilarity="precomputed"表示输入的是已经计算好的距离矩阵
metric=False表示是分类数据，metric=True表示是连续数据
In [3]:
mds.stress_#压力值，可以用来计算应当降为多少维
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In [4]:
# Rescale the data
pos *= np.sqrt((X_true ** 2).sum()) / np.sqrt((pos ** 2).sum())
npos *= np.sqrt((X_true ** 2).sum()) / np.sqrt((npos ** 2).sum())
In [5]:
# Rotate the data
pca = PCA(n_components=2)
X_true = pca.fit_transform(X_true)
pos = pca.fit_transform(pos)
npos = pca.fit_transform(npos)
In [6]:
fig = plt.figure(1)
ax = plt.axes([0., 0., 1., 1.])
s = 100
plt.scatter(X_true[:, 0], X_true[:, 1], color='navy', s=s, lw=0,
label='True Position')
plt.show()
In [7]:
plt.scatter(pos[:, 0], pos[:, 1], color='turquoise', s=s, lw=0, label='MDS')
plt.show()
In [8]:
plt.scatter(npos[:, 0], npos[:, 1], color='darkorange', s=s, lw=0, label='NMDS')
plt.show()
