I want to apply multi-dimensional scaling (MDS) on specific objects; using the Euclidean distance does not make sense for such objects; using another distance metric, I can compute their dissimilarity matrix $D$. Then I compute the embeddings of the objects in dimension 2 with MDS using sklearn:
import numpy as np
import matplotlib.pyplot as plt
from sklearn.manifold import MDS
D = np.array( [ [ 0., 87., 175., 264. ],
[ 87., 0., 87., 175. ],
[ 175., 87., 0., 87. ],
[ 264., 175., 87., 0. ] ])
L = [ "1", "2", "3", "4" ]
embedding = MDS(n_components=2, dissimilarity = "precomputed", random_state = 1235)
X_transformed = embedding.fit_transform(D)
X_transformed.shape
fig = plt.figure( figsize=(10,10), facecolor="white")
ax = fig.add_subplot(1,1,1)
ax.scatter(D[:,0], D[:,1], s = 80)
for i, label in enumerate(L):
ax.annotate(label, (D[i,0]+10,D[i,1]) )
ax.set_aspect("equal")
fig.set_tight_layout(True)
plt.show()
It is obvious from the form of $D$ that all points must be aligned and ordered. However, I get
The point 1 is not correctly positioned. How can I remedy this ? thanks for any hint.
