An illustration of the metric and non-metric MDS on generated noisy data.
The reconstructed points using the metric MDS and non metric MDS are slightly shifted to avoid overlapping.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 | # Author: Nelle Varoquaux <nelle.varoquaux@gmail.com># License: BSDprint(__doc__)import numpy as npfrom matplotlib import pyplot as pltfrom matplotlib.collections import LineCollectionfrom sklearn import manifoldfrom sklearn.metrics import euclidean_distancesfrom sklearn.decomposition import PCAn_samples = 20seed = 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 dataX_true -= X_true.mean()similarities = euclidean_distances(X_true)# Add noise to the similaritiesnoise = np.random.rand(n_samples, n_samples)noise = noise + noise.Tnoise[np.arange(noise.shape[0]), np.arange(noise.shape[0])] = 0similarities += noisemds = 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)# Rescale the datapos *= np.sqrt((X_true ** 2).sum()) / np.sqrt((pos ** 2).sum())npos *= np.sqrt((X_true ** 2).sum()) / np.sqrt((npos ** 2).sum())# Rotate the dataclf = PCA(n_components=2)X_true = clf.fit_transform(X_true)pos = clf.fit_transform(pos)npos = clf.fit_transform(npos)fig = plt.figure(1)ax = plt.axes([0., 0., 1., 1.])s = 100plt.scatter(X_true[:, 0], X_true[:, 1], color='navy', s=s, lw=0, label='True Position')plt.scatter(pos[:, 0], pos[:, 1], color='turquoise', s=s, lw=0, label='MDS')plt.scatter(npos[:, 0], npos[:, 1], color='darkorange', s=s, lw=0, label='NMDS')plt.legend(scatterpoints=1, loc='best', shadow=False)similarities = similarities.max() / similarities * 100similarities[np.isinf(similarities)] = 0# Plot the edgesstart_idx, end_idx = np.where(pos)# a sequence of (*line0*, *line1*, *line2*), where::# linen = (x0, y0), (x1, y1), ... (xm, ym)segments = [[X_true[i, :], X_true[j, :]] for i in range(len(pos)) for j in range(len(pos))]values = np.abs(similarities)lc = LineCollection(segments, zorder=0, cmap=plt.cm.Blues, norm=plt.Normalize(0, values.max()))lc.set_array(similarities.flatten())lc.set_linewidths(0.5 * np.ones(len(segments)))ax.add_collection(lc)plt.show() |
Total running time of the script: (0 minutes 0.176 seconds)
Download Python source code:
plot_mds.py
Download IPython notebook:
plot_mds.ipynb
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