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WOLFRAM NOTEBOOK
Manifold Learning
Manifold Learning
Example dataset
Example dataset
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import matplotlib.pyplot as plt
import seaborn as sns; sns.set()
import numpy as np
import seaborn as sns; sns.set()
import numpy as np
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def make_hello(N=1000, rseed=42):
# Make a plot with "HELLO" text; save as PNG
fig, ax = plt.subplots(figsize=(4, 1))
fig.subplots_adjust(left=0, right=1, bottom=0, top=1)
ax.axis('off')
ax.text(0.5, 0.4, 'HELLO', va='center', ha='center', weight='bold', size=85)
fig.savefig('hello.png')
plt.close(fig)
# Open this PNG and draw random points from it
from matplotlib.image import imread
data = imread('hello.png')[::-1, :, 0].T
rng = np.random.RandomState(rseed)
X = rng.rand(4 * N, 2)
i, j = (X * data.shape).astype(int).T
mask = (data[i, j] < 1)
X = X[mask]
X[:, 0] *= (data.shape[0] / data.shape[1])
X = X[:N]
return X[np.argsort(X[:, 0])]
# Make a plot with "HELLO" text; save as PNG
fig, ax = plt.subplots(figsize=(4, 1))
fig.subplots_adjust(left=0, right=1, bottom=0, top=1)
ax.axis('off')
ax.text(0.5, 0.4, 'HELLO', va='center', ha='center', weight='bold', size=85)
fig.savefig('hello.png')
plt.close(fig)
# Open this PNG and draw random points from it
from matplotlib.image import imread
data = imread('hello.png')[::-1, :, 0].T
rng = np.random.RandomState(rseed)
X = rng.rand(4 * N, 2)
i, j = (X * data.shape).astype(int).T
mask = (data[i, j] < 1)
X = X[mask]
X[:, 0] *= (data.shape[0] / data.shape[1])
X = X[:N]
return X[np.argsort(X[:, 0])]
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X = make_hello(1000)
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from sklearn.metrics import pairwise_distances
D = pairwise_distances(X)
D = pairwise_distances(X)
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exampleDistanceMatrix=Normal[ExternalValue["Python","D"]];
Code
Code
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getCoordinates[distanceMatrix : {___ : {___Real}}, dimensions_Integer] := Normal @ ExternalEvaluate["Python", "Prolog" "from sklearn.manifold import MDSdef manifoldPoints(dim, D): model = MDS(n_components=dim, dissimilarity='precomputed', random_state=1) return model.fit_transform(D)", <| "Command" "manifoldPoints", "Arguments" {dimensions, NumericArray[distanceMatrix, "Real64"]}|>]
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result=getCoordinates[exampleDistanceMatrix,2];
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ListPlot[result,AspectRatioAutomatic]
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With SetReplace
With SetReplace
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<<SetReplace`
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system=SetSubstitutionSystem[FromAnonymousRules[{{0,1},{0,2},{0,3}}{{4,5},{5,4},{4,6},{6,4},{5,6},{6,5},{4,1},{5,2},{6,3},{1,6},{3,4}}],{{0,0},{0,0},{0,0}},6]
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graph=CanonicalGraph@SimpleGraph@Graph[UndirectedEdge@@@system[-1]]
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graphDistanceMatrix=GraphDistanceMatrix[graph];
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graphCoordinates2=getCoordinates[graphDistanceMatrix,2];
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Graphics[(Line@*List)@@@(graphCoordinates2〚#〛&/@List@@@EdgeList[graph])]
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graphCoordinates3=getCoordinates[graphDistanceMatrix,3];
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Graphics3D[(Line@*List)@@@(graphCoordinates3〚#〛&/@List@@@EdgeList[graph])]
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system=SetSubstitutionSystem[FromAnonymousRules[{{0,1},{0,2},{0,3}}{{4,5},{5,4},{4,6},{6,4},{5,6},{6,5},{4,1},{5,2},{6,3},{1,6},{3,4}}],{{0,0},{0,0},{0,0}},7]
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graph=CanonicalGraph@SimpleGraph@Graph[UndirectedEdge@@@system[-1]]
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graphDistanceMatrix=GraphDistanceMatrix[graph];
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graphCoordinates2=getCoordinates[graphDistanceMatrix,2];