Two Types of Distortion in a Variable Density Swiss Roll

In [1]:

import numpy as np
from sklearn.manifold import TSNE
from baselines.scripts.variable_density_swiss_roll import non_uniform_swiss

import numpy as np from sklearn.manifold import TSNE from baselines.scripts.variable_density_swiss_roll import non_uniform_swiss

In [2]:

n_samples = 1500
noise = 0.0
random_state = 20251106
K = 2

n_samples = 1500 noise = 0.0 random_state = 20251106 K = 2

In [3]:

np.random.seed(random_state)
X, t = non_uniform_swiss(2, 1, 0.2, n_samples, pi0=0.25, K=K, dim=3)
rng = np.random.RandomState(random_state)
X_noisy = X + noise * rng.normal(size=X.shape)

np.random.seed(random_state) X, t = non_uniform_swiss(2, 1, 0.2, n_samples, pi0=0.25, K=K, dim=3) rng = np.random.RandomState(random_state) X_noisy = X + noise * rng.normal(size=X.shape)

In [4]:

tsne = TSNE(n_components=2, perplexity=50, random_state=random_state, learning_rate='auto')
X_emb = tsne.fit_transform(X_noisy)

tsne = TSNE(n_components=2, perplexity=50, random_state=random_state, learning_rate='auto') X_emb = tsne.fit_transform(X_noisy)

In [5]:

import pandas as pd
import altair as alt

df = pd.DataFrame({'x': X_emb[:, 0], 'y': X_emb[:, 1], 't': t })
alt.Chart(df)\
    .mark_circle(size=30)\
    .encode(
        x=alt.X('x', title='t-SNE 1'),
        y=alt.Y('y', title='t-SNE 2'),
        color=alt.Color('t:Q', title='unrolled coordinate', scale=alt.Scale(scheme='spectral')),
    )\
    .properties(title=f"t-SNE embedding of Swiss Roll (noise={noise})")

import pandas as pd import altair as alt df = pd.DataFrame({'x': X_emb[:, 0], 'y': X_emb[:, 1], 't': t }) alt.Chart(df)\ .mark_circle(size=30)\ .encode( x=alt.X('x', title='t-SNE 1'), y=alt.Y('y', title='t-SNE 2'), color=alt.Color('t:Q', title='unrolled coordinate', scale=alt.Scale(scheme='spectral')), )\ .properties(title=f"t-SNE embedding of Swiss Roll (noise={noise})")

Out[5]:

In [44]:

from distortions.geometry import Geometry, bind_metric, local_distortions, neighborhood_distances, neighborhoods
from distortions.visualization import dplot
from anndata import AnnData
from sklearn.neighbors import NearestNeighbors

n_neighbors = 40
adata = AnnData(X=X_noisy)
nn = NearestNeighbors(n_neighbors=n_neighbors, metric="euclidean").fit(X_noisy)
knn_graph = nn.kneighbors_graph(X_noisy, mode="distance")  # sparse CSR matrix
adata.obsp["distances"] = knn_graph
adata.obsm["X_tsne"] = X_emb

radius = 0.5 * np.mean(adata.obsp["distances"].data)
geom = Geometry(affinity_kwds={"radius": radius}, adjacency_kwds={"n_neighbors": n_neighbors})
H, Hvv, Hs = local_distortions(X_emb, X_noisy, geom)

embedding = bind_metric(X_emb, Hvv, Hs)
embedding["t"] = t

from distortions.geometry import Geometry, bind_metric, local_distortions, neighborhood_distances, neighborhoods from distortions.visualization import dplot from anndata import AnnData from sklearn.neighbors import NearestNeighbors n_neighbors = 40 adata = AnnData(X=X_noisy) nn = NearestNeighbors(n_neighbors=n_neighbors, metric="euclidean").fit(X_noisy) knn_graph = nn.kneighbors_graph(X_noisy, mode="distance") # sparse CSR matrix adata.obsp["distances"] = knn_graph adata.obsm["X_tsne"] = X_emb radius = 0.5 * np.mean(adata.obsp["distances"].data) geom = Geometry(affinity_kwds={"radius": radius}, adjacency_kwds={"n_neighbors": n_neighbors}) H, Hvv, Hs = local_distortions(X_emb, X_noisy, geom) embedding = bind_metric(X_emb, Hvv, Hs) embedding["t"] = t

In [47]:

distances = neighborhood_distances(adata, "X_tsne")
N = neighborhoods(adata, threshold=.2, outlier_factor=9, embed_key="X_tsne")

plot = dplot(embedding, height=400, width=600)\
    .mapping(x="embedding_0", y="embedding_1", color="t")\
    .geom_ellipse(radiusMin=1, radiusMax=25)\
    .inter_edge_link(N=N, strokeWidth=.2, opacity=0.9, threshold=10, stroke="#F25E7A", highlightColor="#C83F58", backgroundOpacity=0.6)\
    .inter_boxplot(dists=distances, outlier_iqr=10, highlightColor="#F25E7A", strokeWidth=0.4)

plot

distances = neighborhood_distances(adata, "X_tsne") N = neighborhoods(adata, threshold=.2, outlier_factor=9, embed_key="X_tsne") plot = dplot(embedding, height=400, width=600)\ .mapping(x="embedding_0", y="embedding_1", color="t")\ .geom_ellipse(radiusMin=1, radiusMax=25)\ .inter_edge_link(N=N, strokeWidth=.2, opacity=0.9, threshold=10, stroke="#F25E7A", highlightColor="#C83F58", backgroundOpacity=0.6)\ .inter_boxplot(dists=distances, outlier_iqr=10, highlightColor="#F25E7A", strokeWidth=0.4) plot

Out[47]:

dplot(dataset=[{'embedding_0': -13.072385787963867, 'embedding_1': -25.01403045654297, 'x0': -0.94523381485337…

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