Analyzing Topology Failures with Interlocking Links

In [1]:

import numpy as np
import pandas as pd
from distortions.geometry import Geometry, bind_metric, local_distortions

import numpy as np import pandas as pd from distortions.geometry import Geometry, bind_metric, local_distortions

In [2]:

import math
    
def rotate(x, y, z):
    u = x
    cos_val = math.cos(0.4)
    sin_val = math.sin(0.4)
    v = cos_val * y + sin_val * z
    w = -sin_val * y + cos_val * z
    return [u, v, w]

def link_data(n, offset=1):
    """
    https://github.com/kevinrobinson/umap-playground/blob/master/public/assets/demo-datas.js#L311
    """
    points = []
    for i in range(n):
        t = 2 * math.pi * i / n
        sin_t = math.sin(t)
        cos_t = math.cos(t)
        points.append(rotate(cos_t, sin_t, 0))
        points.append(rotate(offset + cos_t, 0, sin_t))
    
    return np.array(points)

import math def rotate(x, y, z): u = x cos_val = math.cos(0.4) sin_val = math.sin(0.4) v = cos_val * y + sin_val * z w = -sin_val * y + cos_val * z return [u, v, w] def link_data(n, offset=1): """ https://github.com/kevinrobinson/umap-playground/blob/master/public/assets/demo-datas.js#L311 """ points = [] for i in range(n): t = 2 * math.pi * i / n sin_t = math.sin(t) cos_t = math.cos(t) points.append(rotate(cos_t, sin_t, 0)) points.append(rotate(offset + cos_t, 0, sin_t)) return np.array(points)

In [3]:

from anndata import AnnData
import scanpy as sc

M = 100
n_neighbors = 50
data = link_data(M)

adata = AnnData(X=data, obs=pd.DataFrame(range(2 * M)))
sc.pp.neighbors(adata, n_neighbors=50)
sc.tl.umap(adata)
embedding = adata.obsm["X_umap"].copy()

from anndata import AnnData import scanpy as sc M = 100 n_neighbors = 50 data = link_data(M) adata = AnnData(X=data, obs=pd.DataFrame(range(2 * M))) sc.pp.neighbors(adata, n_neighbors=50) sc.tl.umap(adata) embedding = adata.obsm["X_umap"].copy()

In [4]:

radius = 3 * np.mean(adata.obsp["distances"].data)
geom = Geometry("brute", laplacian_method="geometric", affinity_kwds={"radius": radius}, adjacency_kwds={"n_neighbors": n_neighbors}, laplacian_kwds={"scaling_epps": 5})
H, Hvv, Hs = local_distortions(embedding, data, geom)
embedding = bind_metric(embedding, Hvv, Hs)
embedding["x_orig"] = data[:, 0]

radius = 3 * np.mean(adata.obsp["distances"].data) geom = Geometry("brute", laplacian_method="geometric", affinity_kwds={"radius": radius}, adjacency_kwds={"n_neighbors": n_neighbors}, laplacian_kwds={"scaling_epps": 5}) H, Hvv, Hs = local_distortions(embedding, data, geom) embedding = bind_metric(embedding, Hvv, Hs) embedding["x_orig"] = data[:, 0]

In [5]:

from distortions.geometry import neighborhoods
from distortions.visualization import dplot

N = neighborhoods(adata, threshold=0.01, outlier_factor=2)
dplot(embedding, width=900, height=500)\
    .mapping(x="embedding_0", y="embedding_1", color="x_orig")\
    .inter_edge_link(N=N, threshold=1)\
    .geom_ellipse()\
    .scale_color()

from distortions.geometry import neighborhoods from distortions.visualization import dplot N = neighborhoods(adata, threshold=0.01, outlier_factor=2) dplot(embedding, width=900, height=500)\ .mapping(x="embedding_0", y="embedding_1", color="x_orig")\ .inter_edge_link(N=N, threshold=1)\ .geom_ellipse()\ .scale_color()

Out[5]:

dplot(dataset=[{'embedding_0': 9.539716720581055, 'embedding_1': 3.1580326557159424, 'x0': -0.8638632514305921…

In [6]:

plots = []
for offset in np.linspace(0.5, 2.5, 5):

    data = link_data(M, offset=offset)
    adata = AnnData(X=data, obs=pd.DataFrame(range(2 * M)))
    sc.pp.neighbors(adata, n_neighbors=50)
    sc.tl.umap(adata)
    embedding = adata.obsm["X_umap"].copy()

    H, Hvv, Hs = local_distortions(embedding, data, geom)
    embedding = bind_metric(embedding, Hvv, Hs)
    embedding["x_orig"] = data[:, 0]

    N = neighborhoods(adata, threshold=0.2, outlier_factor=2)
    metrics = {k: H[k] for k in range(len(H))}
    plots += [dplot(embedding, width=400, height=400)\
        .mapping(x="embedding_0", y="embedding_1", color="x_orig")\
        .geom_ellipse()\
        .inter_edge_link(N=N, threshold=1)\
        .labs(title=f"{offset} Units Apart")\
        .scale_color()]

plots = [] for offset in np.linspace(0.5, 2.5, 5): data = link_data(M, offset=offset) adata = AnnData(X=data, obs=pd.DataFrame(range(2 * M))) sc.pp.neighbors(adata, n_neighbors=50) sc.tl.umap(adata) embedding = adata.obsm["X_umap"].copy() H, Hvv, Hs = local_distortions(embedding, data, geom) embedding = bind_metric(embedding, Hvv, Hs) embedding["x_orig"] = data[:, 0] N = neighborhoods(adata, threshold=0.2, outlier_factor=2) metrics = {k: H[k] for k in range(len(H))} plots += [dplot(embedding, width=400, height=400)\ .mapping(x="embedding_0", y="embedding_1", color="x_orig")\ .geom_ellipse()\ .inter_edge_link(N=N, threshold=1)\ .labs(title=f"{offset} Units Apart")\ .scale_color()]

In [7]:

[display(p) for p in plots]

[display(p) for p in plots]

dplot(dataset=[{'embedding_0': 3.289219617843628, 'embedding_1': 13.244303703308105, 'x0': -0.6242006037121905…

dplot(dataset=[{'embedding_0': 9.539716720581055, 'embedding_1': 3.1580326557159424, 'x0': -0.8638632514305921…

dplot(dataset=[{'embedding_0': 12.08263111114502, 'embedding_1': 9.085368156433105, 'x0': -0.4536952649302679,…

dplot(dataset=[{'embedding_0': 0.22946549952030182, 'embedding_1': 0.14115360379219055, 'x0': -0.5723637280364…

dplot(dataset=[{'embedding_0': 7.340658664703369, 'embedding_1': 4.244654655456543, 'x0': -0.8520414657269931,…

Out[7]:

[None, None, None, None, None]