#!/usr/bin/env python3
"""Measure how faithfully a 2-D/3-D embedding (UMAP, t-SNE, PCA) represents the original data.
Inputs: the high-dimensional CSV and the embedding CSV, same rows in the same order. Metrics:
trustworthiness (Venna & Kaski) are the embedding's k nearest neighbours also near in the original
space? 1.0 = no false neighbours (sklearn.manifold.trustworthiness)
continuity are original neighbours kept as neighbours? 1.0 = none torn apart
kNN preservation mean share of the k original neighbours found among the k embedding
neighbours
distance correlation Spearman correlation of pairwise distances (sampled pairs): global
structure; t-SNE and UMAP typically score low here by design
label checks (--label) k-NN classification accuracy (leave-one-out, majority of k) in the
original space vs in the embedding: a big gain in 2-D means the map
exaggerates separation; a big loss means it hides it
Original features are standardised (--no-scale to skip).
Usage:
python embedding_trust.py --high emb_high.csv --low emb_2d.csv --drop label --label label
python embedding_trust.py --high X.csv --low umap.csv --k 15 --max-rows 1000 --json
Exit codes: 0 computed, 2 usage error (row counts differ, no numeric columns).
"""
import argparse
import csv
import json
import math
import random
import sys
from collections import Counter
def num(v):
try:
x = float(v)
return x if math.isfinite(x) else None
except (TypeError, ValueError):
return None
def read(path, drop, label):
with open(path, newline="", encoding="utf-8-sig") as fh:
rd = csv.DictReader(fh)
header = rd.fieldnames or []
rows = list(rd)
cols = [c for c in header if c not in drop and c != label and all(num(r[c]) is not None for r in rows)]
return [[num(r[c]) for c in cols] for r in rows], ([r[label] for r in rows] if label and label in header else None), cols
def standardise(X):
d = len(X[0])
mu = [sum(x[j] for x in X) / len(X) for j in range(d)]
sd = [math.sqrt(sum((x[j] - mu[j]) ** 2 for x in X) / len(X)) or 1.0 for j in range(d)]
return [[(x[j] - mu[j]) / sd[j] for j in range(d)] for x in X]
def dist_matrix(X):
return [[math.sqrt(sum((a - b) ** 2 for a, b in zip(p, q))) for q in X] for p in X]
def rank_rows(D):
"""rank[i][j] = rank of j among i's neighbours (1 = nearest, self excluded)."""
n = len(D)
ranks = []
for i in range(n):
order = sorted((j for j in range(n) if j != i), key=D[i].__getitem__)
r = [0] * n
for pos, j in enumerate(order, 1):
r[j] = pos
ranks.append(r)
return ranks
def trust(rank_ref, rank_emb, k):
"""Venna-Kaski: penalise points in the emb k-NN that are far in the reference space."""
n = len(rank_ref)
pen = 0
for i in range(n):
for j in range(n):
if j != i and rank_emb[i][j] <= k and rank_ref[i][j] > k:
pen += rank_ref[i][j] - k
return 1 - 2 / (n * k * (2 * n - 3 * k - 1)) * pen
def spearman(a, b):
def rk(v):
o = sorted(range(len(v)), key=v.__getitem__)
r = [0.0] * len(v)
for p, i in enumerate(o):
r[i] = p
return r
ra, rb = rk(a), rk(b)
m = (len(a) - 1) / 2
cov = sum((x - m) * (y - m) for x, y in zip(ra, rb))
var = sum((x - m) ** 2 for x in ra)
return cov / var if var else 0.0
def knn_accuracy(rank, labels, k):
n = len(rank)
ok = 0
for i in range(n):
neigh = [j for j in range(n) if j != i and rank[i][j] <= k]
vote = Counter(labels[j] for j in neigh).most_common(1)[0][0]
ok += vote == labels[i]
return ok / n
def main():
ap = argparse.ArgumentParser(description="Trustworthiness and neighbourhood checks for embeddings.", epilog=__doc__,
formatter_class=argparse.RawDescriptionHelpFormatter)
ap.add_argument("--high", required=True)
ap.add_argument("--low", required=True)
ap.add_argument("--drop", nargs="*", default=[])
ap.add_argument("--label", help="label column (in either file) for k-NN accuracy checks")
ap.add_argument("--k", type=int, default=10)
ap.add_argument("--max-rows", type=int, default=800)
ap.add_argument("--no-scale", action="store_true")
ap.add_argument("--seed", type=int, default=0)
ap.add_argument("--json", action="store_true")
a = ap.parse_args()
try:
Xh, lab_h, ch = read(a.high, set(a.drop), a.label)
Xl, lab_l, cl = read(a.low, set(a.drop), a.label)
except OSError as e:
print(f"error: {e}", file=sys.stderr)
return 2
if len(Xh) != len(Xl) or not ch or not cl:
print(f"error: row counts differ ({len(Xh)} vs {len(Xl)}) or no numeric columns", file=sys.stderr)
return 2
labels = lab_h or lab_l
n = len(Xh)
idx = list(range(n))
if n > a.max_rows:
idx = sorted(random.Random(a.seed).sample(idx, a.max_rows))
Xh = [Xh[i] for i in idx]
Xl = [Xl[i] for i in idx]
labels = [labels[i] for i in idx] if labels else None
if not a.no_scale:
Xh = standardise(Xh)
k = min(a.k, len(Xh) // 4)
Dh, Dl = dist_matrix(Xh), dist_matrix(Xl)
Rh, Rl = rank_rows(Dh), rank_rows(Dl)
t = trust(Rh, Rl, k)
c = trust(Rl, Rh, k)
keep = sum(sum(1 for j in range(len(Xh)) if j != i and Rh[i][j] <= k and Rl[i][j] <= k) / k
for i in range(len(Xh))) / len(Xh)
rng = random.Random(a.seed)
pairs = [(rng.randrange(len(Xh)), rng.randrange(len(Xh))) for _ in range(min(20000, len(Xh) ** 2))]
pairs = [(i, j) for i, j in pairs if i != j]
dc = spearman([Dh[i][j] for i, j in pairs], [Dl[i][j] for i, j in pairs])
out = {"rows": len(Xh), "high_dims": len(ch), "low_dims": len(cl), "k": k, "trustworthiness": t,
"continuity": c, "knn_preservation": keep, "distance_spearman": dc}
if labels:
out["knn_accuracy_high"] = knn_accuracy(Rh, labels, k)
out["knn_accuracy_low"] = knn_accuracy(Rl, labels, k)
if a.json:
print(json.dumps(out, indent=2))
return 0
print(f"{len(Xh)} rows: {len(ch)}-D original vs {len(cl)}-D embedding, k = {k}")
print(f"trustworthiness {t:.3f} (false neighbours in the map; > 0.9 good, < 0.8 the map invents closeness)")
print(f"continuity {c:.3f} (original neighbours torn apart; > 0.9 good)")
print(f"kNN preservation {keep:.3f} (share of the {k} original neighbours kept)")
print(f"distance Spearman {dc:.3f} (global geometry; low values are normal for t-SNE/UMAP - do not read "
"distances between clusters)")
if labels:
hi, lo = out["knn_accuracy_high"], out["knn_accuracy_low"]
print(f"{k}-NN label accuracy: original {hi:.3f}, embedding {lo:.3f}" + (
" <- the map separates labels much more than the data does" if lo - hi > 0.1 else
" <- the map hides separation present in the data" if hi - lo > 0.1 else ""))
return 0
if __name__ == "__main__":
sys.exit(main())
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