vvs
100 lines
3.5 KiB
Python
100 lines
3.5 KiB
Python
"""Demo 1 - Iris boundary rediscovery (no training).
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The Iris dataset (Fisher 1936) contains 50 specimens of three species:
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setosa, versicolor, virginica. setosa is fully separable from the
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other two; versicolor and virginica overlap on petal geometry. Every
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classifier built on Iris since 1936 stumbles on the same handful of
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boundary specimens.
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We find them WITHOUT training a classifier:
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1. Group specimens by species.
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2. Auto-derive a kernel scale from the data's own geometry.
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3. Compute the (150, 3) similarity matrix.
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4. For each specimen, look at how strongly it scores on the
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species it is NOT labelled with. Highest cross-species score
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ranks the most ambiguous specimens.
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Run:
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python 01_iris_boundary.py
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"""
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from __future__ import annotations
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import numpy as np
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from sklearn.datasets import load_iris
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from sem_cython12 import wrapper as cy
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def main() -> int:
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if not cy.available():
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print("ERROR: sem_cython12 compiled extension did not load.")
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return 1
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iris = load_iris()
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X = iris.data # (150, 4)
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y = iris.target # (150,)
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species_names = iris.target_names
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# Auto-derived kernel scale (median pairwise distance over the
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# whole dataset; no human picks this number).
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pd = cy.pairwise_distances(X)
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iu = np.triu_indices(pd.shape[0], k=1)
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lam = float(np.median(pd[iu]))
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print(f"Auto-derived kernel scale lam = {lam:.4f}\n")
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# Per-species reference sets
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member_sets = [X[y == k] for k in range(3)]
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# (150, 3) similarity matrix
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S = cy.concept_support_matrix(X, member_sets, lam=lam)
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# For each specimen, compute the highest similarity to a species
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# OTHER than its own. A specimen with high cross-species support
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# is structurally ambiguous - close to a non-self species.
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cross_score = np.empty(150)
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for i in range(150):
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own = y[i]
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cross_score[i] = max(S[i, j] for j in range(3) if j != own)
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# Rank specimens by cross-species score. Top entries = the famous
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# boundary cases.
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order = np.argsort(cross_score)[::-1]
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print(f"Top 10 most ambiguous specimens (highest cross-species score):\n")
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print(f" {'rank':>4} {'idx':>4} {'species':>11} "
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f"{'sim->setosa':>12} {'sim->versic':>12} {'sim->virgin':>12} cross")
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for rank, idx in enumerate(order[:10], 1):
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sims = S[idx]
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own = species_names[y[idx]]
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print(f" {rank:>4} {idx:>4} {own:>11} "
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f"{sims[0]:>12.4f} {sims[1]:>12.4f} {sims[2]:>12.4f} {cross_score[idx]:.4f}")
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# Distribution of those top 10 by species
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top10_species = [int(y[i]) for i in order[:10]]
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counts = {0: 0, 1: 0, 2: 0}
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for s in top10_species:
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counts[s] += 1
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print()
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print("Top 10 distribution by species:")
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for k, name in enumerate(species_names):
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print(f" {name:12s}: {counts[k]} of 10")
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print()
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print("Observation:")
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print(" setosa is fully separable from the other two (Fisher 1936),")
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print(" so we expect zero or near-zero setosa specimens in the top 10.")
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print(" versicolor and virginica overlap in petal geometry - that")
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print(" overlap is exactly where the boundary specimens live.")
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if counts[0] == 0:
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print()
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print("*** Confirmed: zero setosa specimens; the top-10 boundary cases ***")
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print("*** all come from the famous versicolor/virginica overlap zone. ***")
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return 0
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if __name__ == "__main__":
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raise SystemExit(main())
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