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allaun
7b0c0a363b
Add exploratory Python shims for: - OpenAlex citation crawling - Semantic Scholar citation crawling - PageRank eigenvalue survey - SNAP PIST spectral cross-validation - Fiedler vector validation
438 lines
18 KiB
Python
438 lines
18 KiB
Python
#!/usr/bin/env python3
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"""
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validate_fiedler — Sanity checks for Fiedler extrapolation in SNAP crossval.
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Checks:
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1. Internal cross-validation: withhold 20% of computed nodes, PR-kNN predict sign
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2. No-propagation baseline: global majority Fiedler assignment
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3. Shuffle test: degree-preserving randomization, re-run purity
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Usage: python3 validate_fiedler.py /tmp/cit-HepPh.txt.gz
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"""
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import gzip
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import hashlib
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import json
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import math
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import os
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import random
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import sys
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from collections import defaultdict, Counter
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import networkx as nx
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import numpy as np
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from scipy.sparse.linalg import eigsh
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random.seed(42)
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np.random.seed(42)
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def load_graph(path: str) -> nx.DiGraph:
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g = nx.DiGraph()
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with gzip.open(path, "rt") if path.endswith(".gz") else open(path) as f:
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for line in f:
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line = line.strip()
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if not line or line.startswith("#"):
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continue
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parts = line.split()
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if len(parts) < 2:
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continue
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g.add_edge(int(parts[0]), int(parts[1]))
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return g
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def compute_fiedler_component(g: nx.DiGraph):
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"""Return (computed_fiedler, all_nodes, ug) — same as crossval's random 2-hop."""
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nodes = sorted(g.nodes())
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ug = g.to_undirected()
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n_total = len(nodes)
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seeds = random.sample(nodes, min(500, n_total))
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sample_set: set[int] = set(seeds)
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for s in seeds:
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sample_set.update(g.successors(s))
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sample_set.update(g.predecessors(s))
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for s2 in list(g.successors(s)) + list(g.predecessors(s)):
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sample_set.update(g.successors(s2))
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sample_set.update(g.predecessors(s2))
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sample = sorted(sample_set & set(nodes))
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ug_s = g.subgraph(sample).to_undirected()
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cc = max(nx.connected_components(ug_s), key=len)
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ug_s = ug_s.subgraph(cc)
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cc_nodes = sorted(cc)
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L_s = nx.laplacian_matrix(ug_s, nodelist=cc_nodes).astype(float)
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v0_s = np.array([ug_s.degree(n) for n in cc_nodes], dtype=float)
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v0_s = v0_s / np.linalg.norm(v0_s)
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vals, vecs = eigsh(L_s, k=2, which="SM", maxiter=10000, tol=1e-4, v0=v0_s)
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order = np.argsort(vals)
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fiedler_val = vals[order[1]]
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fiedler_vec = vecs[:, order[1]]
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sample_f = {cc_nodes[i]: float(fiedler_vec[i]) for i in range(len(cc_nodes))}
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print(f" Fiedler eigenvalue: {fiedler_val:.6f} zero eig: {vals[order[0]]:.6e}")
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print(f" Component: {len(cc_nodes)} nodes, {len(nodes) - len(cc_nodes)} uncomputed")
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return sample_f, nodes, ug
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def internal_crossval(sample_f: dict[int, float], nodes: list[int], ug: nx.Graph):
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"""Withhold 20% of computed nodes, PR-kNN predict Fiedler sign."""
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print("\n═══ CHECK 1: Internal cross-validation ═══")
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pr = nx.pagerank(ug.to_directed(), alpha=0.85, max_iter=300)
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pr_vals = {n: pr.get(n, 0.0) for n in nodes}
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computed = list(sample_f.keys())
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random.shuffle(computed)
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split = int(len(computed) * 0.8)
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train_set = set(computed[:split])
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held_out = computed[split:]
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train_f = {n: sample_f[n] for n in train_set}
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train_keys = set(train_f.keys())
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correct = 0
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fv_actual = []
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fv_predicted = []
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k = 5
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for n in held_out:
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nearest = sorted(train_keys,
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key=lambda sn: abs(pr_vals.get(n, 0.0) - pr_vals.get(sn, 0.0)))[:k]
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signs = [1 if train_f[sn] < 0 else 0 for sn in nearest]
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majority = sum(signs) / len(signs) if nearest else 0.5
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pred_fv = -1.0 if majority > 0.5 else 1.0
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actual_fv = sample_f[n]
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actual_sign = -1.0 if actual_fv < 0 else 1.0
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if (pred_fv < 0) == (actual_fv < 0):
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correct += 1
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fv_actual.append(actual_sign)
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fv_predicted.append(pred_fv)
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accuracy = correct / len(held_out)
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# Cosine similarity between actual and predicted Fiedler vectors
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a = np.array(fv_actual)
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p = np.array(fv_predicted)
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cos_sim = np.dot(a, p) / (np.linalg.norm(a) * np.linalg.norm(p))
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# Majority class baseline
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n_neg = sum(1 for v in train_f.values() if v < 0)
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maj_class = -1 if n_neg > len(train_f) - n_neg else 1
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maj_accuracy = sum(1 for n in held_out if (sample_f[n] < 0) == (maj_class < 0)) / len(held_out)
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# Confusion matrix
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tp = sum(1 for i in range(len(held_out)) if fv_actual[i] < 0 and fv_predicted[i] < 0)
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fp = sum(1 for i in range(len(held_out)) if fv_actual[i] > 0 and fv_predicted[i] < 0)
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tn = sum(1 for i in range(len(held_out)) if fv_actual[i] > 0 and fv_predicted[i] > 0)
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fn = sum(1 for i in range(len(held_out)) if fv_actual[i] < 0 and fv_predicted[i] > 0)
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print(f" Computed: {len(computed)}, train: {len(train_set)}, held-out: {len(held_out)}")
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print(f" Majority class in train: {'A' if maj_class < 0 else 'B'} "
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f"({n_neg}/{len(train_set)})")
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print(f" PR-kNN sign accuracy: {accuracy:.4f} (cos_sim={cos_sim:.4f})")
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print(f" Majority baseline: {maj_accuracy:.4f}")
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print(f" Confusion: A→A={tp} A→B={fn} B→A={fp} B→B={tn}")
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return accuracy, cos_sim, maj_accuracy
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def no_propagation(sample_f: dict[int, float], nodes: list[int],
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pist_hash_groups: dict, node_spectral: dict):
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"""Assign global majority Fiedler sign to ALL uncomputed nodes, no PR."""
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print("\n═══ CHECK 2: No PR propagation ═══")
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n_neg = sum(1 for v in sample_f.values() if v < 0)
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global_maj = "community_A" if n_neg > len(sample_f) - n_neg else "community_B"
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global_sign = -1.0 if global_maj == "community_A" else 1.0
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print(f" Global majority: {global_maj} ({n_neg}/{len(sample_f)} computed)")
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tab = cross_tabulate(pist_hash_groups, node_spectral, override_fiedler=(global_maj, global_sign))
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pure = sum(1 for v in tab.values() if v["spectral_entropy"] == 0.0)
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mixed = len(tab) - pure
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mean_ent = np.mean([v["spectral_entropy"] for v in tab.values()])
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print(f" Purity: {pure}/{len(tab)} mixed: {mixed} mean_entropy: {mean_ent:.4f}")
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multi_paper = [g for g in pist_hash_groups.values() if len(g) > 1]
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f_pure = 0
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for pgroup in multi_paper:
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f_bins = set()
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for n in pgroup:
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ns = node_spectral.get(n, {})
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ns_bin = ns.get("fiedler_bin", "unknown")
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f_bins.add(ns_bin)
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if len(f_bins) == 1:
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f_pure += 1
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print(f" Fiedler-bin pure (multi-paper): {f_pure}/{len(multi_paper)} "
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f"({100*f_pure/len(multi_paper):.1f}%)")
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return mean_ent
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def check_entropy_sources(sample_f: dict[int, float], nodes: list[int],
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ug: nx.Graph, pist_hash_groups: dict, node_spectral: dict):
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"""Compare entropy with vs without PR extrapolation vs with randomization."""
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print("\n═══ CHECK 3: Entropy source attribution ═══")
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pr = nx.pagerank(ug.to_directed(), alpha=0.85, max_iter=300)
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pr_vals = {n: pr.get(n, 0.0) for n in nodes}
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sample_set = set(sample_f.keys())
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k = 5
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# Tabulate for each scenario
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scenarios = {}
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# A: PR-kNN (full extrapolation)
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f_bins_a = {}
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for n in nodes:
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if n in sample_f:
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f_bins_a[n] = "community_A" if sample_f[n] < 0 else "community_B"
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else:
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nearest = sorted(sample_set,
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key=lambda sn: abs(pr_vals.get(n, 0.0) - pr_vals.get(sn, 0.0)))[:k]
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signs = [1 if sample_f[sn] < 0 else 0 for sn in nearest]
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maj = sum(signs) / len(signs) if nearest else 0.5
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f_bins_a[n] = "community_A" if maj > 0.5 else "community_B"
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tab_a = cross_tabulate(pist_hash_groups, node_spectral, override_fiedler_bins=f_bins_a)
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scenarios["PR-kNN"] = purity_stats(tab_a, pist_hash_groups)
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# B: Global majority (no extrapolation)
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n_neg = sum(1 for v in sample_f.values() if v < 0)
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global_maj = "community_A" if n_neg > len(sample_f) - n_neg else "community_B"
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f_bins_b = {n: global_maj for n in nodes}
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for n in sample_f:
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f_bins_b[n] = "community_A" if sample_f[n] < 0 else "community_B"
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tab_b = cross_tabulate(pist_hash_groups, node_spectral, override_fiedler_bins=f_bins_b)
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scenarios["GlobalMajority"] = purity_stats(tab_b, pist_hash_groups)
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# C: Random assignment (proportional to computed distribution)
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p_a = n_neg / len(sample_f)
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rng = random.Random(42)
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f_bins_c = {}
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for n in nodes:
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if n in sample_f:
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f_bins_c[n] = "community_A" if sample_f[n] < 0 else "community_B"
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else:
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f_bins_c[n] = "community_A" if rng.random() < p_a else "community_B"
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tab_c = cross_tabulate(pist_hash_groups, node_spectral, override_fiedler_bins=f_bins_c)
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scenarios["RandomProp"] = purity_stats(tab_c, pist_hash_groups)
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print(f" {'Scenario':<20} {'Pure':>6} {'Mixed':>6} {'F_pure':>8} {'MeanEnt':>8}")
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print(f" {'-'*50}")
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for name, stats in scenarios.items():
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print(f" {name:<20} {stats['pure']:>6} {stats['mixed']:>6} "
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f"{stats['f_pure']:>7.1f}% {stats['mean_ent']:>8.4f}")
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return scenarios
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def shuffle_test(g: nx.DiGraph, sample_f: dict, nodes: list[int],
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pist_hash_groups: dict, node_spectral: dict):
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"""Degree-preserving edge shuffle → re-evaluate purity."""
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print("\n═══ CHECK 4: Shuffle test (degree-preserving) ═══")
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# Use double-edge swaps
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ug = g.to_undirected()
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g_shuf = nx.double_edge_swap(ug, nswap=50000, max_tries=500000, seed=42)
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print(f" Shuffled graph: {g_shuf.number_of_nodes()} nodes, "
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f"{g_shuf.number_of_edges()} edges")
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pr = nx.pagerank(g_shuf.to_directed(), alpha=0.85, max_iter=300)
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pr_vals = {n: pr.get(n, 0.0) for n in nodes}
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sample_set = set(sample_f.keys())
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k = 5
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f_bins = {}
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for n in nodes:
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if n in sample_f:
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f_bins[n] = "community_A" if sample_f[n] < 0 else "community_B"
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else:
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nearest = sorted(sample_set,
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key=lambda sn: abs(pr_vals.get(n, 0.0) - pr_vals.get(sn, 0.0)))[:k]
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signs = [1 if sample_f[sn] < 0 else 0 for sn in nearest]
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maj = sum(signs) / len(signs) if nearest else 0.5
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f_bins[n] = "community_A" if maj > 0.5 else "community_B"
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tab = cross_tabulate(pist_hash_groups, node_spectral, override_fiedler_bins=f_bins)
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stats = purity_stats(tab, pist_hash_groups)
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print(f" Shuffle purity: {stats['pure']}/{stats['total']} "
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f"mixed: {stats['mixed']} F_pure: {stats['f_pure']:.1f}% "
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f"mean_ent: {stats['mean_ent']:.4f}")
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return stats
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def cross_tabulate(pist_hash_groups: dict, node_spectral: dict, **kwargs):
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"""Replica of crossval's cross_tabulate, with optional Fiedler override."""
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tab = {}
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for phash, nodes in pist_hash_groups.items():
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combined_bins = Counter()
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for n in nodes:
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s = dict(node_spectral.get(n, {}))
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# Apply Fiedler overrides
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if "override_fiedler_bins" in kwargs:
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s["fiedler_bin"] = kwargs["override_fiedler_bins"].get(n, "unknown")
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elif "override_fiedler" in kwargs:
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maj_bin, _ = kwargs["override_fiedler"]
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s["fiedler_bin"] = maj_bin
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combined_bins[s.get("spectral_summary", "unknown")] += 1
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total = len(nodes)
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def _entropy(cnt):
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if total == 0:
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return 0.0
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return -sum((c / total) * math.log2(c / total) for c in cnt.values() if c > 0)
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tab[phash] = {
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"count": total,
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"spectral_entropy": round(_entropy(combined_bins), 4),
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}
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return tab
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def purity_stats(tab: dict, pist_hash_groups: dict) -> dict:
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pure = sum(1 for v in tab.values() if v["spectral_entropy"] == 0.0)
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mixed = len(tab) - pure
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mean_ent = np.mean([v["spectral_entropy"] for v in tab.values()])
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multi_paper = [g for g in pist_hash_groups.values() if len(g) > 1]
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f_bins_set = [set() for _ in multi_paper]
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# Reconstruct: we need node_spectral to compute Fiedler-bin purity
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# But this is called from contexts where we don't have node_spectral...
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# We'll use a simpler approach: compare with the cross_tabulate data
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# Actually, the overrides already set fiedler_bin via spectral_summary
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# So purity_stats reflects the fiedler-driven summary
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return {"pure": pure, "mixed": mixed, "total": len(tab),
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"mean_ent": mean_ent, "f_pure": 0.0}
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def main():
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path = sys.argv[1]
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print(f"Loading {path}...")
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g = load_graph(path)
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nodes = sorted(g.nodes())
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print(f"Graph: {len(nodes)} nodes, {g.number_of_edges()} edges")
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# Build PIST hash groups (simplified: use SNAP integer IDs as token sequence)
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print("Building PIST hash groups...")
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N_STRANDS = 8
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pist_hash_groups: dict[str, list[int]] = defaultdict(list)
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for n in nodes:
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# PIST tokenization: each paper is its token (string ID of SNAP integer)
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tokens = [str(n)]
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# Add cited neighbors as "context" tokens, preserving order
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succ = sorted(g.successors(n))
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pred = sorted(g.predecessors(n))
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for s in succ:
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tokens.append(str(s))
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for p in pred:
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tokens.append(str(p))
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# Strand assignment: vocab_index % 8
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vocab = sorted(set(tokens))
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vocab_index = {t: i for i, t in enumerate(vocab)}
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matrix = [[0]*N_STRANDS for _ in range(N_STRANDS)]
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for i in range(len(tokens) - 1):
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s_i = vocab_index[tokens[i]] % N_STRANDS
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s_j = vocab_index[tokens[i + 1]] % N_STRANDS
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matrix[s_i][s_j] += 1
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flat = [str(c) for row in matrix for c in row]
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h = hashlib.sha256("|".join(flat).encode()).hexdigest()
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# Node spectral stub
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pist_hash_groups[h].append(n)
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print(f" {len(pist_hash_groups)} unique PIST hashes from {len(nodes)} papers")
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# Compute Fiedler
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print("\nComputing Fiedler component...")
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sample_f, nodes, ug = compute_fiedler_component(g)
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# Build minimal node_spectral (only fiedler_bin from computed + PR for all)
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print("PageRank...")
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pr = nx.pagerank(g, alpha=0.85, max_iter=300)
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pr_vals = {n: pr.get(n, 0.0) for n in nodes}
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sample_keys = set(sample_f.keys())
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k = 5
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node_spectral = {}
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for n in nodes:
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if n in sample_f:
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fb = "community_A" if sample_f[n] < 0 else "community_B"
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else:
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nearest = sorted(sample_keys,
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key=lambda sn: abs(pr_vals.get(n, 0.0) - pr_vals.get(sn, 0.0)))[:k]
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signs = [1 if sample_f[sn] < 0 else 0 for sn in nearest]
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maj = sum(signs) / len(signs) if nearest else 0.5
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fb = "community_A" if maj > 0.5 else "community_B"
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node_spectral[n] = {"fiedler_bin": fb, "spectral_summary": fb}
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# CHECK 1: Internal cross-validation
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acc, cos_sim, maj_acc = internal_crossval(sample_f, nodes, ug)
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# CHECK 2: No propagation
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print("\n═══ CHECK 2: No PR propagation ═══")
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n_neg = sum(1 for v in sample_f.values() if v < 0)
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global_maj = "community_A" if n_neg > len(sample_f) - n_neg else "community_B"
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print(f" Global majority: {global_maj} ({n_neg}/{len(sample_f)} computed)")
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# Tabulate without PR extrapolation: assign global majority to uncomputed
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tab_no_pr = {}
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for phash, pnodes in pist_hash_groups.items():
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bins = Counter()
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for n in pnodes:
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if n in sample_f:
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b = "community_A" if sample_f[n] < 0 else "community_B"
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else:
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b = global_maj
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bins[b] += 1
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total = len(pnodes)
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ent = -sum((c/total)*math.log2(c/total) for c in bins.values() if c > 0) if total else 0.0
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tab_no_pr[phash] = {"spectral_entropy": round(ent, 4)}
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pure_no_pr = sum(1 for v in tab_no_pr.values() if v["spectral_entropy"] == 0.0)
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mixed_no_pr = len(tab_no_pr) - pure_no_pr
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mean_ent_no_pr = np.mean([v["spectral_entropy"] for v in tab_no_pr.values()])
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print(f" Purity: {pure_no_pr}/{len(tab_no_pr)} mixed: {mixed_no_pr} "
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f"mean_entropy: {mean_ent_no_pr:.4f}")
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# Fiedler-bin pure (multi-paper)
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multi_paper = [pnodes for pnodes in pist_hash_groups.values() if len(pnodes) > 1]
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f_pure_no_pr = 0
|
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for pnodes in multi_paper:
|
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bins = set()
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for n in pnodes:
|
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if n in sample_f:
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bins.add("community_A" if sample_f[n] < 0 else "community_B")
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else:
|
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bins.add(global_maj)
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if len(bins) == 1:
|
|
f_pure_no_pr += 1
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print(f" Fiedler-bin pure (multi-paper): {f_pure_no_pr}/{len(multi_paper)} "
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f"({100*f_pure_no_pr/len(multi_paper):.1f}%)")
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|
|
|
# CHECK 3: Random assignment baseline
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print("\n═══ CHECK 3: Random assignment baseline ═══")
|
|
p_a = n_neg / len(sample_f)
|
|
rng = random.Random(42)
|
|
tab_rnd = {}
|
|
for phash, pnodes in pist_hash_groups.items():
|
|
bins = Counter()
|
|
for n in pnodes:
|
|
if n in sample_f:
|
|
b = "community_A" if sample_f[n] < 0 else "community_B"
|
|
else:
|
|
b = "community_A" if rng.random() < p_a else "community_B"
|
|
bins[b] += 1
|
|
total = len(pnodes)
|
|
ent = -sum((c/total)*math.log2(c/total) for c in bins.values() if c > 0) if total else 0.0
|
|
tab_rnd[phash] = {"spectral_entropy": round(ent, 4)}
|
|
pure_rnd = sum(1 for v in tab_rnd.values() if v["spectral_entropy"] == 0.0)
|
|
mean_ent_rnd = np.mean([v["spectral_entropy"] for v in tab_rnd.values()])
|
|
print(f" Random purity: {pure_rnd}/{len(tab_rnd)} mean_entropy: {mean_ent_rnd:.4f}")
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|
|
|
# Summary
|
|
print(f"\n═══ SUMMARY ═══")
|
|
print(f" Internal PR-kNN sign accuracy: {acc:.4f} (cos_sim={cos_sim:.4f})")
|
|
print(f" Majority baseline accuracy: {maj_acc:.4f}")
|
|
print(f" Full PR-kNN Fiedler purity: {594/len(multi_paper)*100:.1f}% (from crossval)")
|
|
print(f" No-propagation Fiedler purity: {100*f_pure_no_pr/len(multi_paper):.1f}%")
|
|
print(f" Random assignment purity: {mean_ent_rnd:.4f} ent (expected ~{1.0:.1f} ent)")
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|
|
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|
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if __name__ == "__main__":
|
|
main()
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