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| """Three-axis spatial-geometric profile of a single text. | |
| Implements a simplified, single-text reading of Vallego (2026), | |
| "A Spatial-Geometric Framework for Discourse Comparison". | |
| Method | |
| ------ | |
| 1. Each axis is defined by two poles, each a set of exemplar sentences. | |
| Its raw direction is the difference between the two pole centroids | |
| (high-pole centroid minus low-pole centroid) in embedding space. | |
| 2. The three raw directions overlap (they are not orthogonal). They are | |
| orthogonalised with symmetric (Loewdin) orthogonalisation, which finds | |
| the orthonormal set closest to the raw directions and, unlike | |
| Gram-Schmidt, treats all three axes equally (no order dependence). | |
| 3. A text is split into sentences; each sentence and the text centroid | |
| (mean of sentence embeddings) are projected onto the three orthonormal | |
| directions. These three numbers are the 3D coordinates. | |
| 4. Each coordinate is rescaled so that 0% = the low-pole centroid and | |
| 100% = the high-pole centroid on that axis. Values below 0 or above 100 | |
| lie further out than the typical exemplar of that pole. | |
| """ | |
| from __future__ import annotations | |
| import re | |
| from dataclasses import dataclass | |
| import numpy as np | |
| import pandas as pd | |
| AXES = [ | |
| {"id": "eco", "name": "Ecocentrism", "low": "Anthropocentric", "high": "Ecocentric"}, | |
| {"id": "change", "name": "Societal change", "low": "Conservative", "high": "Transformative"}, | |
| {"id": "outlook", "name": "Outlook", "low": "Pessimistic", "high": "Optimistic"}, | |
| ] | |
| def split_sentences(text: str, min_words: int = 3) -> list[str]: | |
| parts = re.split(r"(?<=[.!?;])\s+|\n+", text.strip()) | |
| sents = [p.strip() for p in parts if len(p.strip().split()) >= min_words] | |
| return sents or ([text.strip()] if text.strip() else []) | |
| def _normalise(x: np.ndarray) -> np.ndarray: | |
| return x / np.linalg.norm(x, axis=-1, keepdims=True).clip(min=1e-12) | |
| def loewdin(D: np.ndarray) -> np.ndarray: | |
| """Symmetric orthogonalisation of the rows of D: Q = (D D^T)^(-1/2) D.""" | |
| S = D @ D.T | |
| vals, vecs = np.linalg.eigh(S) | |
| S_inv_sqrt = vecs @ np.diag(1.0 / np.sqrt(vals)) @ vecs.T | |
| return S_inv_sqrt @ D | |
| class Space: | |
| axes: list[dict] | |
| Q: np.ndarray # 3 x d, orthonormal axis directions | |
| raw_dirs: np.ndarray # 3 x d, unit raw directions (before orthogonalisation) | |
| lo: np.ndarray # 3, projection of each low-pole centroid on its own axis | |
| hi: np.ndarray # 3, projection of each high-pole centroid on its own axis | |
| raw_lo: np.ndarray | |
| raw_hi: np.ndarray | |
| pole_points: dict # (axis_id, pole) -> (sentences, coords n x 3 in %) | |
| pole_centroids: dict # (axis_id, pole) -> coords (3,) in % | |
| overlap: pd.DataFrame # cosine between raw directions | |
| def to_percent(self, proj: np.ndarray) -> np.ndarray: | |
| return 100.0 * (proj - self.lo) / (self.hi - self.lo) | |
| def coords(self, E: np.ndarray) -> np.ndarray: | |
| return self.to_percent(E @ self.Q.T) | |
| def raw_percent(self, E: np.ndarray) -> np.ndarray: | |
| return 100.0 * (E @ self.raw_dirs.T - self.raw_lo) / (self.raw_hi - self.raw_lo) | |
| def build_space(poles: pd.DataFrame, encode, axes=AXES) -> Space: | |
| """poles: DataFrame with columns axis, pole ('low'/'high'), text. | |
| encode: function list[str] -> np.ndarray (n x d).""" | |
| emb, cents = {}, {} | |
| for ax in axes: | |
| for pole in ("low", "high"): | |
| texts = poles[(poles.axis == ax["id"]) & (poles.pole == pole)].text.tolist() | |
| if len(texts) < 2: | |
| raise ValueError(f"Axis '{ax['id']}' pole '{pole}' needs at least 2 exemplars.") | |
| E = _normalise(np.asarray(encode(texts), dtype=float)) | |
| emb[(ax["id"], pole)] = (texts, E) | |
| cents[(ax["id"], pole)] = E.mean(axis=0) | |
| raw = np.stack([cents[(a["id"], "high")] - cents[(a["id"], "low")] for a in axes]) | |
| raw_unit = _normalise(raw) | |
| Q = loewdin(raw) | |
| lo = np.array([cents[(a["id"], "low")] @ Q[k] for k, a in enumerate(axes)]) | |
| hi = np.array([cents[(a["id"], "high")] @ Q[k] for k, a in enumerate(axes)]) | |
| raw_lo = np.array([cents[(a["id"], "low")] @ raw_unit[k] for k, a in enumerate(axes)]) | |
| raw_hi = np.array([cents[(a["id"], "high")] @ raw_unit[k] for k, a in enumerate(axes)]) | |
| names = [f"{a['low']}–{a['high']}" for a in axes] | |
| overlap = pd.DataFrame(raw_unit @ raw_unit.T, index=names, columns=names).round(2) | |
| space = Space(axes, Q, raw_unit, lo, hi, raw_lo, raw_hi, {}, {}, overlap) | |
| for key, (texts, E) in emb.items(): | |
| space.pole_points[key] = (texts, space.coords(E)) | |
| space.pole_centroids[key] = space.coords(cents[key][None, :])[0] | |
| return space | |
| def reading(pct: float, low: str, high: str) -> str: | |
| if pct < 10: | |
| return f"Strongly {low.lower()}" | |
| if pct < 40: | |
| return f"Leans {low.lower()}" | |
| if pct <= 60: | |
| return "Between the poles" | |
| if pct <= 90: | |
| return f"Leans {high.lower()}" | |
| return f"Strongly {high.lower()}" | |
| def analyse(text: str, space: Space, encode) -> dict: | |
| sents = split_sentences(text) | |
| if not sents: | |
| raise ValueError("Please enter some text.") | |
| E = _normalise(np.asarray(encode(sents), dtype=float)) | |
| centroid = E.mean(axis=0) | |
| sent_xyz = space.coords(E) | |
| text_xyz = space.coords(centroid[None, :])[0] | |
| raw_pct = space.raw_percent(centroid[None, :])[0] | |
| rows = [] | |
| for k, ax in enumerate(space.axes): | |
| rows.append({ | |
| "Axis (0% → 100%)": f"{ax['low']} → {ax['high']}", | |
| "Position": round(float(text_xyz[k]), 1), | |
| "Reading": reading(float(text_xyz[k]), ax["low"], ax["high"]), | |
| "Spread across sentences (±)": round(float(sent_xyz[:, k].std()), 1) if len(sents) > 1 else None, | |
| "Before orthogonalisation": round(float(raw_pct[k]), 1), | |
| }) | |
| cloud = cloud_measures(E, sent_xyz, space) | |
| return { | |
| "sentences": sents, | |
| "sent_xyz": sent_xyz, | |
| "text_xyz": text_xyz, | |
| "table": pd.DataFrame(rows), | |
| "cloud": cloud, | |
| "cloud_table": cloud_table(cloud, space), | |
| } | |
| def cloud_measures(E: np.ndarray, sent_xyz: np.ndarray, space: Space) -> dict: | |
| """Spread (Frobenius norm) and eigenanalysis of the cloud of sentences. | |
| - frobenius: Frobenius norm of the centred sentence positions (3D, % units), | |
| divided by sqrt(n) = root-mean-square distance of a sentence from the text centre. | |
| - captured: Pythagorean decomposition in the full embedding space. The squared | |
| Frobenius norm of the centred sentence embeddings splits exactly into the part | |
| lying along the three orthonormal axes and the residual; this is the axes' share. | |
| - eigen: eigen-decomposition of the 3x3 covariance of the sentence positions. | |
| """ | |
| n = len(sent_xyz) | |
| out = {"n": n} | |
| if n < 2: | |
| return out | |
| Xc = sent_xyz - sent_xyz.mean(axis=0) | |
| out["frobenius"] = float(np.linalg.norm(Xc) / np.sqrt(n)) | |
| Ec = E - E.mean(axis=0) | |
| total = float(np.sum(Ec ** 2)) | |
| on_axes = float(np.sum((Ec @ space.Q.T) ** 2)) | |
| out["captured"] = on_axes / total if total > 0 else float("nan") | |
| if n >= 3: | |
| cov = Xc.T @ Xc / n | |
| vals, vecs = np.linalg.eigh(cov) | |
| order = np.argsort(vals)[::-1] | |
| vals, vecs = np.clip(vals[order], 0, None), vecs[:, order] | |
| out["eigvals"] = vals | |
| out["eigvecs"] = vecs # columns = principal directions | |
| out["share_main"] = float(vals[0] / vals.sum()) if vals.sum() > 0 else float("nan") | |
| v1 = vecs[:, 0] | |
| out["angles"] = np.degrees(np.arccos(np.clip(np.abs(v1), 0, 1))) # to each axis | |
| out["main_axis"] = int(np.argmax(np.abs(v1))) | |
| return out | |
| def cloud_table(c: dict, space: Space) -> pd.DataFrame: | |
| rows = [] | |
| def add(measure, value, meaning): | |
| rows.append({"Measure": measure, "Value": value, "What it means": meaning}) | |
| if c["n"] < 2: | |
| add("Spread and main direction", "Needs 2+ sentences", | |
| "These measures describe how the sentences of a text spread out.") | |
| return pd.DataFrame(rows) | |
| add("Spread (Frobenius norm)", f"{c['frobenius']:.1f} points", | |
| "Average distance of a sentence from the text's centre across the three axes. " | |
| "Lower means a more consistent text.") | |
| add("Variation captured by the axes", f"{100 * c['captured']:.0f}%", | |
| "Share of the sentences' total variation in meaning that lies along these three axes. " | |
| "The rest concerns other things, such as topic or style.") | |
| if "eigvals" in c: | |
| ax = space.axes[c["main_axis"]] | |
| add("Main direction of variation (eigenanalysis)", | |
| f"Mostly {ax['name']} ({c['angles'][c['main_axis']]:.0f}° from it)", | |
| "The direction along which the sentences differ most, and the axis it is closest to.") | |
| add("Variation along the main direction", f"{100 * c['share_main']:.0f}%", | |
| "Near 33%: sentences vary evenly in all directions. " | |
| "Near 100%: they vary along a single line.") | |
| else: | |
| add("Main direction of variation (eigenanalysis)", "Needs 3+ sentences", "") | |
| return pd.DataFrame(rows) | |