DiscourseGeometry

How it works

1. Each axis is defined by two poles, each a set of exemplar sentences (poles.tsv). The axis direction runs from the centre of one pole's exemplars to the centre of the other's.
2. The three axes overlap in meaning (see the table below), so they are orthogonalised: symmetric orthogonalisation finds the three perpendicular directions closest to the originals, treating all three axes equally. This lets them be drawn as the x, y and z of one 3D space.
3. The text is split into sentences. Each sentence, and the text as a whole (the centroid of its sentences), is placed on the three axes. Positions are expressed as percentages between the poles.
4. Spread is the standard deviation of sentence positions on each axis: low spread means the text is consistent on that dimension; high spread means it moves between positions.
5. Frobenius norm: the Frobenius norm of the sentences' positions around the text centre, divided by √(number of sentences), i.e. the average distance of a sentence from the centre across all three axes. Variation captured by the axes splits the sentences' total variation in the full embedding space into the part lying along the three axes and the rest (a Pythagorean decomposition of the squared Frobenius norm).
6. Eigenanalysis: the eigenvectors of the 3×3 covariance of sentence positions give the directions along which the sentences vary; the eigenvalues give how much variation lies along each.

The Before orthogonalisation column shows each position measured on the raw, overlapping axis, so you can see how much orthogonalisation changes the reading.

Sentence encoder: all-mpnet-base-v2.