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Comparison.score.tsallis_entropy

Comparison.score.tsallis_entropy 

tsallis_entropy(
    alpha: float = 1,
    base: float = 2,
    reference_score: float | Literal["mean"] | Expr = 0,
) -> Comparison

Calculates the difference in Tsallis entropy between the reference and comparison corpora.

Example 
import wordlevel as wl

cl = wl.Catalog.from_dict_of_freqs(
    {
        "before": {"good": 12, "bad": 8, "happy": 6, "sad": 4},
        "after": {"good": 5, "bad": 7, "happy": 3, "sad": 9},
    }
)

cl = cl.with_comparisons(wl.comp("before", "after").score.tsallis_entropy())

Tsallis entropy is a generalized measure of textual diversity, parameterized by an order \(\alpha\). This method takes the difference between the entropies of the reference corpus \(R\) and the comparison corpus \(C\):

\[ \Phi^{(C)} - \Phi^{(R)} = \frac{1 - \sum_\tau \left[ p_\tau^{(C)} \right]^\alpha}{\alpha - 1} - \frac{1 - \sum_\tau \left[ p_\tau^{(R)} \right]^\alpha}{\alpha - 1} \]

where \(p_\tau^{(R)}\) and \(p_\tau^{(C)}\) are the normalized frequencies of a token \(\tau\) in \(R\) and \(C\) respectively.

Reference

For more details, see the following paper:

Gallagher, R. J., Frank, M. R., Mitchell, L., Schwartz, A. J., Reagan, A. J., Danforth, C. M., & Dodds, P. S. (2021). Generalized word shift graphs: a method for visualizing and explaining pairwise comparisons between texts. EPJ Data Science, 10(1), 4.

See Also
Score Description
Comparison.score.shannon_entropy Scores corpora in the special case when \(\alpha=1\)

Parameters:

Name Type Description Default

alpha

float

Order of the Tsallis entropy. \(\alpha = 1\) recovers Shannon entropy. Larger values place more weight on common tokens, and smaller values place more weight on rare tokens

 1

base

float

Base of the logarithms used to calculate the entropy when \(\alpha = 1\). Ignored otherwise

 2

reference_score

float | Literal['mean'] | Expr

Baseline against which per-token contributions are interpreted. Defaults to 0. If "mean", uses the Tsallis entropy of the reference corpus as the reference score

 0

Returns:

Type Description
Comparison

A new Comparison scored by the difference in Tsallis entropies

Source