lexical_diversity.py

#Copyright 2017 John Frens
#
#Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
#
#The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
#
#THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

import string

# Global trandform for removing punctuation from words
remove_punctuation = str.maketrans('', '', string.punctuation)

# MTLD internal implementation
def mtld_calc(word_array, ttr_threshold):
    current_ttr = 1.0
    token_count = 0
    type_count = 0
    types = set()
    factors = 0.0
    
    for token in word_array:
        token = token.translate(remove_punctuation).lower() # trim punctuation, make lowercase
        token_count += 1
        if token not in types:
            type_count +=1
            types.add(token)
        current_ttr = type_count / token_count
        if current_ttr <= ttr_threshold:
            factors += 1
            token_count = 0
            type_count = 0
            types = set()
            current_ttr = 1.0
    
    excess = 1.0 - current_ttr
    excess_val = 1.0 - ttr_threshold
    factors += excess / excess_val
    if factors != 0:
        return len(word_array) / factors
    return -1

# MTLD implementation
def mtld(word_array, ttr_threshold=0.72):
    if isinstance(word_array, str):
        raise ValueError("Input should be a list of strings, rather than a string. Try using string.split()")
    if len(word_array) < 50:
        raise ValueError("Input word list should be at least 50 in length")
    return (mtld_calc(word_array, ttr_threshold) + mtld_calc(word_array[::-1], ttr_threshold)) / 2


# HD-D internals

# x! = x(x-1)(x-2)...(1)
def factorial(x):
    if x <= 1:
        return 1
    else:
        return x * factorial(x - 1)

# n choose r = n(n-1)(n-2)...(n-r+1)/(r!)
def combination(n, r):
    r_fact = factorial(r)
    numerator = 1.0
    num = n-r+1.0
    while num < n+1.0:
        numerator *= num
        num += 1.0
    return numerator / r_fact

# hypergeometric probability: the probability that an n-trial hypergeometric experiment results 
#  in exactly x successes, when the population consists of N items, k of which are classified as successes.
#  (here, population = N, population_successes = k, sample = n, sample_successes = x)
#  h(x; N, n, k) = [ kCx ] * [ N-kCn-x ] / [ NCn ]
def hypergeometric(population, population_successes, sample, sample_successes):
    return (combination(population_successes, sample_successes) *\
            combination(population - population_successes, sample - sample_successes)) /\
            combination(population, sample)
    
# HD-D implementation
def hdd(word_array, sample_size=42.0):
    if isinstance(word_array, str):
        raise ValueError("Input should be a list of strings, rather than a string. Try using string.split()")
    if len(word_array) < 50:
        raise ValueError("Input word list should be at least 50 in length")

    # Create a dictionary of counts for each type
    type_counts = {}
    for token in word_array:
        token = token.translate(remove_punctuation).lower() # trim punctuation, make lowercase
        if token in type_counts:
            type_counts[token] += 1.0
        else:
            type_counts[token] = 1.0
    # Sum the contribution of each token - "If the sample size is 42, the mean contribution of any given
    #  type is 1/42 multiplied by the percentage of combinations in which the type would be found." (McCarthy & Jarvis 2010)
    hdd_value = 0.0
    for token_type in type_counts.keys():
        contribution = (1.0 - hypergeometric(len(word_array), sample_size, type_counts[token_type], 0.0)) / sample_size
        hdd_value += contribution

    return hdd_value