You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
390 lines
14 KiB
Python
390 lines
14 KiB
Python
# Natural Language Toolkit: Agreement Metrics
|
|
#
|
|
# Copyright (C) 2001-2019 NLTK Project
|
|
# Author: Lauri Hallila <laurihallila@gmail.com>
|
|
# URL: <http://nltk.org/>
|
|
# For license information, see LICENSE.TXT
|
|
#
|
|
|
|
"""Counts Paice's performance statistics for evaluating stemming algorithms.
|
|
|
|
What is required:
|
|
- A dictionary of words grouped by their real lemmas
|
|
- A dictionary of words grouped by stems from a stemming algorithm
|
|
|
|
When these are given, Understemming Index (UI), Overstemming Index (OI),
|
|
Stemming Weight (SW) and Error-rate relative to truncation (ERRT) are counted.
|
|
|
|
References:
|
|
Chris D. Paice (1994). An evaluation method for stemming algorithms.
|
|
In Proceedings of SIGIR, 42--50.
|
|
"""
|
|
|
|
from math import sqrt
|
|
|
|
|
|
def get_words_from_dictionary(lemmas):
|
|
'''
|
|
Get original set of words used for analysis.
|
|
|
|
:param lemmas: A dictionary where keys are lemmas and values are sets
|
|
or lists of words corresponding to that lemma.
|
|
:type lemmas: dict(str): list(str)
|
|
:return: Set of words that exist as values in the dictionary
|
|
:rtype: set(str)
|
|
'''
|
|
words = set()
|
|
for lemma in lemmas:
|
|
words.update(set(lemmas[lemma]))
|
|
return words
|
|
|
|
|
|
def _truncate(words, cutlength):
|
|
'''Group words by stems defined by truncating them at given length.
|
|
|
|
:param words: Set of words used for analysis
|
|
:param cutlength: Words are stemmed by cutting at this length.
|
|
:type words: set(str) or list(str)
|
|
:type cutlength: int
|
|
:return: Dictionary where keys are stems and values are sets of words
|
|
corresponding to that stem.
|
|
:rtype: dict(str): set(str)
|
|
'''
|
|
stems = {}
|
|
for word in words:
|
|
stem = word[:cutlength]
|
|
try:
|
|
stems[stem].update([word])
|
|
except KeyError:
|
|
stems[stem] = set([word])
|
|
return stems
|
|
|
|
|
|
# Reference: http://en.wikipedia.org/wiki/Line-line_intersection
|
|
def _count_intersection(l1, l2):
|
|
'''Count intersection between two line segments defined by coordinate pairs.
|
|
|
|
:param l1: Tuple of two coordinate pairs defining the first line segment
|
|
:param l2: Tuple of two coordinate pairs defining the second line segment
|
|
:type l1: tuple(float, float)
|
|
:type l2: tuple(float, float)
|
|
:return: Coordinates of the intersection
|
|
:rtype: tuple(float, float)
|
|
'''
|
|
x1, y1 = l1[0]
|
|
x2, y2 = l1[1]
|
|
x3, y3 = l2[0]
|
|
x4, y4 = l2[1]
|
|
|
|
denominator = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4)
|
|
|
|
if denominator == 0.0: # lines are parallel
|
|
if x1 == x2 == x3 == x4 == 0.0:
|
|
# When lines are parallel, they must be on the y-axis.
|
|
# We can ignore x-axis because we stop counting the
|
|
# truncation line when we get there.
|
|
# There are no other options as UI (x-axis) grows and
|
|
# OI (y-axis) diminishes when we go along the truncation line.
|
|
return (0.0, y4)
|
|
|
|
x = (
|
|
(x1 * y2 - y1 * x2) * (x3 - x4) - (x1 - x2) * (x3 * y4 - y3 * x4)
|
|
) / denominator
|
|
y = (
|
|
(x1 * y2 - y1 * x2) * (y3 - y4) - (y1 - y2) * (x3 * y4 - y3 * x4)
|
|
) / denominator
|
|
return (x, y)
|
|
|
|
|
|
def _get_derivative(coordinates):
|
|
'''Get derivative of the line from (0,0) to given coordinates.
|
|
|
|
:param coordinates: A coordinate pair
|
|
:type coordinates: tuple(float, float)
|
|
:return: Derivative; inf if x is zero
|
|
:rtype: float
|
|
'''
|
|
try:
|
|
return coordinates[1] / coordinates[0]
|
|
except ZeroDivisionError:
|
|
return float('inf')
|
|
|
|
|
|
def _calculate_cut(lemmawords, stems):
|
|
'''Count understemmed and overstemmed pairs for (lemma, stem) pair with common words.
|
|
|
|
:param lemmawords: Set or list of words corresponding to certain lemma.
|
|
:param stems: A dictionary where keys are stems and values are sets
|
|
or lists of words corresponding to that stem.
|
|
:type lemmawords: set(str) or list(str)
|
|
:type stems: dict(str): set(str)
|
|
:return: Amount of understemmed and overstemmed pairs contributed by words
|
|
existing in both lemmawords and stems.
|
|
:rtype: tuple(float, float)
|
|
'''
|
|
umt, wmt = 0.0, 0.0
|
|
for stem in stems:
|
|
cut = set(lemmawords) & set(stems[stem])
|
|
if cut:
|
|
cutcount = len(cut)
|
|
stemcount = len(stems[stem])
|
|
# Unachieved merge total
|
|
umt += cutcount * (len(lemmawords) - cutcount)
|
|
# Wrongly merged total
|
|
wmt += cutcount * (stemcount - cutcount)
|
|
return (umt, wmt)
|
|
|
|
|
|
def _calculate(lemmas, stems):
|
|
'''Calculate actual and maximum possible amounts of understemmed and overstemmed word pairs.
|
|
|
|
:param lemmas: A dictionary where keys are lemmas and values are sets
|
|
or lists of words corresponding to that lemma.
|
|
:param stems: A dictionary where keys are stems and values are sets
|
|
or lists of words corresponding to that stem.
|
|
:type lemmas: dict(str): list(str)
|
|
:type stems: dict(str): set(str)
|
|
:return: Global unachieved merge total (gumt),
|
|
global desired merge total (gdmt),
|
|
global wrongly merged total (gwmt) and
|
|
global desired non-merge total (gdnt).
|
|
:rtype: tuple(float, float, float, float)
|
|
'''
|
|
|
|
n = sum(len(lemmas[word]) for word in lemmas)
|
|
|
|
gdmt, gdnt, gumt, gwmt = (0.0, 0.0, 0.0, 0.0)
|
|
|
|
for lemma in lemmas:
|
|
lemmacount = len(lemmas[lemma])
|
|
|
|
# Desired merge total
|
|
gdmt += lemmacount * (lemmacount - 1)
|
|
|
|
# Desired non-merge total
|
|
gdnt += lemmacount * (n - lemmacount)
|
|
|
|
# For each (lemma, stem) pair with common words, count how many
|
|
# pairs are understemmed and overstemmed.
|
|
umt, wmt = _calculate_cut(lemmas[lemma], stems)
|
|
|
|
# Add to total undesired and wrongly-merged totals
|
|
gumt += umt
|
|
gwmt += wmt
|
|
|
|
# Each object is counted twice, so divide by two
|
|
return (gumt / 2, gdmt / 2, gwmt / 2, gdnt / 2)
|
|
|
|
|
|
def _indexes(gumt, gdmt, gwmt, gdnt):
|
|
'''Count Understemming Index (UI), Overstemming Index (OI) and Stemming Weight (SW).
|
|
|
|
:param gumt, gdmt, gwmt, gdnt: Global unachieved merge total (gumt),
|
|
global desired merge total (gdmt),
|
|
global wrongly merged total (gwmt) and
|
|
global desired non-merge total (gdnt).
|
|
:type gumt, gdmt, gwmt, gdnt: float
|
|
:return: Understemming Index (UI),
|
|
Overstemming Index (OI) and
|
|
Stemming Weight (SW).
|
|
:rtype: tuple(float, float, float)
|
|
'''
|
|
# Calculate Understemming Index (UI),
|
|
# Overstemming Index (OI) and Stemming Weight (SW)
|
|
try:
|
|
ui = gumt / gdmt
|
|
except ZeroDivisionError:
|
|
# If GDMT (max merge total) is 0, define UI as 0
|
|
ui = 0.0
|
|
try:
|
|
oi = gwmt / gdnt
|
|
except ZeroDivisionError:
|
|
# IF GDNT (max non-merge total) is 0, define OI as 0
|
|
oi = 0.0
|
|
try:
|
|
sw = oi / ui
|
|
except ZeroDivisionError:
|
|
if oi == 0.0:
|
|
# OI and UI are 0, define SW as 'not a number'
|
|
sw = float('nan')
|
|
else:
|
|
# UI is 0, define SW as infinity
|
|
sw = float('inf')
|
|
return (ui, oi, sw)
|
|
|
|
|
|
class Paice(object):
|
|
'''Class for storing lemmas, stems and evaluation metrics.'''
|
|
|
|
def __init__(self, lemmas, stems):
|
|
'''
|
|
:param lemmas: A dictionary where keys are lemmas and values are sets
|
|
or lists of words corresponding to that lemma.
|
|
:param stems: A dictionary where keys are stems and values are sets
|
|
or lists of words corresponding to that stem.
|
|
:type lemmas: dict(str): list(str)
|
|
:type stems: dict(str): set(str)
|
|
'''
|
|
self.lemmas = lemmas
|
|
self.stems = stems
|
|
self.coords = []
|
|
self.gumt, self.gdmt, self.gwmt, self.gdnt = (None, None, None, None)
|
|
self.ui, self.oi, self.sw = (None, None, None)
|
|
self.errt = None
|
|
self.update()
|
|
|
|
def __str__(self):
|
|
text = ['Global Unachieved Merge Total (GUMT): %s\n' % self.gumt]
|
|
text.append('Global Desired Merge Total (GDMT): %s\n' % self.gdmt)
|
|
text.append('Global Wrongly-Merged Total (GWMT): %s\n' % self.gwmt)
|
|
text.append('Global Desired Non-merge Total (GDNT): %s\n' % self.gdnt)
|
|
text.append('Understemming Index (GUMT / GDMT): %s\n' % self.ui)
|
|
text.append('Overstemming Index (GWMT / GDNT): %s\n' % self.oi)
|
|
text.append('Stemming Weight (OI / UI): %s\n' % self.sw)
|
|
text.append('Error-Rate Relative to Truncation (ERRT): %s\r\n' % self.errt)
|
|
coordinates = ' '.join(['(%s, %s)' % item for item in self.coords])
|
|
text.append('Truncation line: %s' % coordinates)
|
|
return ''.join(text)
|
|
|
|
def _get_truncation_indexes(self, words, cutlength):
|
|
'''Count (UI, OI) when stemming is done by truncating words at \'cutlength\'.
|
|
|
|
:param words: Words used for the analysis
|
|
:param cutlength: Words are stemmed by cutting them at this length
|
|
:type words: set(str) or list(str)
|
|
:type cutlength: int
|
|
:return: Understemming and overstemming indexes
|
|
:rtype: tuple(int, int)
|
|
'''
|
|
|
|
truncated = _truncate(words, cutlength)
|
|
gumt, gdmt, gwmt, gdnt = _calculate(self.lemmas, truncated)
|
|
ui, oi = _indexes(gumt, gdmt, gwmt, gdnt)[:2]
|
|
return (ui, oi)
|
|
|
|
def _get_truncation_coordinates(self, cutlength=0):
|
|
'''Count (UI, OI) pairs for truncation points until we find the segment where (ui, oi) crosses the truncation line.
|
|
|
|
:param cutlength: Optional parameter to start counting from (ui, oi)
|
|
coordinates gotten by stemming at this length. Useful for speeding up
|
|
the calculations when you know the approximate location of the
|
|
intersection.
|
|
:type cutlength: int
|
|
:return: List of coordinate pairs that define the truncation line
|
|
:rtype: list(tuple(float, float))
|
|
'''
|
|
words = get_words_from_dictionary(self.lemmas)
|
|
maxlength = max(len(word) for word in words)
|
|
|
|
# Truncate words from different points until (0, 0) - (ui, oi) segment crosses the truncation line
|
|
coords = []
|
|
while cutlength <= maxlength:
|
|
# Get (UI, OI) pair of current truncation point
|
|
pair = self._get_truncation_indexes(words, cutlength)
|
|
|
|
# Store only new coordinates so we'll have an actual
|
|
# line segment when counting the intersection point
|
|
if pair not in coords:
|
|
coords.append(pair)
|
|
if pair == (0.0, 0.0):
|
|
# Stop counting if truncation line goes through origo;
|
|
# length from origo to truncation line is 0
|
|
return coords
|
|
if len(coords) >= 2 and pair[0] > 0.0:
|
|
derivative1 = _get_derivative(coords[-2])
|
|
derivative2 = _get_derivative(coords[-1])
|
|
# Derivative of the truncation line is a decreasing value;
|
|
# when it passes Stemming Weight, we've found the segment
|
|
# of truncation line intersecting with (0, 0) - (ui, oi) segment
|
|
if derivative1 >= self.sw >= derivative2:
|
|
return coords
|
|
cutlength += 1
|
|
return coords
|
|
|
|
def _errt(self):
|
|
'''Count Error-Rate Relative to Truncation (ERRT).
|
|
|
|
:return: ERRT, length of the line from origo to (UI, OI) divided by
|
|
the length of the line from origo to the point defined by the same
|
|
line when extended until the truncation line.
|
|
:rtype: float
|
|
'''
|
|
# Count (UI, OI) pairs for truncation points until we find the segment where (ui, oi) crosses the truncation line
|
|
self.coords = self._get_truncation_coordinates()
|
|
if (0.0, 0.0) in self.coords:
|
|
# Truncation line goes through origo, so ERRT cannot be counted
|
|
if (self.ui, self.oi) != (0.0, 0.0):
|
|
return float('inf')
|
|
else:
|
|
return float('nan')
|
|
if (self.ui, self.oi) == (0.0, 0.0):
|
|
# (ui, oi) is origo; define errt as 0.0
|
|
return 0.0
|
|
# Count the intersection point
|
|
# Note that (self.ui, self.oi) cannot be (0.0, 0.0) and self.coords has different coordinates
|
|
# so we have actual line segments instead of a line segment and a point
|
|
intersection = _count_intersection(
|
|
((0, 0), (self.ui, self.oi)), self.coords[-2:]
|
|
)
|
|
# Count OP (length of the line from origo to (ui, oi))
|
|
op = sqrt(self.ui ** 2 + self.oi ** 2)
|
|
# Count OT (length of the line from origo to truncation line that goes through (ui, oi))
|
|
ot = sqrt(intersection[0] ** 2 + intersection[1] ** 2)
|
|
# OP / OT tells how well the stemming algorithm works compared to just truncating words
|
|
return op / ot
|
|
|
|
def update(self):
|
|
'''Update statistics after lemmas and stems have been set.'''
|
|
self.gumt, self.gdmt, self.gwmt, self.gdnt = _calculate(self.lemmas, self.stems)
|
|
self.ui, self.oi, self.sw = _indexes(self.gumt, self.gdmt, self.gwmt, self.gdnt)
|
|
self.errt = self._errt()
|
|
|
|
|
|
def demo():
|
|
'''Demonstration of the module.'''
|
|
# Some words with their real lemmas
|
|
lemmas = {
|
|
'kneel': ['kneel', 'knelt'],
|
|
'range': ['range', 'ranged'],
|
|
'ring': ['ring', 'rang', 'rung'],
|
|
}
|
|
# Same words with stems from a stemming algorithm
|
|
stems = {
|
|
'kneel': ['kneel'],
|
|
'knelt': ['knelt'],
|
|
'rang': ['rang', 'range', 'ranged'],
|
|
'ring': ['ring'],
|
|
'rung': ['rung'],
|
|
}
|
|
print('Words grouped by their lemmas:')
|
|
for lemma in sorted(lemmas):
|
|
print('%s => %s' % (lemma, ' '.join(lemmas[lemma])))
|
|
print()
|
|
print('Same words grouped by a stemming algorithm:')
|
|
for stem in sorted(stems):
|
|
print('%s => %s' % (stem, ' '.join(stems[stem])))
|
|
print()
|
|
p = Paice(lemmas, stems)
|
|
print(p)
|
|
print()
|
|
# Let's "change" results from a stemming algorithm
|
|
stems = {
|
|
'kneel': ['kneel'],
|
|
'knelt': ['knelt'],
|
|
'rang': ['rang'],
|
|
'range': ['range', 'ranged'],
|
|
'ring': ['ring'],
|
|
'rung': ['rung'],
|
|
}
|
|
print('Counting stats after changing stemming results:')
|
|
for stem in sorted(stems):
|
|
print('%s => %s' % (stem, ' '.join(stems[stem])))
|
|
print()
|
|
p.stems = stems
|
|
p.update()
|
|
print(p)
|
|
|
|
|
|
if __name__ == '__main__':
|
|
demo()
|