# Source code for nltk.metrics.confusionmatrix

```# Natural Language Toolkit: Confusion Matrices
#
# Copyright (C) 2001-2023 NLTK Project
# Author: Edward Loper <edloper@gmail.com>
#         Steven Bird <stevenbird1@gmail.com>
#         Tom Aarsen <>
# URL: <https://www.nltk.org/>

from nltk.probability import FreqDist

[docs]class ConfusionMatrix:
"""
The confusion matrix between a list of reference values and a
corresponding list of test values.  Entry *[r,t]* of this
matrix is a count of the number of times that the reference value
*r* corresponds to the test value *t*.  E.g.:

>>> from nltk.metrics import ConfusionMatrix
>>> ref  = 'DET NN VB DET JJ NN NN IN DET NN'.split()
>>> test = 'DET VB VB DET NN NN NN IN DET NN'.split()
>>> cm = ConfusionMatrix(ref, test)
>>> print(cm['NN', 'NN'])
3

Note that the diagonal entries *Ri=Tj* of this matrix
corresponds to correct values; and the off-diagonal entries
correspond to incorrect values.
"""

[docs]    def __init__(self, reference, test, sort_by_count=False):
"""
Construct a new confusion matrix from a list of reference
values and a corresponding list of test values.

:type reference: list
:param reference: An ordered list of reference values.
:type test: list
:param test: A list of values to compare against the
corresponding reference values.
:raise ValueError: If ``reference`` and ``length`` do not have
the same length.
"""
if len(reference) != len(test):
raise ValueError("Lists must have the same length.")

# Get a list of all values.
if sort_by_count:
ref_fdist = FreqDist(reference)
test_fdist = FreqDist(test)

def key(v):
return -(ref_fdist[v] + test_fdist[v])

values = sorted(set(reference + test), key=key)
else:
values = sorted(set(reference + test))

# Construct a value->index dictionary
indices = {val: i for (i, val) in enumerate(values)}

# Make a confusion matrix table.
confusion = [[0 for _ in values] for _ in values]
max_conf = 0  # Maximum confusion
for w, g in zip(reference, test):
confusion[indices[w]][indices[g]] += 1
max_conf = max(max_conf, confusion[indices[w]][indices[g]])

#: A list of all values in ``reference`` or ``test``.
self._values = values
#: A dictionary mapping values in ``self._values`` to their indices.
self._indices = indices
#: The confusion matrix itself (as a list of lists of counts).
self._confusion = confusion
#: The greatest count in ``self._confusion`` (used for printing).
self._max_conf = max_conf
#: The total number of values in the confusion matrix.
self._total = len(reference)
#: The number of correct (on-diagonal) values in the matrix.
self._correct = sum(confusion[i][i] for i in range(len(values)))

def __getitem__(self, li_lj_tuple):
"""
:return: The number of times that value ``li`` was expected and
value ``lj`` was given.
:rtype: int
"""
(li, lj) = li_lj_tuple
i = self._indices[li]
j = self._indices[lj]
return self._confusion[i][j]

def __repr__(self):
return f"<ConfusionMatrix: {self._correct}/{self._total} correct>"

def __str__(self):
return self.pretty_format()

[docs]    def pretty_format(
self,
show_percents=False,
values_in_chart=True,
truncate=None,
sort_by_count=False,
):
"""
:return: A multi-line string representation of this confusion matrix.
:type truncate: int
:param truncate: If specified, then only show the specified
number of values.  Any sorting (e.g., sort_by_count)
will be performed before truncation.
:param sort_by_count: If true, then sort by the count of each
label in the reference data.  I.e., labels that occur more
frequently in the reference label will be towards the left
edge of the matrix, and labels that occur less frequently
will be towards the right edge.

"""
confusion = self._confusion

values = self._values
if sort_by_count:
values = sorted(
values, key=lambda v: -sum(self._confusion[self._indices[v]])
)

if truncate:
values = values[:truncate]

if values_in_chart:
value_strings = ["%s" % val for val in values]
else:
value_strings = [str(n + 1) for n in range(len(values))]

# Construct a format string for row values
valuelen = max(len(val) for val in value_strings)
value_format = "%" + repr(valuelen) + "s | "
# Construct a format string for matrix entries
if show_percents:
entrylen = 6
entry_format = "%5.1f%%"
zerostr = "     ."
else:
entrylen = len(repr(self._max_conf))
entry_format = "%" + repr(entrylen) + "d"
zerostr = " " * (entrylen - 1) + "."

# Write the column values.
s = ""
for i in range(valuelen):
s += (" " * valuelen) + " |"
for val in value_strings:
if i >= valuelen - len(val):
s += val[i - valuelen + len(val)].rjust(entrylen + 1)
else:
s += " " * (entrylen + 1)
s += " |\n"

# Write a dividing line
s += "{}-+-{}+\n".format("-" * valuelen, "-" * ((entrylen + 1) * len(values)))

# Write the entries.
for val, li in zip(value_strings, values):
i = self._indices[li]
s += value_format % val
for lj in values:
j = self._indices[lj]
if confusion[i][j] == 0:
s += zerostr
elif show_percents:
s += entry_format % (100.0 * confusion[i][j] / self._total)
else:
s += entry_format % confusion[i][j]
if i == j:
prevspace = s.rfind(" ")
s = s[:prevspace] + "<" + s[prevspace + 1 :] + ">"
else:
s += " "
s += "|\n"

# Write a dividing line
s += "{}-+-{}+\n".format("-" * valuelen, "-" * ((entrylen + 1) * len(values)))

# Write a key
s += "(row = reference; col = test)\n"
if not values_in_chart:
s += "Value key:\n"
for i, value in enumerate(values):
s += "%6d: %s\n" % (i + 1, value)

return s

[docs]    def key(self):
values = self._values
str = "Value key:\n"
indexlen = len(repr(len(values) - 1))
key_format = "  %" + repr(indexlen) + "d: %s\n"
for i in range(len(values)):
str += key_format % (i, values[i])

return str

[docs]    def recall(self, value):
"""Given a value in the confusion matrix, return the recall
that corresponds to this value. The recall is defined as:

- *r* = true positive / (true positive + false positive)

and can loosely be considered the ratio of how often ``value``
was predicted correctly relative to how often ``value`` was
the true result.

:param value: value used in the ConfusionMatrix
:return: the recall corresponding to ``value``.
:rtype: float
"""
# Number of times `value` was correct, and also predicted
TP = self[value, value]
# Number of times `value` was correct
TP_FN = sum(self[value, pred_value] for pred_value in self._values)
if TP_FN == 0:
return 0.0
return TP / TP_FN

[docs]    def precision(self, value):
"""Given a value in the confusion matrix, return the precision
that corresponds to this value. The precision is defined as:

- *p* = true positive / (true positive + false negative)

and can loosely be considered the ratio of how often ``value``
was predicted correctly relative to the number of predictions
for ``value``.

:param value: value used in the ConfusionMatrix
:return: the precision corresponding to ``value``.
:rtype: float
"""
# Number of times `value` was correct, and also predicted
TP = self[value, value]
# Number of times `value` was predicted
TP_FP = sum(self[real_value, value] for real_value in self._values)
if TP_FP == 0:
return 0.0
return TP / TP_FP

[docs]    def f_measure(self, value, alpha=0.5):
"""
Given a value used in the confusion matrix, return the f-measure
that corresponds to this value. The f-measure is the harmonic mean
of the ``precision`` and ``recall``, weighted by ``alpha``.
In particular, given the precision *p* and recall *r* defined by:

- *p* = true positive / (true positive + false negative)
- *r* = true positive / (true positive + false positive)

The f-measure is:

- *1/(alpha/p + (1-alpha)/r)*

With ``alpha = 0.5``, this reduces to:

- *2pr / (p + r)*

:param value: value used in the ConfusionMatrix
:param alpha: Ratio of the cost of false negative compared to false
positives. Defaults to 0.5, where the costs are equal.
:type alpha: float
:return: the F-measure corresponding to ``value``.
:rtype: float
"""
p = self.precision(value)
r = self.recall(value)
if p == 0.0 or r == 0.0:
return 0.0
return 1.0 / (alpha / p + (1 - alpha) / r)

[docs]    def evaluate(self, alpha=0.5, truncate=None, sort_by_count=False):
"""
Tabulate the **recall**, **precision** and **f-measure**
for each value in this confusion matrix.

>>> reference = "DET NN VB DET JJ NN NN IN DET NN".split()
>>> test = "DET VB VB DET NN NN NN IN DET NN".split()
>>> cm = ConfusionMatrix(reference, test)
>>> print(cm.evaluate())
Tag | Prec.  | Recall | F-measure
----+--------+--------+-----------
DET | 1.0000 | 1.0000 | 1.0000
IN | 1.0000 | 1.0000 | 1.0000
JJ | 0.0000 | 0.0000 | 0.0000
NN | 0.7500 | 0.7500 | 0.7500
VB | 0.5000 | 1.0000 | 0.6667
<BLANKLINE>

:param alpha: Ratio of the cost of false negative compared to false
positives, as used in the f-measure computation. Defaults to 0.5,
where the costs are equal.
:type alpha: float
:param truncate: If specified, then only show the specified
number of values. Any sorting (e.g., sort_by_count)
will be performed before truncation. Defaults to None
:type truncate: int, optional
:param sort_by_count: Whether to sort the outputs on frequency
in the reference label. Defaults to False.
:type sort_by_count: bool, optional
:return: A tabulated recall, precision and f-measure string
:rtype: str
"""
tags = self._values

# Apply keyword parameters
if sort_by_count:
tags = sorted(tags, key=lambda v: -sum(self._confusion[self._indices[v]]))
if truncate:
tags = tags[:truncate]

tag_column_len = max(max(len(tag) for tag in tags), 3)

s = (
f"{' ' * (tag_column_len - 3)}Tag | Prec.  | Recall | F-measure\n"
f"{'-' * tag_column_len}-+--------+--------+-----------\n"
)

# Construct the body
for tag in tags:
s += (
f"{tag:>{tag_column_len}} | "
f"{self.precision(tag):<6.4f} | "
f"{self.recall(tag):<6.4f} | "
f"{self.f_measure(tag, alpha=alpha):.4f}\n"
)

return s

[docs]def demo():
reference = "DET NN VB DET JJ NN NN IN DET NN".split()
test = "DET VB VB DET NN NN NN IN DET NN".split()
print("Reference =", reference)
print("Test    =", test)
print("Confusion matrix:")
print(ConfusionMatrix(reference, test))
print(ConfusionMatrix(reference, test).pretty_format(sort_by_count=True))

print(ConfusionMatrix(reference, test).recall("VB"))

if __name__ == "__main__":
demo()
```