Source code for sentarget.metrics.functional
r"""
Elementary functions used for statistical reports.
"""
import numpy as np
[docs]def true_positive(matrix):
r"""True positive values from a confusion matrix.
.. math::
TP(M) = \text{Diag}(M)
Args:
matrix (numpy.ndarray): confusion matrix of shape :math:`(C, C)`.
Returns:
numpy.ndarray
"""
return np.diag(matrix)
[docs]def true_negative(matrix):
r"""True negatives values from a confusion matrix.
.. math::
TN(M) = \sum_{i=0}^{C-1}{\sum_{j=0}^{C-1}{M_{i, j}}} - FN(M) + FP(M) + TP(M)
Args:
matrix (numpy.ndarray): confusion matrix of shape :math:`(C, C)`.
Returns:
numpy.ndarray
"""
return np.sum(matrix) - (false_positive(matrix) + false_negative(matrix) + true_positive(matrix))
[docs]def false_positive(matrix):
r"""False positives values from a confusion matrix.
.. math::
FP(M) = \sum_{i=0}^{C-1}{M_i} - \text{Diag}(M)
Args:
matrix (numpy.ndarray): confusion matrix of shape :math:`(C, C)`.
Returns:
numpy.ndarray
"""
return np.sum(matrix, axis=0) - np.diag(matrix)
[docs]def false_negative(matrix):
r"""False negatives values from a confusion matrix.
.. math::
FN(M) = \sum_{j=0}^{C-1}{M_j} - \text{Diag}(M)
Args:
matrix (numpy.ndarray): confusion matrix of shape :math:`(C, C)`.
Returns:
numpy.ndarray
"""
return np.sum(matrix, axis=1) - np.diag(matrix)
[docs]def true_positive_rate(matrix):
r"""True positive rate from a confusion matrix.
.. math::
TPR(M) = \frac{TP(M)}{TP(M) + FN(M)}
Args:
matrix (numpy.ndarray): confusion matrix of shape :math:`(C, C)`.
Returns:
numpy.ndarray
"""
top = true_positive(matrix)
bottom = true_positive(matrix) + false_negative(matrix)
return np.where(bottom != 0, top / bottom, 0)
[docs]def true_negative_rate(matrix):
r"""True negative rate from a confusion matrix.
.. math::
TNR(M) = \frac{TN(M)}{TN(M) + FP(M)}
Args:
matrix (numpy.ndarray): confusion matrix of shape :math:`(C, C)`.
Returns:
numpy.ndarray
"""
top = true_negative(matrix)
bottom = true_negative(matrix) + false_positive(matrix)
return np.where(bottom != 0, top / bottom, 0)
[docs]def positive_predictive_value(matrix):
r"""Positive predictive value from a confusion matrix.
.. math::
PPV(M) = \frac{TP(M)}{TP(M) + FP(M)}
Args:
matrix (numpy.ndarray): confusion matrix of shape :math:`(C, C)`.
Returns:
numpy.ndarray
"""
top = true_positive(matrix)
bottom = true_positive(matrix) + false_positive(matrix)
return np.where(bottom != 0, top / bottom, 0)
[docs]def negative_predictive_value(matrix):
r"""Negative predictive value from a confusion matrix.
.. math::
NPV(M) = \frac{TN(M)}{TN(M) + FN(M)}
Args:
matrix (numpy.ndarray): confusion matrix of shape :math:`(C, C)`.
Returns:
numpy.ndarray
"""
top = true_negative(matrix)
bottom = true_negative(matrix) + false_negative(matrix)
return np.where(bottom != 0, top / bottom, 0)
[docs]def false_positive_rate(matrix):
r"""False positive rate from a confusion matrix.
.. math::
FPR(M) = \frac{FP(M)}{FP(M) + FN(M)}
Args:
matrix (numpy.ndarray): confusion matrix of shape :math:`(C, C)`.
Returns:
numpy.ndarray
"""
top = false_positive(matrix)
bottom = false_positive(matrix) + false_negative(matrix)
return np.where(bottom != 0, top / bottom, 0)
[docs]def false_negative_rate(matrix):
r"""False negative rate from a confusion matrix.
.. math::
FNR(M) = \frac{FN(M)}{FN(M) + TP(M)}
Args:
matrix (numpy.ndarray): confusion matrix of shape :math:`(C, C)`.
Returns:
numpy.ndarray
"""
top = false_negative(matrix)
bottom = true_positive(matrix) + false_negative(matrix)
return np.where(bottom != 0, top / bottom, 0)
[docs]def false_discovery_rate(matrix):
r"""False discovery rate from a confusion matrix.
.. math::
FDR(M) = \frac{FP(M)}{FP(M) + TP(M)}
Args:
matrix (numpy.ndarray): confusion matrix of shape :math:`(C, C)`.
Returns:
numpy.ndarray
"""
top = false_positive(matrix)
bottom = true_positive(matrix) + false_positive(matrix)
return np.where(bottom != 0, top / bottom, 0)
[docs]def accuracy(matrix):
r"""Per class accuracy from a confusion matrix.
.. math::
ACC(M) = \frac{TP(M) + TN(M)}{TP(M) + TN(M) + FP(M) + FN(M)}
Args:
matrix (numpy.ndarray): confusion matrix of shape :math:`(C, C)`.
Returns:
numpy.ndarray
"""
top = true_positive(matrix) + true_negative(matrix)
bottom = true_positive(matrix) + true_negative(matrix) + false_positive(matrix) + false_negative(matrix)
return np.where(bottom != 0, top / bottom, 0)
[docs]def flatten_matrix(matrix, axis_label=0, axis_pred=1, map=None):
r"""Flatten a confusion matrix to retrieve its prediction and gold labels.
Args:
matrix (numpy.ndarray): confusion matrix of shape :math:`(C, C)`.
axis_label (int): axis index corresponding to the gold labels.
axis_pred (int): axis index corresponding to the predictions.
map (dict): dictionary to map indices to label.
Returns:
gold labels and predictions.
"""
gold_labels = []
predictions = []
# Change the index order ?
matrix = np.array(matrix)
if axis_label != 0 or axis_pred != 1:
matrix = matrix.T
# Make sure the matrix is a confusion matrix
C = len(matrix)
map = {idx: idx for idx in range(C)} if map is None else map
assert matrix.shape == (C, C), 'the provided matrix is not square'
for i in range(C):
for j in range(C):
gold_labels.extend([map[i]] * int(matrix[i, j]))
predictions.extend([map[j]] * int(matrix[i, j]))
return gold_labels, predictions
