Confusion Matrix

This function evaluates the (multiclass[^1]) Confusion Matrix (CM) associated to a classifier output predictions. The CM is a metric that measures the misclassification rates between all the classes in the classification task.

Mathematical definition

Mathematically, if the classification task has $N_c$ target classes, the CM is an $N_c \times N_c$ matrix whose entry $C_{i,j}$ is the number of predictions known to be in group $i$ and predicted to be in group $j$. The matrix can then be normalized in different ways, obtaining rates of misclassifications instead of raw counts (more on that in normalization).

Implementation

The function confusion_matrix in puma.utils.confusion_matrix computes the CM from two arrays of target and predicted labels. The basic usage is:

targets = np.array([2, 0, 2, 2, 0, 1])
predictions = np.array([0, 0, 2, 2, 0, 2])
confusion_matrix(targets, predictions)

Eventually, samples can be weighted by their relative importance by providing an array of weights $w_i \in [0,1]$:

targets = np.array([2, 0, 2, 2, 0, 1])
predictions = np.array([0, 0, 2, 2, 0, 2])
weights = np.array([1, 0.5, 0.5, 1, 0.2, 1])
confusion_matrix(targets, predictions, sample_weights=weights)

Normalization

There are four possible normalization choices, which can be selected through the normalize argument of the function: - None: Give raw counts; - "rownorm": Normalize across the prediction class, i.e. such that the rows add to one (default); - "colnorm": Normalize across the target class, i.e. such that the columns add to one; - "all": Normalize across all examples, i.e. such that all matrix entries add to one. Defaults to "all".

Example

from __future__ import annotations

import numpy as np

from puma.utils.confusion_matrix import confusion_matrix

# Sample size
N = 100

# Number of target classes
Nclass = 3

# Dummy target labels
targets = np.random.randint(0, Nclass + 1, size=N)

# Dummy predicted labels
predictions = np.random.randint(0, Nclass + 1, size=N)


# Confusion matrix examples:

# Unweighted confusion matrix, normalized on all entries
unweighted_cm = confusion_matrix(targets, predictions, normalize="all")
print("Unweighted, normalized on all entries, CM:")
print(unweighted_cm)
print(" ")

# Unweighted confusion matrix, normalized on true labels
unweighted_cm = confusion_matrix(targets, predictions, normalize="rownorm")
print("Unweighted, normalized true labels (rownorm), CM:")
print(unweighted_cm)
print(" ")

# Unweighted confusion matrix, with raw counts (non-normalized)
unweighted_cm = confusion_matrix(targets, predictions, normalize=None)
print("Unweighted, non-normalized, CM:")
print(unweighted_cm)
print(" ")

# Weighted Confusion Matrix
# Dummy sample weights
sample_weights = np.random.rand(N)

weighted_cm = confusion_matrix(targets, predictions, sample_weights=sample_weights)
print("Weighted CM:")
print(weighted_cm)

[^1] In a multiclass task, each sample belongs to one and only class (the true label, or target label).