I wrote a confusion matrix calculation code in Python:
def conf_mat(prob_arr, input_arr):
# confusion matrix
conf_arr = [[0, 0], [0, 0]]
for i in range(len(prob_arr)):
if int(input_arr[i]) == 1:
if float(prob_arr[i]) < 0.5:
conf_arr[0][1] = conf_arr[0][1] + 1
else:
conf_arr[0][0] = conf_arr[0][0] + 1
elif int(input_arr[i]) == 2:
if float(prob_arr[i]) >= 0.5:
conf_arr[1][0] = conf_arr[1][0] +1
else:
conf_arr[1][1] = conf_arr[1][1] +1
accuracy = float(conf_arr[0][0] + conf_arr[1][1])/(len(input_arr))
prob_arr is an array that my classification code returned and a sample array is like this:
[1.0, 1.0, 1.0, 0.41592955657342651, 1.0, 0.0053405015805891975, 4.5321494433440449e-299, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.70943426182688163, 1.0, 1.0, 1.0, 1.0]
input_arr is the original class labels for a dataset and it is like this:
[2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1]
What my code is trying to do is: i get prob_arr and input_arr and for each class (1 and 2) I check if they are misclassified or not.
But my code only works for two classes. If I run this code for a multiple classed data, it doesn't work. How can I make this for multiple classes?
For example, for a data set with three classes, it should return: [[21,7,3],[3,38,6],[5,4,19]]
18 Answers
Scikit-Learn provides a confusion_matrix function
from sklearn.metrics import confusion_matrix
y_actu = [2, 0, 2, 2, 0, 1, 1, 2, 2, 0, 1, 2]
y_pred = [0, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 2]
confusion_matrix(y_actu, y_pred)
which output a Numpy array
array([[3, 0, 0],
[0, 1, 2],
[2, 1, 3]])
But you can also create a confusion matrix using Pandas:
import pandas as pd
y_actu = pd.Series([2, 0, 2, 2, 0, 1, 1, 2, 2, 0, 1, 2], name='Actual')
y_pred = pd.Series([0, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 2], name='Predicted')
df_confusion = pd.crosstab(y_actu, y_pred)
You will get a (nicely labeled) Pandas DataFrame:
Predicted 0 1 2
Actual
0 3 0 0
1 0 1 2
2 2 1 3
If you add margins=True like
df_confusion = pd.crosstab(y_actu, y_pred, rownames=['Actual'], colnames=['Predicted'], margins=True)
you will get also sum for each row and column:
Predicted 0 1 2 All
Actual
0 3 0 0 3
1 0 1 2 3
2 2 1 3 6
All 5 2 5 12
You can also get a normalized confusion matrix using:
df_conf_norm = df_confusion / df_confusion.sum(axis=1)
Predicted 0 1 2
Actual
0 1.000000 0.000000 0.000000
1 0.000000 0.333333 0.333333
2 0.666667 0.333333 0.500000
You can plot this confusion_matrix using
import matplotlib.pyplot as plt
def plot_confusion_matrix(df_confusion, title='Confusion matrix', cmap=plt.cm.gray_r):
plt.matshow(df_confusion, cmap=cmap) # imshow
#plt.title(title)
plt.colorbar()
tick_marks = np.arange(len(df_confusion.columns))
plt.xticks(tick_marks, df_confusion.columns, rotation=45)
plt.yticks(tick_marks, df_confusion.index)
#plt.tight_layout()
plt.ylabel(df_confusion.index.name)
plt.xlabel(df_confusion.columns.name)
plot_confusion_matrix(df_confusion)
Or plot normalized confusion matrix using:
plot_confusion_matrix(df_conf_norm)
You might also be interested by this project and its Pip package
With this package confusion matrix can be pretty-printed, plot. You can binarize a confusion matrix, get class statistics such as TP, TN, FP, FN, ACC, TPR, FPR, FNR, TNR (SPC), LR+, LR-, DOR, PPV, FDR, FOR, NPV and some overall statistics
In [1]: from pandas_ml import ConfusionMatrix
In [2]: y_actu = [2, 0, 2, 2, 0, 1, 1, 2, 2, 0, 1, 2]
In [3]: y_pred = [0, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 2]
In [4]: cm = ConfusionMatrix(y_actu, y_pred)
In [5]: cm.print_stats()
Confusion Matrix:
Predicted 0 1 2 __all__
Actual
0 3 0 0 3
1 0 1 2 3
2 2 1 3 6
__all__ 5 2 5 12
Overall Statistics:
Accuracy: 0.583333333333
95% CI: (0.27666968568210581, 0.84834777019156982)
No Information Rate: ToDo
P-Value [Acc > NIR]: 0.189264302376
Kappa: 0.354838709677
Mcnemar's Test P-Value: ToDo
Class Statistics:
Classes 0 1 2
Population 12 12 12
P: Condition positive 3 3 6
N: Condition negative 9 9 6
Test outcome positive 5 2 5
Test outcome negative 7 10 7
TP: True Positive 3 1 3
TN: True Negative 7 8 4
FP: False Positive 2 1 2
FN: False Negative 0 2 3
TPR: (Sensitivity, hit rate, recall) 1 0.3333333 0.5
TNR=SPC: (Specificity) 0.7777778 0.8888889 0.6666667
PPV: Pos Pred Value (Precision) 0.6 0.5 0.6
NPV: Neg Pred Value 1 0.8 0.5714286
FPR: False-out 0.2222222 0.1111111 0.3333333
FDR: False Discovery Rate 0.4 0.5 0.4
FNR: Miss Rate 0 0.6666667 0.5
ACC: Accuracy 0.8333333 0.75 0.5833333
F1 score 0.75 0.4 0.5454545
MCC: Matthews correlation coefficient 0.6831301 0.2581989 0.1690309
Informedness 0.7777778 0.2222222 0.1666667
Markedness 0.6 0.3 0.1714286
Prevalence 0.25 0.25 0.5
LR+: Positive likelihood ratio 4.5 3 1.5
LR-: Negative likelihood ratio 0 0.75 0.75
DOR: Diagnostic odds ratio inf 4 2
FOR: False omission rate 0 0.2 0.4285714
I noticed that a new Python library about Confusion Matrix named PyCM is out: maybe you can have a look.
Nearly a decade has passed, yet the solutions (without sklearn) to this post are convoluted and unnecessarily long. Computing a confusion matrix can be done cleanly in Python in a few lines. For example:
import numpy as np
def compute_confusion_matrix(true, pred):
'''Computes a confusion matrix using numpy for two np.arrays
true and pred.
Results are identical (and similar in computation time) to:
"from sklearn.metrics import confusion_matrix"
However, this function avoids the dependency on sklearn.'''
K = len(np.unique(true)) # Number of classes
result = np.zeros((K, K))
for i in range(len(true)):
result[true[i]][pred[i]] += 1
return result
Scikit-learn (which I recommend using anyways) has it included in the metrics module:
>>> from sklearn.metrics import confusion_matrix
>>> y_true = [0, 1, 2, 0, 1, 2, 0, 1, 2]
>>> y_pred = [0, 0, 0, 0, 1, 1, 0, 2, 2]
>>> confusion_matrix(y_true, y_pred)
array([[3, 0, 0],
[1, 1, 1],
[1, 1, 1]])
If you don't want scikit-learn to do the work for you...
import numpy
actual = numpy.array(actual)
predicted = numpy.array(predicted)
# calculate the confusion matrix; labels is numpy array of classification labels
cm = numpy.zeros((len(labels), len(labels)))
for a, p in zip(actual, predicted):
cm[a][p] += 1
# also get the accuracy easily with numpy
accuracy = (actual == predicted).sum() / float(len(actual))
Or take a look at a more complete implementation here in NLTK.
A Dependency Free Multiclass Confusion Matrix
# A Simple Confusion Matrix Implementation
def confusionmatrix(actual, predicted, normalize = False):
"""
Generate a confusion matrix for multiple classification
@params:
actual - a list of integers or strings for known classes
predicted - a list of integers or strings for predicted classes
normalize - optional boolean for matrix normalization
@return:
matrix - a 2-dimensional list of pairwise counts
"""
unique = sorted(set(actual))
matrix = [[0 for _ in unique] for _ in unique]
imap = {key: i for i, key in enumerate(unique)}
# Generate Confusion Matrix
for p, a in zip(predicted, actual):
matrix[imap[p]][imap[a]] += 1
# Matrix Normalization
if normalize:
sigma = sum([sum(matrix[imap[i]]) for i in unique])
matrix = [row for row in map(lambda i: list(map(lambda j: j / sigma, i)), matrix)]
return matrix
The approach here is to pair up the unique classes found in the actual vector into a 2-dimensional list. From there, we simply iterate through the zipped actual and predicted vectors and populate the counts using the indices to access the matrix positions.
Usage
cm = confusionmatrix(
[1, 1, 2, 0, 1, 1, 2, 0, 0, 1], # actual
[0, 1, 1, 0, 2, 1, 2, 2, 0, 2] # predicted
)
# And The Output
print(cm)
[[2, 1, 0], [0, 2, 1], [1, 2, 1]]
Note: the actual classes are along the columns and the predicted classes are along the rows.
# Actual
# 0 1 2
# # #
[[2, 1, 0], # 0
[0, 2, 1], # 1 Predicted
[1, 2, 1]] # 2
Class Names Can be Strings or Integers
cm = confusionmatrix(
["B", "B", "C", "A", "B", "B", "C", "A", "A", "B"], # actual
["A", "B", "B", "A", "C", "B", "C", "C", "A", "C"] # predicted
)
# And The Output
print(cm)
[[2, 1, 0], [0, 2, 1], [1, 2, 1]]
You Can Also Return The Matrix With Proportions (Normalization)
cm = confusionmatrix(
["B", "B", "C", "A", "B", "B", "C", "A", "A", "B"], # actual
["A", "B", "B", "A", "C", "B", "C", "C", "A", "C"], # predicted
normalize = True
)
# And The Output
print(cm)
[[0.2, 0.1, 0.0], [0.0, 0.2, 0.1], [0.1, 0.2, 0.1]]
