The true positive (TP), together with true negative (TN) (*) is a type of accurately predicted outcome, meaning that the prediction matches the true observation/ condition in terms of the class (positive/ negative).  
 
TP occurs when a positive class prediction (classification) was accurately made.  


True Positive (TP)

The true negative (TN), together with true positive (TP), is a type of accurately predicted outcome, meaning that the prediction matches the true observation/ condition in terms of the class (positive/ negative).  
 
TN occurs when a negative class prediction (classification) was accurately made.  




True Negative (TN) 

The false positive (FP), together with false negative (FN) (*), is a type of inaccurately predicted outcome, meaning that the prediction does not match the true observation/ condition in terms of the class (positive/ negative).  
 
FP occurs when a positive class prediction (classification) was inaccurately made when a negative class prediction, when accurately predicted, should have been made.  

In the example of the mammogram: 
If the woman who is tested positive for breast cancer does not actually have the disease, such an incorrect prediction is called FP.   



False Positive (FP) 

The false negative (FN), together with false positive (FP), is a type of inaccurately predicted outcome, meaning that the prediction does not match the true observation/ condition in terms of the class (positive/ negative).  
 
FN occurs when a negative class prediction (classification) was inaccurately made when a positive class prediction, when accurately predicted, should have been made.  


False Negative (FN)

- True Positive (TP)
- True Negative (TN)
- False Positive (FP)
- False Negative (FN)

University of Michigan - Ann Arbor

The confusion matrix is a performance measurement method that can be used for binary classification and multi-class classifications.  It is usually shown shown in a table format with the four possible outcomes: True Positive (TP), True Negative (TN), False Positive (FP), and False Negative (FN).  

Confusion Matrix

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, pp. 3-7). New York: springer.

An Introduction to Statistical Learning with Applications in R

Chapter 10: Evaluating Model Performance
Section: A closer look at confusion matrices

Lantz, Brett. Machine Learning with R - Second Edition: Expert techniques for predictive modeling to solve all your data analysis problems (p. 317-318). Kindle Edition. 


How to read confusion matrix for binary classification

Components of Confusion Matrix

The multi-class confusion matrix is a straightforward extension of the binary classifier two by two confusion matrix.
For example, for classification of hand-written digits, there are ten classes for each digit, zero through nine. So, the ten-class confusion matrix is a 10x10 matrix with the true digit class indexed by row and the predicted digit class indexed by column. Like the 2x2 case, the correct prediction is by the classifier where the true class matches the predicted class are all along the diagonal and misclassifications are off the diagonal.

In this example, most of the predictions are correct with only a few misclassifications. The most frequent type of mistake here is misclassifying the true digit, 8 as a predicted digit 1 which happened three times.
And the overall accuracy is high, about 97%.

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