Calculate True Negative Rate for Convolutional Neural Network

The true negative rate (TNR) is a key performance metric for evaluating the effectiveness of a convolutional neural network (CNN) in correctly identifying negative cases. This guide explains how to calculate TNR for CNNs, including the formula, practical examples, and interpretation guidance.

What is True Negative Rate?

The true negative rate measures the proportion of actual negative cases that were correctly identified by the CNN. In medical imaging or other classification tasks, this metric indicates how well the model avoids false alarms for negative cases.

TNR is particularly important when false negatives (missed positive cases) are more critical than false positives. For example, in cancer detection, missing a positive case (false negative) is more dangerous than incorrectly flagging a healthy patient (false positive).

Formula

True Negative Rate (TNR) = TN / (TN + FP)

Where:

TN = True Negatives (correctly identified negative cases)
FP = False Positives (incorrectly identified positive cases)

The result is typically expressed as a decimal between 0 and 1, or as a percentage. A higher TNR indicates better performance in identifying negative cases.

How to Calculate

Determine the number of true negatives (TN) in your test dataset.
Determine the number of false positives (FP) in your test dataset.
Apply the formula: TNR = TN / (TN + FP)
Convert the decimal to a percentage if needed.

For CNNs, these values are typically obtained from a confusion matrix after evaluating the model on a test dataset.

Example Calculation

Suppose you have a CNN for detecting pneumonia in X-rays:

Actual \ Predicted	Positive	Negative
Positive	85 (TP)	15 (FN)
Negative	10 (FP)	90 (TN)

Using the formula:

TNR = TN / (TN + FP) = 90 / (90 + 10) = 0.90 or 90%

This means the CNN correctly identified 90% of the actual negative cases.

Interpreting Results

A TNR of 1 (or 100%) indicates perfect performance in identifying negative cases. In practice, values between 0.8 and 1.0 are generally considered good, depending on the application.

If your TNR is low, consider:

Improving the CNN architecture
Collecting more training data
Adjusting the classification threshold
Evaluating the quality of negative cases in your dataset

FAQ

What is the difference between TNR and specificity?: TNR and specificity are the same metric. The terms are used interchangeably in machine learning and statistics.
How does TNR relate to false positive rate?: False positive rate (FPR) is calculated as FP / (FP + TN). These two metrics are complementary: TNR = 1 - FPR.
Is a high TNR always good?: Not necessarily. In some applications, a high TNR might come at the cost of a lower true positive rate (TPR). You need to balance TNR with other metrics like precision and recall.
Can TNR be greater than 1?: No, TNR is a proportion and cannot exceed 1 (or 100%). If you get a value greater than 1, check your calculations for errors in counting TN and FP.