# What does harmonic mean tell us?

## What does harmonic mean tell us?

The harmonic mean helps to find multiplicative or divisor relationships between fractions without worrying about common denominators. Harmonic means are often used in averaging things like rates (e.g., the average travel speed given a duration of several trips).

## What is harmonic mean in machine learning?

The harmonic mean is calculated as the number of values N divided by the sum of the reciprocal of the values (1 over each value). Harmonic Mean = N / (1/x1 + 1/x2 + … + 1/xN)

What is the formula for precision and recall?

For example, a perfect precision and recall score would result in a perfect F-Measure score: F-Measure = (2 * Precision * Recall) / (Precision + Recall) F-Measure = (2 * 1.0 * 1.0) / (1.0 + 1.0) F-Measure = (2 * 1.0) / 2.0.

What is F1 score in NLP?

F1 score – F1 Score is the weighted average of Precision and Recall. Therefore, this score takes both false positives and false negatives into account. Intuitively it is not as easy to understand as accuracy, but F1 is usually more useful than accuracy, especially if you have an uneven class distribution.

### What is the harmonic mean of 5/6 and 7?

Search. What are the harmonic means of 5, 6 and 7? 3/(1/5+1/6+1/7) = 3/(42/210 + 35/210 + 30/210 ) = 3/( 107/210) = 3 x 210/107= 630/107 = 5.89.

### Is harmonic mean based on all observations?

Like the arithmetic and geometric means, harmonic mean is based on all observations. If any value of the data set equals zero, the harmonic mean cannot be calculated.

Why F1 score is harmonic mean of precision and recall?

Precision and recall both have true positives in the numerator, and different denominators. To average them it really only makes sense to average their reciprocals, thus the harmonic mean.

What is recall in machine learning?

Recall literally is how many of the true positives were recalled (found), i.e. how many of the correct hits were also found. Precision (your formula is incorrect) is how many of the returned hits were true positive i.e. how many of the found were correct hits.

#### Can precision and recall be the same?

So we know precision, recall and F1 can have the same value in general. Now, this does not apply to your specific result. If we solve the system of equations, we find another solution: FP = FN . So, if the number of false positives is the same as the number of false negatives, all three metrics have identical values.

#### What is the meaning of recall in government?

A recall election (also called a recall referendum, recall petition or representative recall) is a procedure by which, in certain polities, voters can remove an elected official from office through a referendum before that official’s term of office has ended.

Why F-score is harmonic mean?

So, from the plot of the harmonic mean, both the precision and recall should contribute evenly for the F1 score to rise up unlike the Arithmetic mean. This is for the arithmetic mean. This is for the Harmonic mean.

What is recall score?

The recall is the ratio tp / (tp + fn) where tp is the number of true positives and fn the number of false negatives. The recall is intuitively the ability of the classifier to find all the positive samples. The best value is 1 and the worst value is 0.

## Why is F1-score a harmonic mean of precision and recall?

Have you asked why F1-Score is a Harmonic Mean (HM) of Precision and Recall? Well, I did. The reason is simple and clever. Let me go back to the definitions of Precision and Recall. Precision (P) is the Ratio of True Positives to All the positives predicted by the model.

## What is the relationship between recall and precision?

This decision increases precision but reduces recall. That is to say, greater recall increases the chances of removing healthy cells (negative outcome) and increases the chances of removing all cancer cells (positive outcome).

What is the difference between high precision and high recall?

Higher precision means that an algorithm returns more relevant results than irrelevant ones, and high recall means that an algorithm returns most of the relevant results (whether or not irrelevant ones are also returned).

How sensitive is the harmonic mean to the lowest value?

Let’s see the 3D plot of the harmonic mean. We can see that the harmonic mean is sensitive to the lowest value, especially the harmonic mean is 0 when at least one is 0, which doesn’t hold for the simple arithmetic mean. For more visualization of this topic, please refer to this article: F1 score explained.