Class correlation and its effects

user_7327085 0
Viewed 1331

I was going through the iris dataset here : https://archive.ics.uci.edu/ml/machine-learning-databases/iris/ and I found this:

 Summary Statistics:
 Min  Max   Mean    SD   Class Correlation
sepal length: 4.3  7.9   5.84  0.83    0.7826   
sepal width: 2.0  4.4   3.05  0.43   -0.4194
petal length: 1.0  6.9   3.76  1.76    0.9490  (high!)
petal width: 0.1  2.5   1.20  0.76    0.9565  (high!)

What does class correlation signify and what can one infer from it being high or low for a particular feature?

correlation machine-learning dataset
2 Answers

Class Correlation is Pearson's Correlation Coefficient between a Class (a.k.a Target Variable or Response) and other Features (a.k.a Independent Variables).

Pearson's Correlation Coefficient Absolute Value ranges between 0 to 1 (1 means perfect relation).

For example, in your Iris dataset, there are 3 Classes (i.e. Species of Iris), namely: Setosa, Versicolour and Virginica.

On the other hand, you have 4 Features, namely: sepal length, sepal width, petal length and petal width.

It's good to find the correlation between a class from above, and one of the features in the dataset, ...Why? To see how much that feature/attribute worth to the class. In other words, the reliability of the class on that attribute.

From your dataset for example, petal width has the highest correlation with the classes (corr=0.9565), that means: the changes in petal widths highly cause changes in the classes linearly!

So as a result, the feature petal width is very important to model the dataset as well as to predict any future unseen new example!

The same for petal length which has very high correlation with other classes.

As a rule of thumb, Pearson's Correlation Absolute Value can be interpreted as the follows:

  • Weak: from 0.1 to 0.29
  • Intermediate: from 0.3 to 0.49
  • Strong: 0.5 to 1

and that's according to Cohen's Standard.

user_63651120

The parameter seems to describe Intraclass correlation, which is a measure of similarity within a class or group.

A higher value indicates that samples from that class tend to be similar, while a lower value indicates the opposite.

user_104841310
Related