<p>I tend to see <strong>correlation versus covariance</strong> as an opposition between a quick <strong>dry mathematical relation overview</strong> and a more <strong>raw relation analysis</strong>. Imagine yourself joining a project in a field you know approximately nothing about:</p>

<ul>
<li>if a team member gives you a correlation coefficient for two key variables/indicators associated with the project, you will be able to extract all the information out of this coefficient immediately, without knowing the samples respective scales</li>
<li>if he gives you a covariance, you will probably want to have a look at the data to appreciate exactly what it implies</li>
</ul>

<p>Covariance is easily understood when the samples being compared live on a similar scale/have a similar nature, since the value you'll be considering will not try to compare two completely different things with an intuitively absurd compromise in nature/scale (remember that to compute the covariance you use the products of two things possibly very different with <code>(x-mean(x))(y-mean(y))</code>). Correlation being standardized, issues associated with varying scales and nature in the data are simply absent of your indicator, leading to an "easier interpretation" feeling. </p>

<p>One should therefore realize that <strong>while correlation can make it easier to understand a mathematical relationship, it obfuscates the actual nature of the data you're playing with.</strong> Looking at both can't hurt you to appreciate what's going on with your samples, and that's probably why you'll like considering both. If you aren't convinced you can also read this <a href="https://stats.stackexchange.com/questions/53/pca-on-correlation-or-covariance">related stats.stackexchange question</a>.</p>

<p>In case you wonder why would you want to keep close to the nature and scales of your data while trying to highlight relations between samples, a good example would be the efforts deployed in AI to extract useful features in images to feed models: you want to emphasize discriminatory descriptions of data, without filtering out other potentially interesting information with a standardization. See for example <a href="https://arxiv.org/abs/1409.0083" rel="nofollow noreferrer">this paper</a> that uses covariance matrices to build a dictionary on images.</p>
Importance of covariance
<p>If I have calculated coefficient of correlation, I already have the idea of covariance. But I have seen many data scientist calculates the covariance after it. If I have coefficient of correlation with me, I can say that data is positively or negatively correlated with the strength, while covariance give the same thing without the strength. Then what is the importance of covariance if I have coefficient of correlation.</p>

<p>Please suggest, apologies if my question is of low importance.</p>