# Question regarding Lecture 5 CS229

I was at the part where we are using one covariance matrix and two mean vectors for fitting our Gaussian. I understood that we are using one covariance matrix and we can use different ones that would lead to a non-linear decision boundary. What I was unable to comprehend was the shape of the contours. They seem perfectly circular to me (if we incorporate the y axis range (-7, 1) and x -axis range (-2,7)) but looking at the data points in the scatter plot, there is some correlation between the values of y-axis and x-axis (large values on y-axis are corresponding to large values in x-axis and the other way as well) which should result in an elliptical Gaussian. Is there something that I am missing?

• It would be helpful if you would add the plots, here Commented Sep 9, 2023 at 15:18
• Just did. Thanks for the suggestion. Commented Sep 11, 2023 at 14:44

It is hard to tell without extracting the data and having a close look, but I do see two explanations, here:

##### This is not an accurate plot

This is the easy explanation: The circles do not fit exactly to the data. Either the data was altered a bit and someone forgot to adjust the Gaussians or the Gaussians were not computed from the data, but just plotted to look fitting.

Nevertheless, I consider this quite unlikely as it is no big effort to create accurate plots and probably these figures have been checked multiple times.

##### Your brain is playing tricks on you

Most important first: This is no flaw on your side.

Our brains are very good at dectecting patterns (that's one reason, why we use plots to gain insides). Unfortunately, our brains detect patterns everywhere, even if they do not exist. This is a fact every data scientist should be aware off.

In this case, my guess would be that the plotted Gassian circles guide your brain to concentrate on the points outside these circles. So I took a painting tool and removes these lines and only left the data points.

Do you still spot the correlations?
To me, these two point clouds now look quite circular and not so elliptic. I would not be able to spot a major direction, especially, if you keep in mind, that both distributions share the same covariance matrix.

##### Take-Aways:
• Always question patterns, that "can be seen in the figure".
• How you display data will influence, what people will see in the plots. (There is a whole field taking care of how to make good plots)