Errors in the final exams

Question

Hello,
I would like to report some issues about the final exam.
In the question 4, the correct matrix D isn't in the list, in the position (1,0) should be zero.
Also I couldn't get the correct answer for between-scatter matrix calculation (the maximum value). In my calculations it is

5940.8

Which is not presented in the answer options.
Maybe you should double check it, it would be great addition, if you insert in the explanation section - the correct code lines to obtain the same result as you have.

Thank you!

Answer 1

Hi Tatiana,
thanks for reaching out and for the feedback! I'll revise question 4 to include the correct eigenvalues.
The code you'd need to obtain the between scatter matrix is the following:

overall_mean=np.mean(X_std,axis=0)

S_b=np.zeros((5,5))
for i,mean_vec in enumerate(mean_vectors):
    n=X_std[y==i+1,:].shape[0]
 
    mean_vec=mean_vec.reshape(5,1)
    overall_mean=overall_mean.reshape(5,1)
    S_b+=n*(mean_vec-overall_mean).dot((mean_vec-overall_mean).T)


print('Between class scatter matrix:\n',round(S_b.max(),1))

You'd need to create the X and y matrix and column vector first, and then standardize X with a standardscaler to obtain X_std.
Let me know if you have any furhter questions.

Best,
365 Eli

Answer 2

Hi,
I guess you meant question 5 where we should calculate matrix D square.
In description matrix D is 2x2 - [[1 0],[0 10]], main diagonal is eigenvalue of matrix A - 1 and 10, outside diagonal are zeros. so D square had to be [[1 0],[0 100]] as Tatiana wrote.
Also could you please add better explanation for answers 4 and 5 because I could not understood on the beginning what I did wrong?

Thank you in advance!

Answer 3

Please also review question nine,
inverted matrix A was correctly calculated but then when applied to formula of calculation eigenvalues position (2,2) was replaced with 6 instead of 1 so entire result was incorrect for second root

Answer 4

Tatiana Kolesnik

Posted on:

13 Dec 2022

0

Yes, exactly that question, thank you, Vladyslav!

Answer 5

Elitsa, thank you for the answer!
I reviewed the code, could we please discuss this line?

<span class="colour" style="color: rgb(116, 129, 144);"><b><span class="colour" style="color: unset;">**<span class="colour" style="color: unset;">**<span class="colour" style="color: unset;">**<span class="colour" style="color: unset;">**for**</span>**</span>**</span>**</span></b> i,mean\_vec <b><span class="colour" style="color: unset;">**<span class="colour" style="color: unset;">**<span class="colour" style="color: unset;">**<span class="colour" style="color: unset;">**in**</span>**</span>**</span>**</span></b> enumerate(mean\_vectors):</span></b> enumerate(mean_vectors):
</span>        n=X_std[y==i+1,:].shape[0]

In this code i takes values 0 and 1, so in the brackets you check the conditions in which y takes values 1 and 2, but it is not correct as the labels for classes are 0 and 1, so in my code it is

for i,mean_vec in enumerate(mean_vectors):
       n=X_std[y==i,:].shape[0]

And the result matrix is different. Could you please check this piece of code and explain why are you incrementing i in the brackets?

Errors in the final exams

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