Questions Exercise 1

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DreamFlasher
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Questions Exercise 1

Beitrag von DreamFlasher » 2. Mär 2012 10:46

Hi,

we should start using the forum for some questions of generel interest ;)
So our questions to exercise 1:
- 1.3: Why isn't the acceleration force for component q1: \((m1+m2)*\ddot{q_1}\) as both masses affect joint 1?

...TBC...
Marcel Ackermann
http://www.dreamflasher.de
Machine Learning, Natural Language Processing, Algorithms

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franzose
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Re: Questions Exercise 1

Beitrag von franzose » 3. Mär 2012 01:04

Please apologize if I haven't understood your question, but actually I think that in the solution the mass matrix for \(u_1\) exactly does what you suggested (at least for the part that is dependent from \(\ddot{q_1}\)):

You have \(M(q) * \ddot{q}\) so you have to multiply the matrix with the vector \((\ddot{q_1}, \ddot{q_2})^T\) and in the first row and first col of the matrix there is \(m_1 + m_2\).

This results to \(u_1 = (m_1 + m_2) * \ddot{q_1} + k * \ddot{q_2}\) with \(k\) being the term in the first row and second col of the mass matrix.
Zuletzt geändert von franzose am 27. Nov 2012 00:05, insgesamt 1-mal geändert.

lustiz
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Re: Questions Exercise 1

Beitrag von lustiz » 26. Nov 2012 22:34

Another question for you guys, concerning exercise 1.2 b) (Linear Least Squares):

Are we supposed to include a bias term? As far as I know you usually include a bias yet if we talk about 2 features, does that mean
a) [ sin(x); sin(2x) ] or
b) [ 1; sin(x); sin(2x) ] ?

Thanks in advance!

Cheers!

lustiz
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Re: Questions Exercise 1

Beitrag von lustiz » 27. Nov 2012 01:38

Also: Is the kernel function right in 1.2 (f) ?
I get pretty good results when I use
\(k(x_i, x_j) = e ^ \frac{- 0.5 || x_i - x_j ||^2}{\sigma^2}\)

However, there is no hope when I use the proposed one:
\(k(x_i, x_j) = e ^ \frac{|| x_i - x_j ||^2}{\sigma^2}\)

Any suggestions?

eesti
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Re: Questions Exercise 1

Beitrag von eesti » 27. Nov 2012 11:59

as it was written in the email, there is a type - a minus is missing:
\(k(x_i, x_j) =e^\frac{-\|x_i−x_j\|^2}{\sigma^2}\)

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