Multiplication matrix X and its transpose
Hello,
I'm trying to compute the pseudoinverse of matrix X with dimensions [d+1 x N], where N is the number of data points. Lecture 3, slide 16 shows that the dimensions "shrink" when multiplying (X^T)X from [d+1 x N][N x d+1] to [d+1 x d+1]. Although LFD on page 86 states that "In practice, (X^T)T is invertible in most of the cases since N is often much bigger than d+1, so there will likely be d+1 linearly independent vectors xn," I don't know if this statement is meant to explain the reason for the simplification to [d+1 x d+1] dimensions. Moreover, when creating X and computing (X^T)T, I obtain a matrix with [N x N] dimensions, not [d+1 x d+1] dimensions. Could some please clarify this for me? Thank you. 
Re: Multiplication matrix X and its transpose
Quote:
2. The remark about independent vectors is only meant to argue that the d+1 x d+1 matrix has full rank (d+1) since in principle it could be singular, with rank less than d+1 hence not invertible. 3. I am not clear on what (X^T)T is. 
Re: Multiplication matrix X and its transpose
Thank you professor. Sorry, I meant to write (X^T)X to symbolize the transpose of matrix X multiplied by X.
I now know why my matrix was not "shrinking." I was multiplying X(X^T) instead of (X^T)X so that is why I was not obtaining a [d+1 x d+1] dimensional matrix. However, the g hypotheses I'm obtaining with w = (X^dagger)y are usually not close to target functions f... random, really. I'm obtaining an average Ein of approximately 0.5. Sometimes my code gives a g with an extremely large or small yintercept value (e.g., 3.60288*10^16  0.5x). Any pointers would be appreciated. Thank you. 
Re: Multiplication matrix X and its transpose
Just want to point out that a regular session of the course is starting this week at edX:
http://www.edx.org/course/caltechx/c...ningdata2516 I am attending to the discussion forum over there, so I'll check here less frequently during that session. 
Re: Multiplication matrix X and its transpose
I made a simple program coding error which was leading to the aberrant weights and Ein. Once I fixed the coding error, I obtained the correct weights and Ein.

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