bv_cvxbook_extra_exercises

# We choose the oset and the regressor functions to

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: arn) a quadratic pseudo-metric d, d(x, y ) = (x − y )T P (x − y ) 1/2 , with P ∈ Sn , which approximates the given distances, i.e., d(xi , yi ) ≈ di . (The pseudo-metric d is + a metric only when P ≻ 0; when P 0 is singular, it is a pseudo-metric.) To do this, we will choose P ∈ Sn that minimizes the mean squared error objective + 1 N N i=1 (di − d(xi , yi ))2 . (a) Explain how to ﬁnd P using convex or quasiconvex optimization. If you cannot ﬁnd an exact formulation (i.e., one that is guaranteed to minimize the total squared error objective), give a formulation that approximately minimizes the given objective, subject to the constraints. (b) Carry out the method of part (a) with the data given in quad_metric_data.m. The columns of the matrices X and Y are the points xi and yi ; the row vector d gives the distances di . Give the optimal mean squared distance error. We also provide a test set, with data X_test, Y_test, and d_test. Report the mean squared distance error on the...
View Full Document

## This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.

Ask a homework question - tutors are online