How can a covariance matrix C be used with a new test sample 'x' to make a prediction? A friend of mine was trying to show me the following: (x-u)' C (x-u)

Any idea what he was talking about?

asked Sep 11 '10 at 22:57

bciguy's gravatar image

bciguy
31225


2 Answers:

This is the (squared) mahalanobis distance between x and u. exp(-this) is proportional to the gaussian probability of x. I don't understand what this has to do with prediction, however (unless in the case of fisher discriminants, in which you choose the class that minimizes that).

Wasn't your friend talking about gaussian processes? They use covariance matrices (actually covariance functions, sampled appropriately in a matrix), but in a rather different way.

answered Sep 11 '10 at 23:35

Alexandre%20Passos's gravatar image

Alexandre Passos ♦
2549653277421

edited Sep 11 '10 at 23:36

no, it must have been Mahalanobis distance. Thank you! What he was doing was he created a Covariance matrix for each of the class distributions, then used this measure to classify a new test point.

answered Sep 11 '10 at 23:59

bciguy's gravatar image

bciguy
31225

1

That is the fisher discriminant: http://en.wikipedia.org/wiki/Linear_discriminant_analysis

(Sep 12 '10 at 00:28) Alexandre Passos ♦
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