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Vertical projection and orthogonal projection?

The lecture note remarks that they are different, but could anyone explain about their difference exactly?

Posted by Sungyeon Hong on Tuesday 29 October 2013 at 17:46
Comments
Vertical projections are in the direction of the y-axis, while orthogonal projections have the property that the residual is orthogonal to the subspace onto which you are projecting. Look for example at the 3rd slide with the title "Maximum Likelihood Estimation" at lecture slides 2. These are vertical projections. For orthogonal projections, the red residuals would be perpendicular to the regression line.
Posted by Mikael Kuusela on Tuesday 29 October 2013 at 22:11
Thanks a lot! :)
Posted by Sungyeon Hong on Tuesday 29 October 2013 at 22:56
Then is the hyperplane a sort of a subspace on where the vertical projections lie (if this verb does not fit, then can I use "arrive")?
Posted by Sungyeon Hong on Tuesday 29 October 2013 at 23:00
Well, a hyperplane is not necessarily a subspace since it doesn't have to go through the origin. But I guess you can think of it as an analogue of the range space of an orthogonal projection.
Posted by Mikael Kuusela on Tuesday 29 October 2013 at 23:57