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Topic: How to find a bounding line?
Replies: 39   Last Post: Jul 12, 2013 5:39 AM

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Leon Aigret

Posts: 31
Registered: 12/2/12
Re: How to find a bounding line?
Posted: Jul 11, 2013 7:50 PM
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On Thu, 11 Jul 2013 15:54:29 -0700 (PDT), ols6000@sbcglobal.net wrote:

>On Thursday, July 11, 2013 2:11:21 PM UTC-7, Leon Aigret wrote:
>> The cost function SUM(y_i - y(x_i)) for the line y = a x + b becomes
>> SUM(y_i - a x_i - b) = N (y_mean - a x_mean - b), so minimizing this
>> function corresponds with maximizing a x_mean +b. Calculating x_mean
>> is O(N), but has to be done just once.

>
>Carrying this one step further, minimizing the cost function is just maximizing a. The problem with this is that the cost is subject to y_i-y(x_i)>=0


At this point in the analysis the cost function can and will be used
to evaluate every line y = a x + b which lies below all data points
(i.e. y_i-y(x_i)>=0 for all i) or, equivalently, lies below all points
of the convex hull, so just maximizing a is not an option.

>> Actually, since a x_mean + b has the geometrical interpretation of
>> y-coordinate of the intersection of y = a x + b and x = x_mean,
>> repeated evaluation of that expression can be replaced by the
>> geometrical argument that the best line is the line with the highest
>> intersection point, which must (and can) be the point where the line
>> x = x_mean reaches the convex hull.

>
>Can you explain what you mean by "the line with the highest intersection point"?


More precisely: the line that, among all lines y = a x + b that lie
below the convex hull, has the highest intersection point
(x_mean, a x_mean + b) with the line x = x_mean.

Leon


Date Subject Author
7/7/13
Read How to find a bounding line?
Woody
7/7/13
Read Re: How to find a bounding line?
Scott Berg
7/7/13
Read Re: How to find a bounding line?
Peter Percival
7/7/13
Read Re: How to find a bounding line?
Woody
7/7/13
Read Re: How to find a bounding line?
quasi
7/7/13
Read Re: How to find a bounding line?
quasi
7/8/13
Read Re: How to find a bounding line?
quasi
7/8/13
Read Re: How to find a bounding line?
Woody
7/8/13
Read Re: How to find a bounding line?
quasi
7/8/13
Read Re: How to find a bounding line?
LudovicoVan
7/8/13
Read Re: How to find a bounding line?
LudovicoVan
7/10/13
Read Re: How to find a bounding line?
Woody
7/10/13
Read Re: How to find a bounding line?
quasi
7/8/13
Read Re: How to find a bounding line?
Leon Aigret
7/8/13
Read Re: How to find a bounding line?
Woody
7/10/13
Read Re: How to find a bounding line?
Leon Aigret
7/10/13
Read Re: How to find a bounding line?
Leon Aigret
7/10/13
Read Re: How to find a bounding line?
Woody
7/10/13
Read Re: How to find a bounding line?
RGVickson@shaw.ca
7/10/13
Read Re: How to find a bounding line?
Woody
7/10/13
Read Re: How to find a bounding line?
quasi
7/7/13
Read Re: How to find a bounding line?
quasi
7/7/13
Read Re: How to find a bounding line?
quasi
7/7/13
Read Re: How to find a bounding line?
quasi
7/8/13
Read Re: How to find a bounding line?
William Elliot
7/8/13
Read Re: How to find a bounding line?
Peter Percival
7/8/13
Read Re: How to find a bounding line?
quasi
7/11/13
Read Re: How to find a bounding line?
Woody
7/11/13
Read Re: How to find a bounding line?
quasi
7/11/13
Read Re: How to find a bounding line?
LudovicoVan
7/11/13
Read Re: How to find a bounding line?
quasi
7/11/13
Read Re: How to find a bounding line?
Leon Aigret
7/11/13
Read Re: How to find a bounding line?
Woody
7/11/13
Read Re: How to find a bounding line?
Leon Aigret
7/12/13
Read Re: How to find a bounding line?
Woody
7/12/13
Read Re: How to find a bounding line?
Leon Aigret
7/11/13
Read Re: How to find a bounding line?
Woody
7/12/13
Read Re: How to find a bounding line?
quasi
7/12/13
Read Re: How to find a bounding line?
Woody
7/12/13
Read Re: How to find a bounding line?
quasi

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