### A Day

Many emails are about the flat segments. Each one takes me five minutes to think. I think Martin and Daniel are better persons to work on it. Hopefully I convinced them the necessity of flat segments.

I want to move on to the multi dimension case. I will use the partial definition, just one step to go beyond the one dimension. Daniel probably is going to ask me why I want this not elegant method, instead of topology. First, I don’t know topology. Second, I find it is too complex to use in multi dimension case. Well, it is nice to play the theorems. But now I want to reach what Suc can do by his learning algorithm.

I went over Suc’s paper again, and computed the complexity of his algorithm. Surprisingly it is O(n^2logn). I thought it should be higher order. Daniel told me O(n^2) is not good enough. It is if there is O(n). But it is not bad for most of the problems. I am sending several emails to ask people about complexity of learning algorithms. I know there is answer, but I have no time and energy to find it out myself. Who can tell me?

I booked my trip to Spain and I discussed vacation. I even read the rouge guide of Spain during my lunch time. Valencia is the third largest city in Spain and the famous tomato throwing fest is in a near by town called Bunol. And most important is that the tomato throwing only happens once per year on the last Wednesday of August! Exactly the date of ECAI! Am I going to see the tomato throwing? I found I have several old T-shirts in my closet.

Time never is enough. I promised to work on web service this month. I have to do it. But research needs me to focus on a problem until finding the answer.

I want to move on to the multi dimension case. I will use the partial definition, just one step to go beyond the one dimension. Daniel probably is going to ask me why I want this not elegant method, instead of topology. First, I don’t know topology. Second, I find it is too complex to use in multi dimension case. Well, it is nice to play the theorems. But now I want to reach what Suc can do by his learning algorithm.

I went over Suc’s paper again, and computed the complexity of his algorithm. Surprisingly it is O(n^2logn). I thought it should be higher order. Daniel told me O(n^2) is not good enough. It is if there is O(n). But it is not bad for most of the problems. I am sending several emails to ask people about complexity of learning algorithms. I know there is answer, but I have no time and energy to find it out myself. Who can tell me?

I booked my trip to Spain and I discussed vacation. I even read the rouge guide of Spain during my lunch time. Valencia is the third largest city in Spain and the famous tomato throwing fest is in a near by town called Bunol. And most important is that the tomato throwing only happens once per year on the last Wednesday of August! Exactly the date of ECAI! Am I going to see the tomato throwing? I found I have several old T-shirts in my closet.

Time never is enough. I promised to work on web service this month. I have to do it. But research needs me to focus on a problem until finding the answer.

## 2 Comments:

Have a good trip in Spain.

Yes, you've convinced me that we should try to define flatness, but I still don't know how to do it while preserving elegance.

As for the multidimensional case, I think you want to use bimonotonicity. That is, f(x,y) is monotone if it is monotone in both x and y.

Bimonotonicity is fine, but it is a very strong condition. The problem is that you'll end up with many more pieces than you may want... but I agree that it is a reasonable compromise for many applications.

By Daniel Lemire, at 6:55 AM

I was thinking the bi-monotone today. I'd rather call it partial monotone, because it is like the partial derivative. The problem is on aggregating the points which have the same sign. It makes me think the edge detection algorithm in image processing. Then we can use polynomial to approximate the edge.

By flydragon, at 9:14 PM

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