- #1
wvguy8258
- 50
- 0
Hi,
Not sure if this is the correct sub-forum or not. Perhaps, general math is better. Anyways..
In the following, a simple reference covering what I am after would be very helpful.
Let's say you have a 4x4 grid of cells each cell contains either a 1 or 0. Let's say it is this.
0101
1010
0101
1010
And it covers a certain spatial area of let's say 4 m X 4, so the resolution of each cell is 1 by 1 m.
If I coarsen the resolution of the grid so that it is now a 2X2 grid covering the same area then I will take the average value for each of the four cells collapsed by aggregation and assign the average value to the new cells. So we have
0.5 0.5
0.5 0.5
Is there a way to capture the information lost in this aggregation? I suppose it could be thought of as the aggregate grid being known and then the original 4x4 grid being a signal and determining how much information is in the original grid given that you know the aggregate values.
Further, if I attempted to estimate the values in the 2x2 grid using some method and came up with
0.4 0.6
0.3 0.2
Is there a way to determine the amount of information held in the 2x2 grid of 0.5 values given that we know the estimate? I suppose this is the amount of "surprise" in the values of the 2x2 grid given the model.
The reason I am asking this. I model land use change using satellite imagery to determine land cover and then try to predict locations of change by using information on things that likely influence land cover change (like road location, topographic slope, etc). You can often increase model accuracy by aggregating the satellite imagery. So, you gain predictive ability but on a data set where information has been lost. I am trying to better understand this trade-off so that recommendations can be made regarding the appropriate level of data coarsening.
Thanks for reading,
Seth
Not sure if this is the correct sub-forum or not. Perhaps, general math is better. Anyways..
In the following, a simple reference covering what I am after would be very helpful.
Let's say you have a 4x4 grid of cells each cell contains either a 1 or 0. Let's say it is this.
0101
1010
0101
1010
And it covers a certain spatial area of let's say 4 m X 4, so the resolution of each cell is 1 by 1 m.
If I coarsen the resolution of the grid so that it is now a 2X2 grid covering the same area then I will take the average value for each of the four cells collapsed by aggregation and assign the average value to the new cells. So we have
0.5 0.5
0.5 0.5
Is there a way to capture the information lost in this aggregation? I suppose it could be thought of as the aggregate grid being known and then the original 4x4 grid being a signal and determining how much information is in the original grid given that you know the aggregate values.
Further, if I attempted to estimate the values in the 2x2 grid using some method and came up with
0.4 0.6
0.3 0.2
Is there a way to determine the amount of information held in the 2x2 grid of 0.5 values given that we know the estimate? I suppose this is the amount of "surprise" in the values of the 2x2 grid given the model.
The reason I am asking this. I model land use change using satellite imagery to determine land cover and then try to predict locations of change by using information on things that likely influence land cover change (like road location, topographic slope, etc). You can often increase model accuracy by aggregating the satellite imagery. So, you gain predictive ability but on a data set where information has been lost. I am trying to better understand this trade-off so that recommendations can be made regarding the appropriate level of data coarsening.
Thanks for reading,
Seth