How to Envelope a Dataset?

I have a series of data points (in some cases they're in the order of over 1000 points), after some data processing and iterations i.e. sorting, duplicate elimination etc. they will look like a numerical array like "B". B(:,1) will represent the data set on the X-Axis and B(:,2) is the corresponding Y-Axis data.

B =

                        20                      0.01
                        34                     0.017
                        40                      0.02
                        56                       0.5
                        71                       0.2
                        71                       0.5
                        80                      0.04
                       100                     0.075
                       200                       0.2
                       260                      0.04
                       400                       0.5
                       800                      0.04
                      2000                      0.01
                      2000                      0.02

*Please note that there are 2 corresponding values for 71.

I'd like to create an array that envelopes these data to represent the characteristics of "B". I came up with the enveloping dataset manually (which is acceptable for this case). I called this enveloped data set, "Enveloped":

Enveloped =

                        20                      0.01
                        30                      0.02
                        45                       0.5
                       400                       0.5
                      2000                      0.02

I have uploaded a figure at the following link; it can visually show you what I'm looking for:

http://imgur.com/7o6wA

The Red plot represents "B" and the blue plot is the "Enveloped". I'm looking to recreate "Enveloped" in Matlab. Any help is greatly appreciated!

Answer 1

[Junaid]

Dear Aviator, Sorry I was away so could not reply on time. Actually you can play trick with this.

k = convhull(x,y)

So you can process k after getting convhull. To avoid box around point it is straight forward that delete the last point. However there can be many exceptions. One good trick can be that. You loop over k and check values of K. Keep plotting while K is increasing. Whenever K start decreasing then you stop. You will see that you don't get box and get the exactly same figure which you showed as example. Sorry I don't have installed matlab to test but I am sure it will work. Try and let us know.

Answer 2

[Junaid]

Dear Aviator,

Actually your problem is quite related to finding the Convex hull. The data points you have shown are not good enough so that I could show you example visuall. But take a look at this.

http://www.mathworks.co.jp/help/techdoc/ref/convhull.html

I hope this will solve your problem. You have to find the convex hull that you are calling an envelope :-). Do let me know if you understood your question wrong.

[Aviator]

Thanks - I thought about "convhull" but unfortunately there are couple of issues with the convhull:

convhull boxes the dataset which is not working for me; if the first and the last points are connected to each other that interpretes differently in my line of work and it's "wrong".

Second, for this particular example, the plot should stop at (2000, 0.02). if it continues on, that means an unsuccessful data point was achieved, between the two points with equal values (2000 in rows 13 and 14 of "B"), the one with greater corresponding value in column 2 should be picked; in this example, [2000 0.02] was picked.

[Sean de Wolski]

Use accumarray with the function max() to group your data and keep the ones you want. (histc or unique to get the indices to feed accumarray)

[Aviator]

Can you be a little more specific? For this particular problem I happen to know the end result so I could pick what I wanted to get to my desired plot but in all other cases that I don't have the end result to compare my Matlab outcome to, it's a different story. I'm trying to come up with a general approach to envelope a set of data. It's exacly similar to the "convhull" but with some restrictions...