How can I detect number that does not follow an increasing order?

I have a vector like this:

• 1 2 3 4 100 5 6 7

or it could also be like this:

• 153 158 161 163 172 123 179 181

if I look at the vector, I know I should delete 100 in 1st one and 123 in 2nd one. After that, either vector is in an increasing order.

I tried to use code diff(vector) to solve the problem in Matlab.

For 1st vector, the difference: 1 1 1 96 -95 1 1. The negative appears at 5th and I should delete No.5 in original sample.

For 2nd vector, the difference: 5 3 2 9 -49 56 2. The negative appears at 5th but I should delete No.6 in original sample.

The code diff cannot handle both cases at the same time. I am wondering if there is a more effective way.

Thank you very much!

[Sandy]

For both vectors, besides keeping an increasing order, I would like to keep as many numbers as possible and delete as few numbers as possible.

The right result for the 1st vector should be: 1 2 3 5 6 7 and 2nd vector should be 153 158 161 163 172 179 181.

[José-Luis]

The solution to that problem is not unique. You might need to better define your conditions, I'm afraid.

[Sandy]

Thanks, Jose-Luis. I agree with you, but I was reluctant to put more conditions. I think I have to do as you said...

[José-Luis]

My pleasure.

[Joseph Cheng]

perhaps some peak detection. performing the convolution of the pattern will lineup max of the convolution with the point that you want to take out. (works with b as well) [a;0 conv(a,[-.5 1 -.5],'valid') 0]

    1.0000    2.0000    3.0000    4.0000  100.0000    5.0000    6.0000    7.0000
         0         0         0   47.5000   95.5000   48.0000         0         0

and for b

153.0000  158.0000  161.0000  163.0000  172.0000  123.0000  179.0000  181.0000
       0    1.0000    0.5000    3.5000   29.0000   52.5000   27.0000         0

might not work for all cases, more sophisticated methods for finding local maximum and local minimum may be what you are looking for.

Answer 1

[Azzi Abdelmalek]

s=[153 158 161 163 172 123 179 181 4 5 190]
while any(diff(s)<0)
  ii=[1==0  diff(s)<0]
  s(ii)=[];
end

[Sandy]

Hi Azzi,

It works perfectly for the 2nd vector, but it returns 1 2 3 4 100 for the 1st case, which is not what I am looking for.

Do you have any idea that can work for both cases?

thank you very much!

[Azzi Abdelmalek]

Your problem is not clear, because from your question, the increasing order is

1 2 3 4 100

[Sandy]

Thanks for pointing it out. I update my question.

[Azzi Abdelmalek]

this is not sufficient as criterion