Mathematical logic

[Dumi]

Hi everyone.
I have two data set as bellow. Data set 1 have 11 values and data set 2 have 6 values. I want to bring those both data in to same values. I meant I want to bring both data sets last number to 20 and also there should be 20 values. Is my explanation clear. What is the method to do it. Please someone help me to do it. is there any mathematical Logic to do it. what is the method to do it. I don't want to know a equation to do it if there is. I want to know the logic. Please someone help me. Thank you.

 

[Ishuda]

Hi everyone.
I have two data set as bellow. Data set 1 have 11 values and data set 2 have 6 values. I want to bring those both data in to same values. I meant I want to bring both data sets last number to 20 and also there should be 20 values. Is my explanation clear. What is the method to do it. Please someone help me to do it. is there any mathematical Logic to do it. what is the method to do it. I don't want to know a equation to do it if there is. I want to know the logic. Please someone help me. Thank you.

First of all, do you want to extend the points or do you want them to be interior. For example, looking at data set 1, do you want to know the next 9 points in the series [extrapolate], or do you want to fill in 9 more points in between the given points [interpolate]? Obviously you might want a little of both since you want the last point to be (20, 20)

 

[Dumi]

First of all, do you want to extend the points or do you want them to be interior. For example, looking at data set 1, do you want to know the next 9 points in the series [extrapolate], or do you want to fill in 9 more points in between the given points [interpolate]? Obviously you might want a little of both since you want the last point to be (20, 20)

Thank you loads for replying Ishuda !!!

Yes, I want to know extra 9 points of data set 1 related to given points. Also extra 14 points in data set 2. sorry I dont want to bring last point in to 20. just want to know extra points.
Thank you again.

 

[Dumi]

Thank you loads Ishuda,

yes, I want to know extra 9 points of data set 1 related to given points. and also extra 14 point of data set 2. sorry I dont want to bring last point to 20. i just want 20 point. so what is the method i want to use. thank you again !!

 

[Dumi]

yes Denis, that is what i want to do. I want to know missing values. Can I do it.

Actually this is what i want to do. I want to compare two data sets. but one data set have 11 values and other set have only 6 values. so i thought to normalize both data sets in to 20 values and find missing values. After that compare those two data sets.

 

[Deleted member 4993]

yes Denis, that is what i want to do. I want to know missing values. Can I do it.

Actually this is what i want to do. I want to compare two data sets. but one data set have 11 values and other set have only 6 values. so i thought to normalize both data sets in to 20 values and find missing values. After that compare those two data sets.

Are you interested in statistical comparison?

 

[Dumi]

hi Subhotosh Khan,
yes I like. please subhotosh help me. How I do this. Actually I need to do this for my final year research. In there one data set have 300 points and other data set have 400 points likewise. I have to extends this to 1000 points.

Help me please !!

 

[Deleted member 4993]

hi Subhotosh Khan,
yes I like. please subhotosh help me. How I do this. Actually I need to do this for my final year research. In there one data set have 300 points and other data set have 400 points likewise. I have to extends this to 1000 points.

Help me please !!

You cannot extend data set to the level it does not exist!

Only politicians are allowed to do that.

What kinds of comparisons are trying to make?

You should take your problem to the math department of your local college and have a face-to-face discussion.

 

[Ishuda]

Thank you loads for replying Ishuda !!!

Yes, I want to know extra 9 points of data set 1 related to given points. Also extra 14 points in data set 2. sorry I dont want to bring last point in to 20. just want to know extra points.
Thank you again.

There are many [actually an infinite number of] ways to do what you want and should depend in some sense on what you want the final answer to look like. For example suppose I had the points
x,y
1, 3
2, 0
3,-3
4, 0
A 'perfect fit' to those points is
f(x) = x (x-2) (x-4)
and if we wanted to know what the values were at 1.5, 2.5, and 3.5 that function would give a reasonable looking 1.875, -1.875, and -2.625 for

X	Y
1	3
1.5	1.875
2	0
2.5	-1.875
3	-3
3.5	-2.625
4	0

However if we extended the points to values 5, 6, and 7 there would be larger numbers at the end

X	Y
1	3
2	0
3	-3
4	0
5	15
6	48
7	105

which, again depending on what your final product is, might be reasonable.

Unless there are boundary conditions 'keeping things in bounds', both interpolation and extrapolation can give wildly unpredictable results.

For interpolation, b-splines
https://en.wikipedia.org/wiki/B-spline
are very useful sometimes

For extrapolation one might well use the points from a linear regression fit (or quadratic or ... as the data suggests)
https://en.wikipedia.org/wiki/Regression_analysis

 

[Dumi]

Thank you very much Ishuda,

Ok i am going to consider your point and analyse my data.

Also can you Please tell me is it ok if i reduce data from large data set to fit the length of small data set as bellow by removing the data which are available at every Z points. In my cause i am getting xy coordinates to data set.

(Max_count) - (Min_count) = P

(Max_count)/P = Z

 

[Deleted member 4993]

Are you trying to decide whether [set(1)] is equivalent to [set(2)]?

What type of data are these? What level "equivalency" (significance level) do you want?

Rejecting or adding data arbitrarily is not allowed - in most cases!

 

[Dumi]

Yes Subhotosh,
I want to compare whether two data set is equal or not. My project is signature recognition system. In there Im checking whether two signatures are equal. My data set contain X Y coordinates.

 

[Ishuda]

Thank you very much Ishuda,

Ok i am going to consider your point and analyse my data.

Also can you Please tell me is it ok if i reduce data from large data set to fit the length of small data set as bellow by removing the data which are available at every Z points. In my cause i am getting xy coordinates to data set.

(Max_count) - (Min_count) = P

(Max_count)/P = Z

As has been suggested already, deciding whether two different sample sets come from the same distribution [which is sort of how I can now read your question], there does not need to be the same number of points in each of the two different sample sets. For example, you could compute a sample mean and standard deviation for each set and then use those quantities to come to some sort of conclusion about them being from the same distribution.

You might look around
https://duckduckgo.com/?q=comparison+of+data+sets&t=lm&ia=web

 

[Otis]

What's your point, buddy?

avantika's profile contains an URL that reads (in part) "write-my-essay-for-me", so the point may be to promote some online student-cheating service.

 

[Dumi]

Thank you very much Ishuda and subhotosh khan !!!

I have solved my problem. Now I can extend points of my data sets to any number. If you guys interest I can explain my method.
Thank you.

 

[Dumi]

Denis, why you here?? Do you solving Maths problems or correcting English grammar. This is Math Forum. We don't need an English teacher here. We are just here to present our maths problems. we don't care about language.

 

[Ishuda]

Thank you very much Ishuda and subhotosh khan !!!

I have solved my problem. Now I can extend points of my data sets to any number. If you guys interest I can explain my method.
Thank you.

I would be interested in your method.

 

[Dumi]

Ishuda, this will be a long method if it is doing manually. But i am going to code this using C#. So that method will be easy for me.
Ok this is the method. Please see the attached image below.

here i have 6 values. i am going to extend it to 10 values. in my image, Array1 means the original data i have. 1st of all we want to get minimum value and maximum value of the data set. then reduce min value from max value and divide it by number of points - 1. then get the answer and add that answer to minimum number and add it again and again. array 2 is made by using that method. Array 3 is made after divide by the points ( no of points we want to extend) -1. Array 4 include the answer we want. it include the all extended values. After making array 2 and 3 1st we consider array 3. In there we ignore 1st value and consider 2nd value.Lets take that value as X. after that we search what is the 1st two values we found in array2 which are grater than and less than to X. then we take those numbers as X1 and X2 (Please refer image). then choose values from array 1 related to X1 and X2 and get them as Y1 and Y2 as below figure. then use those values to solve following equation. this equation is y=mx+c method. Now we know two points so we can make that equation.

Y = (y1-y2/x1-x2)*X -(y1-y2/x1-x2)*x1 +y1

here using Y we can fill array 4.

i am not good at explaining and my English knowledge is very poor, sorry for that. I know my explanation is not clear. Please try to understand it using figure below.

You can understand it by looking at figure. Also i attach the excel work i did. excel work concluded that this method is correct. Thank you.

 

[Ishuda]

Ishuda, this will be a long method if it is doing manually. But i am going to code this using C#. So that method will be easy for me.
Ok this is the method. Please see the attached image below.

here i have 6 values. i am going to extend it to 10 values. in my image, Array1 means the original data i have. 1st of all we want to get minimum value and maximum value of the data set. then reduce min value from max value and divide it by number of points - 1. then get the answer and add that answer to minimum number and add it again and again. array 2 is made by using that method. Array 3 is made after divide by the points ( no of points we want to extend) -1. Array 4 include the answer we want. it include the all extended values. After making array 2 and 3 1st we consider array 3. In there we ignore 1st value and consider 2nd value.Lets take that value as X. after that we search what is the 1st two values we found in array2 which are grater than and less than to X. then we take those numbers as X1 and X2 (Please refer image). then choose values from array 1 related to X1 and X2 and get them as Y1 and Y2 as below figure. then use those values to solve following equation. this equation is y=mx+c method. Now we know two points so we can make that equation.

Y = (y1-y2/x1-x2)*X -(y1-y2/x1-x2)*x1 +y1

here using Y we can fill array 4.

i am not good at explaining and my English knowledge is very poor, sorry for that. I know my explanation is not clear. Please try to understand it using figure below.

You can understand it by looking at figure. Also i attach the excel work i did. excel work concluded that this method is correct. Thank you.

It appears to me that what you are doing is a linear interpolation between the original data points on an evenly spaced grid. You use those functions to compute n 'equally spaced points' where n is the number of points you want'.

That is certainly a legitimate way to introduce new points IF you have reason to believe that the behaviour of the data is linear between data points. Certainly though, you should keep the original data points for extending the number of points if you need to do several extensions.

BTW: If your purpose is to compare two signatures I don't believe that a linear interpolation is the way to go. Knowing nothing about how one goes about that, I would be more inclined to really read more about it. 6 points for a signature is really sparse and it seems to me that it would tell you very little about the signature itself. Now if it were for a single letter, there might be some hope.

 

[Dumi]

hi ishuda,
yeah this is linear interpolation as you suggest earlier. yeah using this method my original data points are lost. Then Can you please tell me is there any method to keep my original data points. Also here I got 6 data point just as an example. In my data set I have closely 500-600 points. and I wanna extend it to 1000 data points. Please can you give any solution. Here I attached my original data set.
Thank you.