Working of 'interpolation' to impute missing values & the importance of the order of data points for the process

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Definition of interpolation - Interpolation predicts values at a point by studying its neighbouring points (within the same column), as opposed to data modeling where all the columns are taken into considering when studying the relationship between points.

What I have tried:

Following are the points gathered as part of my research on interpolation & my doubts:

1. Interpolation assumes smoothness & continuity between consecutive data points when connected using curves/lines. So mixing up/sorting of values in the column will affect the interpolation lines/curves & the subsequent results negatively. Hence, we must not modify the order of data points in the dataset.

Doubt - When these data points are plotted on a graph, then the proximity of the values/data points to one another will depend on the magnitude of the values anyways, i.e., values closer in number will lie closer to each other. It doesn't matter how they were ordered in the dataset. So why is there so much emphasis on preserving the original order of the dataset values?

And how practical is it to assume that the person who has prepared the dataset has arranged the values in an order that ensures continuity & smoothness between data points of the column under consideration? We don't know which column has been considered as the key for the ordering of rows.

Note: I have explained my understanding & doubts as detailed as possible. In case my understanding is wrong or my questions aren't clear, do let me know.

Posted 9-Dec-23 2:29am

Apoorva666

Updated 9-Dec-23 3:40am

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[no name] 10-Dec-23 11:31am

The "order" is a reflection of the order in which these points came into existence. Interpolating (or extrapolating) uses that information to "predict" missing points. Without that condition, you just have a bunch of random points that have no relation to each other.

RedDk 5-Oct-24 14:30pm

Since you're not asking anything about generating data points in a "graph", by using the word "interpolation", and since by using that word "graph" I'm assuming you need a display which will automatically contain distance information, I think you'll be simulating.

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Kenneth Haugland · Answer 1 · 2023-12-09T03:50:00

First off, there is no code to give feedback to here, so the answer is not very good in that respect.

In mathematics, there are different ways of interpolating points. There is the Lagrangian ineterpolation, or Newton interpolation. These are the same principles that use all the points to fit the highest-order polynomial curve that goes through each point.

There are splines that use lower-order polynomial fits to generate a curve, and here you could use the least squares fit of a given degree polynomial.

The problem you have is actually specifying what you actually want, and you didn't.

0x01AA · Answer 2 · 2024-08-17T05:38:00

Your statment:
'Interpolation assumes smoothness & continuity between consecutive data points when connected using curves/lines'
No, at least not in general.

Linear problem (most probably not what you are looking for):
In case your task is related to a linear problem, then you can try 'linear regression'.
This means all your data (x/y sample pairs) can be completely unorderd. Especally this means you can have several 'y' values for one and the same 'x' value.

Polynomial, whatever:
Here we come to a basic thing that we need first to realize what a mathematical function means. E.g. Function (mathematics) - Wikipedia[^]
E.g. a 2D function (at least a 'Continuous function') can never have more than one 'y' value for a given 'x' value. Otherwhise it is not a function in therm of math.

Working of 'interpolation' to impute missing values & the importance of the order of data points for the process

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