Types of Data Interpolation

There are many types of interpolation methods which could be used as per the nature of data present and the available computational resources, let’s discuss about some of the most important interpolation methods that can be useful to us in our data science projects:

Linear Interpolation:

Linear Interpolation is a data interpolation technique in which the relationship in between different data points is taken to be linear in nature and the value of unknown data points is estimated through the linear plot in between known points. For example two of the data points are given which have the coordinates () and () then a straight line is plotted in between these data points as and the data points are estimated according to this equation. Linear interpolation is good if the relationship between different variables are linear in nature.

Polynomial Interpolation:

Polynomial Interpolation on the other hand uses polynomial equation to find out missing data values. It passes through all the data points present in the dataset and the degree of the polynomial is one less than the total number of data points present in the dataset. Polynomial interpolation can fit complex datasets to it but if the dataset is really large this might lead to the interpolation method to overfit the dataset and the estimates of the unknown value gets poor in nature. Still polynomial interpolation method is way more flexible than linear interpolation and it could be used for complex datasets. There are different types of polynomial interpolation methods, let’s discuss about some of the most commonly used polynomial interpolation methods:

• Lagrange Interpolation: Lagrange’s Interpolation method creates a polynomial which passes through all the data points which are given. For a total no n given data points this method creates a polynomial of n-1 degree. As it considers all the given data points, it is considered to be computionally expensive.
• Newton Interpolation: Newton’s interpolation develops a polynomial function using the concept of divided difference. Newton’s method builds up the polynomial by adding terms that consider an increasing number of points. It is computationally better than the lagrange’s interpolation.
• Hermite Interpolation: Hermite Interpolation extends the idea of polynomial interpolation by considering the derivatives at the points of given data with the given data. It is considered to be more complex as it is also considering slope at each points.

Spline Interpolation:

In Spline interpolation the data set is divided into small chunks of data on which the low degree polynomials are applied. This method reduces the risk of overfitting that comes with polynomial interpolation as lower degree polynomial equations are used instead of higher degree polynomial equations. Spline interpolation produces smoother results than polynomial interpolation, majorly third degree polynomials are used for the interpolation method to estimate missing unknown values.

Nearest Neighbor Interpolation:

The Nearest Neighbor Interpolation is the data interpolation technique in which the unknown data is assigned some value based on it’s nearest neighbor. This method is considered one of the most important interpolation method which is used for image processing, it assumes that the nearest unknown point to the known data point must have similar characteristics as of the known data point. The major drawback that is seen in this method is that there might be a possibility of the so called ‘staircase effect‘ which produces less smooth transition between pixels, since nearest neighbor interpolation only considers the nearest neighbor and not other neighbors surrounding the missing value.

The use of real-world data in machine learning tasks can sometimes present challenges due to missing values or incomplete datasets. Such data can lead to inaccurate predictions, and ignoring the missing values can cause bias in model training and distort the original distribution of the data. As machine learning algorithms are not designed to handle missing data, it is important to either remove the missing values or fill the missing positions with other data. One way to fill in missing data values is through a process called Data Interpolation. In this blog, we will be thoroughly discussing about data interpolation.