Data Interpolation: What It Is & How To Do It?

Data interpolation helps you tackle a common challenge in data analysis—incomplete or unevenly spaced data points. If you have a set of temperature readings but some missing values due to sensor malfunctions or irregular sampling intervals. How do you fill these gaps to get a complete temperature trend?

Data interpolation is the answer—it is essential because it allows you to estimate missing values between known data points, providing a more comprehensive and continuous dataset. This process is crucial for various applications across numerous fields.

This article will explore data interpolation, various data interpolation techniques, and data interpolation vs extrapolation.

What is Data Interpolation?

Data interpolation is a technique used in data analysis to estimate values between known data points. It involves filling in missing data points or estimating values at points where data is not directly measured. The goal of interpolation is to create a continuous representation of a dataset, which can be useful for various purposes, such as smoothing out irregularities in data, creating visualizations, or making predictions.

Think of interpolation as connecting the dots between known data points to create a smooth curve or line. This allows for a more complete and accurate understanding of the underlying trends or patterns in the data.

How to Interpolate Data?

Interpolating data involves estimating values between known data points, filling in missing values, or predicting values where data is not directly measured. It's a critical step in data analysis, particularly when dealing with incomplete datasets or irregularly sampled data.

Understanding various data interpolation techniques is crucial for accurately evaluating missing values and smoothing out datasets. Here's a breakdown of some key interpolation methods and how to interpolate data effectively based on the nature of your data and available computational resources.

Linear Interpolation

Linear interpolation is a method used to estimate unknown data points by assuming a linear relationship between known data points. It works by fitting a straight line between two given data points, represented by coordinates (x1,y1) and (x2,y2). The formula used for linear interpolation is y-y1=y2-y1x2-x1 . (x-x1), where y represents the estimated value at a point x between x1 and x2. This method is effective when the relationship between different variables is linear.

Polynomial Interpolation

Polynomial interpolation is a method that utilizes polynomial equations to estimate missing data values. It ensures that the polynomial passes through all the available data points in the dataset. The degree of the polynomial is typically one less than the total number of data points. 

While polynomial interpolation is recommended for handling complex datasets, it may overfit the data if the dataset is large, resulting in poor estimates of unknown values. Despite this limitation, polynomial interpolation offers greater flexibility compared to linear interpolation and can be applied to diverse datasets.

There are various types of polynomial interpolation methods, among which Lagrange interpolation, Newton interpolation, and Hermite interpolation are commonly used:

• Lagrange Interpolation: This method constructs a polynomial that passes through all the given data points. For n given data points, Lagrange interpolation creates a polynomial of degree n-1. However, since it considers all data points, it can be computationally intensive.‍
• Newton Interpolation: Newton's interpolation builds a polynomial function using divided differences. It incrementally adds terms to the polynomial, taking into account an increasing number of data points. Compared to Lagrange interpolation, Newton's method is computationally more efficient.‍
• Hermite Interpolation: Hermite interpolation extends the concept of polynomial interpolation by considering the derivatives at the given data points. It incorporates slope information at each point, making it more complex but potentially more accurate, especially when dealing with datasets involving varying rates of change.

Spline Interpolation

Spline interpolation involves dividing the dataset into smaller segments treated with low-degree polynomials. This approach mitigates the overfitting risk associated with higher-degree polynomials in polynomial interpolation. Typically, third-degree polynomials are employed in spline interpolation to estimate missing values, resulting in smoother outcomes compared to polynomial interpolation.

Nearest Neighbor Interpolation

Nearest Neighbor interpolation involves assigning a value to unknown data based on its closest known neighbor. Widely utilized in image processing, this method assumes that the nearest unknown point shares similar characteristics with its closest known data point. 

However, a notable drawback is the potential for the "staircase effect," which results in less smooth transitions between pixels. This effect arises because nearest neighbor interpolation solely considers the closest neighbor without taking into account other surrounding neighbors when estimating the missing value.

Advantages and Disadvantages of Data Interpolation

Understanding the advantages and disadvantages of data interpolation is crucial for ensuring its effective application in data science projects. Here's an overview of both aspects:

Advantages of Data Interpolation

• Fill Missing Data: Data interpolation plays a vital role in handling missing values within datasets by replacing them with estimated interpolated values. This ensures that the dataset remains complete and usable for analysis.‍
• Spatial Analysis: In spatial analysis, data interpolation is indispensable as it facilitates the estimation of values in areas where measurements are not directly taken. This enables the creation of continuous spatial datasets for various applications.‍
• Algorithmic Efficiency: By effectively managing missing data, you can enhance the efficiency of machine learning algorithms, leading to improved learning and prediction performance. This enables algorithms to better understand and generalize patterns in the data.‍
• Smoothing: Interpolation smooths out data values where measurements are absent, thereby ensuring the continuity of the dataset. This results in a more visually appealing and interpretable dataset for analysis.

Disadvantages of Data Interpolation

• Loss of Information: Since interpolation relies on known data to estimate missing values, it assumes a smooth and continuous relationship between data points, potentially leading to information loss. This can result in oversimplification of the data and masking important patterns or trends.‍
• Extrapolation Uncertainty: Interpolation deals only with data within the range of known values, making it unsuitable for extrapolating unknown data lying outside this range. Attempting to extrapolate beyond the known data range can lead to unreliable predictions and increased uncertainty.‍
• Computational Intensity: Some interpolation methods can be computationally intensive, potentially slowing the interpolation process. Hence, considerations are necessary when selecting an interpolation method to ensure computational efficiency. This may require balancing between accuracy and the computational resources available.

Data Interpolation vs Extrapolation

Data interpolation and extrapolation are fundamental techniques in data analysis used to estimate values within or beyond known data points, respectively. Understanding the differences between these two methods is important for effectively analyzing and interpreting data. The following table compares data interpolation and extrapolation.

Feature	Data Interpolation	Extrapolation
Definition	Estimating values within known data points.	Estimating values beyond known data points.
Purpose	Filling in missing values or estimating values between existing data points.	Predicting or estimating values outside the range of existing data.
Method	Curve fitting techniques like linear interpolation or polynomial interpolation.	Extending the curve or line fitted to known data points.
Range	Deals with data points within the range of known values.	Deals with data points outside the range of known values.
Use Cases	Handling missing data, smoothing datasets.	Forecasting, trend analysis.
Potential Drawbacks	Assumes smoothness, limited to known range.	Assumes continuation of an existing trend, may lack accuracy if trend changes.
Example	Estimating temperature between recorded measurements.	Forecasting future stock prices based on historical data.

Conclusion

Data interpolation techniques are invaluable in data analysis. They allow you to estimate missing values, smooth out datasets, and make predictions based on existing data. By understanding different data interpolation methods and how to apply them, you can use them to analyze data effectively.