# Adaptive RBF Interpolation for Estimating Missing Values in Geographical Data

## TL;DR

This paper introduces an adaptive RBF interpolation method to estimate missing values in geographical data, improving accuracy over traditional methods by adaptively selecting local data points and shape factors.

## Contribution

The paper presents a novel adaptive RBF interpolation algorithm that enhances missing data estimation in geographical datasets by dynamically adjusting local data selection and shape parameters.

## Key findings

- Outperforms kNN and AIDW in accuracy
- Less efficient than kNN and AIDW
- Effective for improving data quality in geographical datasets

## Abstract

The quality of datasets is a critical issue in big data mining. More interesting things could be mined from datasets with higher quality. The existence of missing values in geographical data would worsen the quality of big datasets. To improve the data quality, the missing values are generally needed to be estimated using various machine learning algorithms or mathematical methods such as approximations and interpolations. In this paper, we propose an adaptive Radial Basis Function (RBF) interpolation algorithm for estimating missing values in geographical data. In the proposed method, the samples with known values are considered as the data points, while the samples with missing values are considered as the interpolated points. For each interpolated point, first, a local set of data points are adaptively determined. Then, the missing value of the interpolated point is imputed via interpolating using the RBF interpolation based on the local set of data points. Moreover, the shape factors of the RBF are also adaptively determined by considering the distribution of the local set of data points. To evaluate the performance of the proposed method, we compare our method with the commonly used k Nearest Neighbors (kNN) interpolation and Adaptive Inverse Distance Weighted (AIDW) methods, and conduct three groups of benchmark experiments. Experimental results indicate that the proposed method outperforms the kNN interpolation and AIDW in terms of accuracy, but worse than the kNN interpolation and AIDW in terms of efficiency.