Adaptive RBF Interpolation for Estimating Missing Values in Geographical Data

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.

Elements of Bi-cubic Polynomial Natural Spline Interpolation for Scattered Data: Boundary Conditions Meet Partition of Unity Technique

“…Of course, it is also suggested that to choose more interpolatory points uniformly for data collection. In the future, the refined partition of unity will be considered and the large scale real scattered data (e.g., geographical data [18]) will be tested.…”

Spatio-Temporal Changes in Air Quality of the Urban Area of Chongqing from 2015 to 2021 Based on a Missing-Data-Filled Dataset

“…Various methods of data interpolation, such as mean imputation [12], local least-squares fitting [13], and k-nearest neighbors (KNN) [14], were widely used to fill the missing values [15] before analysis. State-of-the-art interpolating Atmosphere 2022, 13, 1473 2 of 16 methods include an adaptive radial basis function (RBF) interpolation algorithm by [16], a multidimensional interpolating based on long short-term memory (LSTM) [17], and a combination of KNN and random forest algorithm (RF-KNN) [18]. The methods mentioned above could consider either the spatial or temporal relationship of data and provide reasonable interpolating solutions, but air quality data are influenced by time and location at the same time, considering that either spatial or temporal characteristics likely results in a large error.…”