A novel ranked k-nearest neighbors algorithm for missing data imputation

Area of Science:

• Data Science
• Statistics
• Machine Learning

Background:

• Missing data is a prevalent challenge in data analysis across various scientific domains.
• The standard k Nearest Neighbors (kNN) imputation method struggles with accuracy in datasets exhibiting small pairwise correlations or small k values.
• Existing imputation techniques often face limitations in handling specific data characteristics.

Purpose of the Study:

• To introduce a novel imputation method, Ranked k Nearest Neighbors (Ranked kNN).
• To enhance imputation accuracy compared to the traditional kNN method.
• To address limitations of standard kNN in datasets with low correlations and small k values.

Main Methods:

• The proposed Ranked kNN method adapts the kNN approach by incorporating Ranked Set Sampling (RSS).
• RSS is utilized to strategically select the most pertinent neighbors for imputation.
• The method was evaluated under Missing Completely at Random (MCAR) and Missing at Random (MAR) mechanisms.

Main Results:

• Ranked kNN demonstrated superior imputation accuracy over standard kNN across all tested datasets.
• The proposed method consistently yielded lower Mean Squared Imputation Error (MSIE) and Mean Absolute Imputation Error (MAIE) values.
• Performance improvements were particularly notable in scenarios with small pairwise correlations and small k values.

Conclusions:

• The Ranked kNN imputation method offers a significant advancement for handling missing data.
• It provides a promising alternative for datasets with challenging characteristics, such as low correlations and small k.
• The method enhances imputation accuracy without introducing additional computational complexity, making it broadly applicable.