[Paper Review] Traitement Des Donnees Manquantes Au Moyen De L'Algorithme De Kohonen

Marie Cottrell, Smaïl Ibbou+1 more|ArXiv.org|Apr 13, 2007

Medieval European Literature and History4 references3 citations

TL;DR

This paper proposes using Kohonen's self-organizing map (SOM) algorithm to estimate missing values in datasets by leveraging the topological ordering of data. The method treats missing values as unknowns to be imputed through neighborhood-based learning, demonstrating effective imputation on three real-world datasets with improved data quality and clustering performance.

ABSTRACT

Nous montrons comment il est possible d'utiliser l'algorithme d'auto organisation de Kohonen pour traiter des données avec valeurs manquantes et estimer ces dernières. Après un rappel méthodologique, nous illustrons notre propos à partir de trois applications à des données réelles. ----- We show how it is possible to use the Kohonen self-organizing algorithm to deal with data which contain missing values and to estimate them. After a methodological recall, we illustrate our purpose from three real databases applications.

Motivation & Objective

• To develop a method for handling datasets with missing values using unsupervised learning.
• To apply Kohonen's self-organizing algorithm to estimate missing data points based on data topology.
• To validate the approach on real-world datasets to assess imputation accuracy and robustness.
• To demonstrate that SOM-based imputation preserves data structure and improves downstream analysis.

Proposed method

• The Kohonen self-organizing map (SOM) is trained on incomplete data, treating missing values as unknowns during weight adjustment.
• During training, the algorithm uses only observed features to compute the best-matching unit (BMU) and update weights.
• Missing values are estimated iteratively by averaging the values of neighboring neurons in the map.
• The imputation process is integrated into the SOM learning rule, updating weights based on observed data only.
• The method preserves the topological structure of the data, enabling consistent estimation of missing entries.
• Three real datasets are used to validate the approach, with imputation accuracy assessed via clustering and data consistency.

Experimental results

Research questions

• RQ1 Can Kohonen's self-organizing map effectively estimate missing values in incomplete datasets?
• RQ2 How does SOM-based imputation compare to traditional imputation methods in preserving data structure?
• RQ3 What is the impact of SOM-based imputation on clustering performance in real-world datasets?
• RQ4 To what extent does the method maintain data integrity and topology during missing value estimation?

Key findings

• The SOM-based method successfully estimates missing values by leveraging neighborhood relationships in the data.
• The imputation process maintains the topological structure of the original data, supporting meaningful clustering.
• Three real-world applications demonstrated the method's effectiveness in handling missing data without prior data preprocessing.
• The approach outperformed baseline methods in preserving data quality and enabling accurate downstream analysis.