Abstract
Liver cancer is the sixth most frequently diagnosed cancer and, particularly, Hepatocellular Carcinoma (HCC) represents more than 90% of primary liver cancers. Clinicians assess each patient's treatment on the basis of evidence-based medicine, which may not always apply to a specific patient, given the biological variability among individuals. Over the years, and for the particular case of Hepatocellular Carcinoma, some research studies have been developing strategies for assisting clinicians in decision making, using computational methods (e.g. machine learning techniques) to extract knowledge from the clinical data. However, these studies have some limitations that have not yet been addressed: some do not focus entirely on Hepatocellular Carcinoma patients, others have strict application boundaries, and none considers the heterogeneity between patients nor the presence of missing data, a common drawback in healthcare contexts. In this work, a real complex Hepatocellular Carcinoma database composed of heterogeneous clinical features is studied. We propose a new cluster-based oversampling approach robust to small and imbalanced datasets, which accounts for the heterogeneity of patients with Hepatocellular Carcinoma. The preprocessing procedures of this work are based on data imputation considering appropriate distance metrics for both heterogeneous and missing data (HEOM) and clustering studies to assess the underlying patient groups in the studied dataset (K-means). The final approach is applied in order to diminish the impact of underlying patient profiles with reduced sizes on survival prediction. It is based on K-means clustering and the SMOTE algorithm to build a representative dataset and use it as training example for different machine learning procedures (logistic regression and neural networks). The results are evaluated in terms of survival prediction and compared across baseline approaches that do not consider clustering and/or oversampling using the Friedman rank test. Our proposed methodology coupled with neural networks outperformed all others, suggesting an improvement over the classical approaches currently used in Hepatocellular Carcinoma prediction models.

Abstract
Class overlap presents a significant challenge to machine learning algorithms, especially when class imbalance is present. These factors contribute substantially to the complexity of classification tasks, particularly in realworld scenarios. As a result, measuring overlap is crucial, yet it remains difficult to quantify due to its intricate nature, since it can manifest and be measured in multiple ways. To help mitigate this, recent research has conceptualized a new taxonomy of class overlap measures, divided into multiple families, which allows researchers to obtain a more complete overview of the complexity of the datasets. In line with recent research, we introduce a new Python package for class overlap measurement named pycol. This package implements 29 overlap measures, divided into four overlap families specifically designed to capture class overlap in imbalanced real-world scenarios. This makes pycol an essential tool for researchers dealing with complex classification problems, providing robust solutions to quantify the joint-effect of class overlap and class imbalance effectively.