Relating instance hardness to classification performance in a dataset: a visual approach

Machine Learning studies often involve a series of computational experiments in which the predictive performance of multiple models are compared across one or more datasets. The results obtained are usually summarized through average statistics, either in numeric tables or simple plots. Such approaches fail to reveal interesting subtleties about algorithmic performance, including which observations an algorithm may find easy or hard to classify, and also which observations within a dataset may present unique challenges. Recently, a methodology known as Instance Space Analysis was proposed for visualizing algorithm performance across different datasets. This methodology relates predictive performance to estimated instance hardness measures extracted from the datasets. However, the analysis considered an instance as being an entire classification dataset and the algorithm performance was reported for each dataset as an average error across all observations in the dataset. In this paper, we developed a more fine-grained analysis by adapting the ISA methodology. The adapted version of ISA allows the analysis of an individual classification dataset by a 2-D hardness embedding, which provides a visualization of the data according to the difficulty level of its individual observations. This allows deeper analyses of the relationships between instance hardness and predictive performance of classifiers. We also provide an open-access Python package named PyHard, which encapsulates the adapted ISA and provides an interactive visualization interface. We illustrate through case studies how our tool can provide insights about data quality and algorithm performance in the presence of challenges such as noisy and biased data.