Feature dimensionality reduction via homological properties of observability

Feature selection and its subsequent dimensionality reduction are significant problems in machine learning and it is at the core of several data science techniques. The 'shape' of data, or in other words its related topological properties, can provide crucial insights into the corresponding data types and sources and it enables the identification of general properties that facilitate its analysis and assessment. In this article, we discuss an information theoretic approach combined with data homological properties to assess dimensionality reduction, which can be applied to semantic feature selection.