Data can naturally be modeled using topological terms. Indeed, the field of topological data analysis relies fundamentally on the idea that the shape of data carries important invariants that can be utilized to study and analyze the underlying data. In this article, we define a topological framework of data in the context of a supervised machine learning problem. Using this topological setting, we prove that in order to achieve a successful classification task, the neural networks architecture must not be chosen independently without considering the nature of data.