An Effective Manifold Learning Approach to Parametrize Data for Generative Modeling of Biosignals

Modeling data generated by physiological systems is a crucial step in many problems such as classification, signal reconstruction and data augmentation. However finding appropriate models from high-dimensional data sampled from biosignals is in general unpracticable due to the problem known as the “curse of dimensionality”. Dimensionality reduction, that is representing data in some lower-dimensional space, is the commonly adopted technique to handle these data. In this context manifold learning has drawn great interests as a promising nonlinear dimensionality reduction method. Neverthless the main drawback of methods based on manifold learning is that they learn data implicitly, that is with no explicit model of data belonging to the manifold. The aim of this article is to develop a manifold learning approach to parametrize data for generative modeling of biosignals, by deriving an explicit function that represents the local parametrization of the manifold. The approach involves two main stages, i) estimation of the intrinsic dimension of data, that is the dimension of the manifold, and ii) estimation of the function representing the local parametrization of the manifold. Experimental results both on synthetic and real-world data shown the effectiveness of the presented approach. The source code of the algorithm for unsupervised learning of data is available at https://codeocean.com/capsule/6692152/tree/v3