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.

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一种有效的流形学习方法来参数化数据以进行生物信号的生成建模

对生理系统生成的数据进行建模是分类、信号重建和数据增强等许多问题的关键步骤。然而，由于被称为“维度灾难”的问题，从生物信号采样的高维数据中找到合适的模型通常是不切实际的。降维，即在一些低维空间中表示数据，是处理这些数据的常用技术。在这种情况下，流形学习作为一种有前途的非线性降维方法引起了极大的兴趣。尽管如此，基于流形学习的方法的主要缺点是它们隐式地学习数据，即没有属于流形的数据的显式模型。本文的目的是开发一种流形学习方法，通过推导表示流形局部参数化的显式函数，对数据进行参数化，以用于生物信号的生成建模。该方法涉及两个主要阶段，i) 估计数据的内在维数，即流形的维数，以及 ii) 估计表示流形局部参数化的函数。合成数据和真实数据的实验结果都表明了所提出方法的有效性。用于数据无监督学习的算法的源代码可在 https://codeocean.com/capsule/6692152/tree/v3 获得。i) 估计数据的内在维数，即流形的维数，以及 ii) 估计表示流形局部参数化的函数。合成数据和真实数据的实验结果都表明了所提出方法的有效性。数据无监督学习算法的源代码可在 https://codeocean.com/capsule/6692152/tree/v3 获得。i) 估计数据的内在维数，即流形的维数，以及 ii) 估计表示流形局部参数化的函数。合成数据和真实数据的实验结果都表明了所提出方法的有效性。用于数据无监督学习的算法的源代码可在 https://codeocean.com/capsule/6692152/tree/v3 获得。