The rise in data has led to the need for dimension reduction techniques, especially in the area of non-scalar variables, including time series, natural language processing, and computer vision. In this paper, we specifically investigate dimension reduction for time series through functional data analysis. Current methods for dimension reduction in functional data are functional principal component analysis and functional autoencoders, which are limited to linear mappings or scalar representations for the time series, which is inefficient. In real data applications, the nature of the data is much more complex. We propose a non-linear function-on-function approach, which consists of a functional encoder and a functional decoder, that uses continuous hidden layers consisting of continuous neurons to learn the structure inherent in functional data, which addresses the aforementioned concerns in the existing approaches. Our approach gives a low dimension latent representation by reducing the number of functional features as well as the timepoints at which the functions are observed. The effectiveness of the proposed model is demonstrated through multiple simulations and real data examples.

翻译：数据上升导致需要减少尺寸技术,特别是在非星际变量领域,包括时间序列、自然语言处理和计算机视觉。在本文件中,我们特别通过功能数据分析来调查时间序列的尺寸减少情况。功能数据的现有减少方法是功能性主要组成部分分析和功能性自动校正器,这些功能性数据仅限于线性绘图或时间序列的标尺,效率不高。在实际数据应用中,数据的性质要复杂得多。我们提议采用非线性功能即运行函数法,由功能编码器和功能解码器组成,使用由连续神经元组成的连续隐藏层来学习功能性数据所固有的结构,从而解决现有方法中的上述关切问题。我们的方法通过减少功能性特征的数量和观察功能的时间点,提供了低度的维度潜在代表性。通过多次模拟和真实数据实例来显示拟议模型的有效性。