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A Functional approach for Two Way Dimension Reduction in Time Series | | Aniruddha Rajendra Rao
; Haiyan Wang
; Chetan Gupta
; | | Date: |
1 Jan 2023 | | Abstract: | 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. | | Source: | arXiv, 2301.00357 | | Services: | Forum | Review | PDF | Favorites | |
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