# A Functional approach for Two Way Dimension Reduction in Time Series

arXiv: https://arxiv.org/abs/2301.00357 · HTML: https://mlsanity.com/paper/2301.00357/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 29 references that are in the map.
- First posted on arXiv 1 Jan 2023.

## Builds on (most cited first, 9 of 9)

- [Unsupervised Learning of Video Representations using LSTMs](https://mlsanity.com/paper/1502.04681/) (2015)
- [Recent Advances in Autoencoder-Based Representation Learning](https://mlsanity.com/paper/1812.05069/) (2018)
- [Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains](https://mlsanity.com/paper/1509.02029/) (2015)
- [Deep Learning with Functional Inputs](https://mlsanity.com/paper/2006.09590/) (2020)
- [Non-linear Functional Modeling using Neural Networks](https://mlsanity.com/paper/2104.09371/) (2021)
- [Modern Non-Linear Function-on-Function Regression](https://mlsanity.com/paper/2107.14151/) (2021)
- [A Non-linear Function-on-Function Model for Regression with Time Series Data](https://mlsanity.com/paper/2011.12378/) (2020)
- [Capabilities and Limitations of Time-lagged Autoencoders for Slow Mode Discovery in Dynamical Systems](https://mlsanity.com/paper/1906.00325/) (2019)
- [Spatio-Temporal Functional Neural Networks](https://mlsanity.com/paper/2009.05665/) (2020)

## Built on by (most cited first, 1 of 1)

- [An ensemble of convolution-based methods for fault detection using vibration signals](https://mlsanity.com/paper/2305.05532/) (2023)

## Abstract (arXiv)

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.