Dimensionality reduction for time series data
This work addresses the need for time series-specific dimensionality reduction in fields like neuroimaging, though it appears incremental as it builds upon existing Bayesian models.
The paper tackles the problem of applying dimensionality reduction to time series data by introducing a factor decomposition based on a Bayesian multivariate autoregressive model, which avoids the independence assumption of classic methods like PCA, and demonstrates its application on synthetic and neuroimaging data.
Despite the fact that they do not consider the temporal nature of data, classic dimensionality reduction techniques, such as PCA, are widely applied to time series data. In this paper, we introduce a factor decomposition specific for time series that builds upon the Bayesian multivariate autoregressive model and hence evades the assumption that data points are mutually independent. The key is to find a low-rank estimation of the autoregressive matrices. As in the probabilistic version of other factor models, this induces a latent low-dimensional representation of the original data. We discuss some possible generalisations and alternatives, with the most relevant being a technique for simultaneous smoothing and dimensionality reduction. To illustrate the potential applications, we apply the model on a synthetic data set and different types of neuroimaging data (EEG and ECoG).