Linear Dimensionality Reduction for Time Series

Visualisation by dimensionality reduction is an important tool for data exploration. In this work we are interested in visualising time series. To that end we formulate a latent variable model that mirrors probabilistic principal component analysis (PPCA). However, as opposed to PPCA which maps the latent variables directly to the data space, we first map the latent variables to the parameter space of a recurrent neural network, i.e. each latent projection instantiates a recurrent network. Each instantiated recurrent network in turn is responsible for modelling a time series in the dataset. Hence, each latent variable is indirectly mapped to a time series. Incorporating the recurrent network in the latent variable model helps us account for the temporal nature of the time series and capture their underlying dynamics. The proposed algorithm is demonstrated on two benchmark problems and a real world dataset.