Order-preserving factor analysis (OPFA)

We present a novel factor analysis method that can be applied to discovery of common factors shared among trajectories in multivariate time series data. These factors satisfy a precedence-ordering property: certain factors are recruited only after some other factors are activated. Precedence ordering arise in applications where variables are activated in a specific order, which is unknown. The proposed method is based on a linear model that accounts for each factor’s inherent delays and relative order. We present an algorithm to fit the model in an unsupervised manner using techniques from convex and non-convex optimization that enforce sparsity of the factor scores and consistent precedence order of the factor loadings. We illustrate the OPFA method for the problem of extracting precedence-ordered factors from gene expression data.