Linear dimension reduction for evolutionary data

We consider the problem of linear dimensionality reduction for high-dimensional evolutionary data, whose distribution changes over time or with respect to a parameter. Supervised dimensionality reduction methods have proven to be very successful in real-world classification problems. When dealing with evolutionary data, we would like to perform classification that is not only robust to noise and short-term changes, but also adaptive to long-term drifts in the data distribution. In order to capture this notion of temporal smoothness, we propose the use of an additional penalty term in classic optimization-based formulations of dimensionality reduction. The penalty term prevents the reduced space in one time step to differ too much from the one in the previous time step. Experiments with synthetic and real-world data provide evidence that such an approach leads to improved classification performance.