Conditional Random Fields (CRFs) and Hidden Conditional Random Fields (HCRFs) are a staple of many sequence tagging and classification frameworks. An underlying assumption in those models is that the state sequences (tags), observed or latent, take their values from a set of nominal categories. These nominal categories typically indicate tag classes (e.g., part-of-speech tags) or clusters of similar measurements. However, in some sequence modeling settings it is more reasonable to assume that the tags indicate ordinal categories or ranks. Dynamic envelopes of sequences such as emotions or movements often exhibit intensities growing from neutral, through raising, to peak values.
In this project we develop models and algorithms for sequences of ranks or ordinal categories. Our first model, CORF (Conditional Ordinal Random Field)  extends is to ordinal latent data what CRF is to nominal data. HCORF (Hidden Conditional Ordinal Random Field)  generalizes this idea to latent settings, where we cannot observe ordinal ranks but still want to model dynamics in this space.
We have applied these models to analysis of facial emotions and facial emotion intensities, as well as classification of human activities from video sequences.
-  M. Kim and V. Pavlovic. “Structured output ordinal regression for dynamic facial emotion intensity prediction”. Computer Vision – ECCV 2010. Daniilidis, Kostas, Maragos, Petros, Paragios and Nikos eds. 2010. pp. 649-662.
-  M. Kim and V. Pavlovic. “Hidden Conditional Ordinal Random Fields for Sequence Classification”. ECML/PKDD. 2010. pp. 51-65.