Multi-Attribute Probabilistic Linear Discriminant Analysis for 3D Facial Shapes

Component Analysis (CA) consists of a set of statistical techniques that decompose data to appropriate latent components that are relevant to the task-at-hand (e.g., clustering, segmentation, classification). During the past years, an explosion of research in probabilistic CA has been witnessed, with the introduction of several novel methods (e.g., Probabilistic Principal Component Analysis, Probabilistic Linear Discriminant Analysis (PLDA), Probabilistic Canonical Correlation Analysis). A particular subset of CA methods such as PLDA, inspired by the classical Linear Discriminant Analysis, incorporate the knowledge of data labeled in terms of an attribute in order to extract a suitable discriminative subspace. Nevertheless, while many modern datasets incorporate labels with regards to multiple attributes (e.g., age, ethnicity, weight), existing CA methods can exploit at most a single attribute (i.e., one set of labels) per model. That is, in case multiple attributes are available, one needs to train a separate model per attribute, in effect not exploiting knowledge of other attributes for the task-at-hand. In this light, we propose the first, to the best of our knowledge, Multi-Attribute Probabilistic LDA (MAPLDA), that is able to jointly handle data annotated with multiple attributes. We demonstrate the performance of the proposed method on the analysis of 3D facial shapes, a task with increasing value due to the rising popularity of consumer-grade 3D sensors, on problems such as ethnicity, age, and weight identification, as well as 3D facial shape generation.