Multiclass Continuous Correspondence Learning

We extend the Structural Correspondence Learning (SCL) domain adaptation algorithm of Blitzer et al. [4] to the realm of continuous signals. Given a set of labeled examples belonging to a “source” domain, we select a set of unlabeled examples in a related “target” domain that play similar roles in both domains. Using these “pivot samples,” we map both domains into a common feature space, allowing us to adapt a classifier trained on source examples to classify target examples. We show that when between-class distances are relatively preserved across domains, we can automatically select target pivots to bring the domains into correspondence. 1 Structural Correspondence Learning for Continuous Feature Spaces We extend the Structural Correspondence Learning (SCL) algorithm of Blitzer et al. [4] to continuous signals. SCL is a domain adaptation technique which creates a mapping between a “source” domain consisting of labeled examples, and an unlabeled “target” domain using a set of “pivot features” common to both domains. In text classification scenarios, these consist of terms (words) that serve similar roles in both domains, so that the role of other features can be inferred by correlation. We extend this concept to continuous domains where the objects we classify are continuous-valued functions, making SCL applicable to data such as time series or electromagnetic spectral signatures. Recent work by Balcan et al. [1] provides an elegant method to define a correspondence mapping between continuous feature spaces. They illustrated that designing a good feature space is similar to designing a good kernel function, and under certain conditions, a kernel which approximately preserves the margin of a max-margin separator can be constructed using a set of unlabeled samples. By projecting samples into a space defined by (distances to) the unlabeled samples, one can potentially harness the power of a high-dimensional kernel mapping in this lower-dimensional feature space. In a similar vein, we define our correspondence mapping using distances to canonical samples, or pivot samples. These distances become the pivot features we use to reconcile differences between the source and target domains. Determining a mapping between domains is closely related to the topic of manifold alignment. Most manifold alignment algorithms assume knowledge of the target domain in the form of paired (source to target) correspondences [11], [13] or a number of labeled target examples [8], to define a transformation that reconciles the feature spaces, but recent work (e.g., [12]) determines the correspondence mapping automatically by matching local geometric properties across feature spaces. This work presents Multiclass Continuous Correspondence Learning (MCCL): a domain adaptation technique for high-dimensional continuous data. In previous work [5], [6], we demonstrated the feasibility of a similar domain adaptation technique for continous data – specifically, hyperspectral imagery. In this work, we show that by exploiting structured relationships between a diverse set of source classes, we can automatically select a set of pivot samples to reconcile differences between source and target domains.