Influence of Data Centring in Kernel-Cross Alignment: Application to Transfer Learning
Bruno Müller, Régis Lengelle · IET conference proceedings. · 2021
Most classification tasks rely on a source dataset of known labels and a target dataset of unknown labels. There might exist multiple variabilities between the source and the target; this is the case, for instance, in our application (classification of physiological data). This is one of the situations tackled by transfer learning, the improvement of the classification performances on a target dataset (of unknown labels) by considering the knowledge acquired on a (known) source dataset. We previously introduced two kernel-based methods of transferring knowledge: Quadratic Loss Transfer Learning (QLTL) and Kernel-Cross Alignment Transfer Learning (KCATL). The latter has been introduced in an applicative paper (currently submitted to a journal) and one of the perspectives was the improvement of the method through the centring of the cross- Gram matrix. In this paper, we focus on data centring; we show that, for our criteria, only the source centre impacts the detector's Receiver Operating Characteristics (ROC) curve. We also compare two centring strategies, in the Reproducing-Kernel Hilbert Space (RKHS) H and in the input space χ, with joint optimisation on the sought target labels YT . As shown in this paper, Kernel- Cross Polarisation (KCP) and its normalised equivalent, the Kernel-Cross Alignment (KCA), are optimised by the same YT . Considering the expressions of the gradients of our criteria w.r.t., first, the unknown labels and second, the centres, we propose an alternate directions optimisation scheme.