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Slow feature analysis (SFA) is an unsupervised learning algorithm thatextracts slowly varying features from a time series. Graph-based SFA (GSFA) isa supervised extension that can solve regression problems if followed by apost-processing regression algorithm. A training graph specifies arbitraryconnections between the training samples. The connections in current graphs,however, only depend on the rank of the involved labels. Exploiting the exactlabel values makes further improvements in estimation accuracy possible.  In this article, we propose the exact label learning (ELL) method to create agraph that codes the desired label explicitly, so that GSFA is able to extracta normalized version of it directly. The ELL method is used for three tasks:(1) We estimate gender from artificial images of human faces (regression) andshow the advantage of coding additional labels, particularly skin color. (2) Weanalyze two existing graphs for regression. (3) We extract compactdiscriminative features to classify traffic sign images. When the number ofoutput features is limited, a higher classification rate is obtained comparedto a graph equivalent to nonlinear Fisher discriminant analysis. The method isversatile, directly supports multiple labels, and provides higher accuracycompared to current graphs for the problems considered.

Theoretical Analysis of the Optimal Free Responses of Graph-Based SFA for the Design of Training Graphs