Daniel Herrera-Esposito¹ (), Johannes Burge; ¹University of Pennsylvania

Vision begins with the extraction of features in the retinal images that carry information useful for estimating and classifying properties of the environment. Here, we present a novel feature-learning technique called Supervised Quadratic Feature Analysis (SQFA) that maps class-conditional data (e.g. labeled image set) to a low-dimensional feature space that maximally preserves second-order class-differences, and thus second-order class discriminability. Differences in class-conditional second-order statistics can aid task performance, but few dimensionality reduction methods focus on second-order differences. SQFA exploits a theoretical relation between class discriminability (i.e. Fisher Information) and the Information geometry of second-moment (or covariance) matrices as points on the symmetric positive definite (SPD) manifold. The technique learns the features that maximize the distances between points (i.e. second-moment matrices) in this manifold. We demonstrate the usefulness of SQFA on a set of vision tasks where second-order statistics are known to be crucial. In many cases, SQFA finds features that are similar to the optimal features learned with Accuracy Maximization Analysis, a more computationally intensive approach. SQFA is distinct from other well-known methods in several respects. Unlike unsupervised techniques (e.g. ICA, PCA), SQFA learns task-specific features that are useful for classification and/or estimation. Unlike many supervised techniques (e.g. LDA), SQFA learns features that are sensitive to information other than first-order class differences. And unlike many non-linear and machine-learning methods (e.g. kernel methods, DNN’s), SQFA results are easily interpretable. Thus, besides representing an encouraging first step in the use of Information-geometry-based methods for feature learning, SQFA should be a useful addition to the vision scientist’s toolkit. Further, because SQFA can also be used to find features that exploit correlations in neural population activity, it should find broad application in neuroscience as well.

Acknowledgements: This work was supported by the National Eye Institute and the Office of Behavioral and Social Sciences Research, National Institutes of Health Grant R01-EY028571 to J.B.