Place: Large Lecture Room
Affiliation: Univ. de València, Spain
Observations of a source change depending on the acquisition conditions. Adaptation to these changes can be understood as maximizing the correspondence between the responses to these different observations. Methods related to Canonical Correlation Analysis (CCA) have been proposed to explain adaptation of biological color vision mechanisms under different illumination conditions. Optimal coding (related to Independent Components Analysis -ICA-) has been proposed to reproduce the spatio-chromatic structure of V1 receptive fields in fixed illumination conditions. However, on the one hand, CCA does not yield optimal representations of color images in information theoretic terms since it is based just on 2nd order statistics. On the other hand, separate ICAs applied to datasets with different illuminations do not give rise to appropriate correspondences.
In this work we propose an extension of CCA, the Higher-Order Canonical Correlation Analysis (HOCCA), which combines desirable properties of CCA and ICA. HOCCA enforces independence between sources inside each dataset as in ICA. At the same time, HOCCA generalizes CCA since not only correlation but also variance dependencies between datasets are maximized. This statistical tool is appropriate to explain visual adaptation since organization of biological sensors not only requires an appropriate response coupling in corresponding situations, but it is also guided by optimal coding principles. Advantages of HOCCA in spatio-chromatic adaptation are twofold:
- The filters identified by HOCCA have similar independence performance as separate ICA filters, and their shape resembles that of V1 receptive fields (thus over performing CCA).
- HOCCA has similar correspondence behavior as CCA and reproduces psychophysical corresponding pairs data (thus over performing separate ICAs).