Data Representation using the Weyl Transform
This addresses representation learning for data analysis, but appears incremental as it builds on existing transform methods.
The paper tackles the problem of data representation by introducing the Weyl transform as a framework, showing it enables compact and discriminative features through pooling, and demonstrates effectiveness with textured image classification.
The Weyl transform is introduced as a rich framework for data representation. Transform coefficients are connected to the Walsh-Hadamard transform of multiscale autocorrelations, and different forms of dyadic periodicity in a signal are shown to appear as different features in its Weyl coefficients. The Weyl transform has a high degree of symmetry with respect to a large group of multiscale transformations, which allows compact yet discriminative representations to be obtained by pooling coefficients. The effectiveness of the Weyl transform is demonstrated through the example of textured image classification.