MoTIF: An Efficient Algorithm for Learning Translation Invariant Dictionaries

Philippe Jost, Pierre Vandergheynst, Sylvain Lesage, Rémi Gribonval

Abstract: The performance of approximation using redundant expansions rely on having dictionaries adapted to the signals. In natural high-dimensional data, the statistical dependencies are, most of the time, not obvious. Learning fundamental patterns is an alternative to analytical design of bases and is nowadays a popular problem in the field of approximation theory. In many situations, the basis elements are shift invariant, thus the learning should try to find the best matching filters. We present a new algorithm for iteratively learning generating functions that can be shifted at all positions in the signal to generate a highly redundant dictionary