Deterministic decoupling of features: a normalization framework for signal and data science
Machine learning in Madrid (zoom)
Monday, December 20, 2021, 12-13h
Speaker: Javier Portilla (Institute of Optics «Daza de Valdés» – CSIC)
In recent years we are witnessing explosive development and impressive
advances in machine learning, signal processing, and simulation. A large part of these advances is based, direct or indirectly, on the concept of
“features”, a set of values that are extracted from the data to capture
relevant information. Extracted features are used to classify, identify, or detect patterns, and also to modify the data/signals themselves, e.g., by “modulating” those features values at our will, or transferring them from one observation to another (e.g., for changing the “style” of an image).
Traditional approaches to data analysis have mainly focused on statistics.
Here we follow a different approach, based on studying and compensating for the algebraic coupling existing among differentiable functions (e.g., sample statistics expressed as averages) which play the role of global features in signal models. After decoupling, the new features’ gradients become mutually orthogonal, a very strong constraint that opens exciting possibilities for machine learning.
Here we focus on two feature families widely used in signal analysis and
synthesis: (1) marginal moments, and (2) moments at the output of a set of filters. We will present both a theoretical framework and a practical
algorithm, allowing either perfect or approximate feature decoupling.
Joint work with Mar González (mathematics) and Eduardo Martínez (engineering applications)
