Departamento de Matemáticas UAM

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 transfering 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) mean square value 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.