Overview

A large number of methods for dimensionality reduction is available nowadays, but there is no single method which is superior to all others in all situations. The right choice of method depends on the task at hand. For SENSOPAC we are considering two scenarios. In the first, we are looking for fast, local dimensionality reduction to incorporate into online learning. In the second, dimensionality reduction is used globally to discover sensorimotor structures.

Local Dimensionality Reduction

In order to discover structure which results as a consequence of motor functions as opposed to sensor only analysis, we learn representations of these motor functions which capture their most important features and thus generalize to situations different from the learned ones (see subproject Learning Kinematics and Dynamics). Within this framework we were looking at dimensionality reduction techniques suitable for locally-linear regression and online learning. We found that only techniques which take input-output correlation into account achieve robust performance. In particular Partial Least Squares (PLS) is well suited for this task. Heiko Hoffmann completed the work on local dimensionality reduction in 2006.
It has been submitted as Deliverable 2.1 in January 2007.

Global Dimensionality Reduction

The sensorimotor space, a space in which motor actions and sensory inputs are combined, has a very high dimensionality. Motor actions and sensory inputs, however, do not change independently. Motor actions lead to certain, principled changes in sensory input. These regularities are known under the concept of sensorimotor contingencies, but they can also be described as structures in sensorimotor space. We investigate methods to infer such lower dimensional structures in a data driven way. Our aim is to find low dimensional spaces which capture the most important aspects of sensorimotor data, which are robust against noise in the data and, very importantly, which allow generalization such that new points in low dimensional space map to points in original sensorimotor space which are consistent with the data. Additionally, the hope is that the low dimensional spaces relate easily to properties of the environment and can therefore be interpreted as defining cognitive notions about the environment.
One central aspect of sensorimotor data is its dynamical nature. Most dimensionality reduction methods, however, ignore temporal dependencies between data points. Consequently we are focusing in collaboration with subproject Dynamical Systems for Motion Planning on extensions for dimensionality reduction techniques compatible with the dynamics of the data.