Geometrical complexity of data approximators
This work addresses the need for a standardized complexity measure in machine learning to balance accuracy and complexity, though it appears incremental as it builds on existing methods without introducing a new paradigm.
The paper tackles the problem of measuring the complexity of various data approximators, such as principal curves and self-organizing maps, by proposing a unified geometrical complexity measure that enables comparison across different types of approximators.
There are many methods developed to approximate a cloud of vectors embedded in high-dimensional space by simpler objects: starting from principal points and linear manifolds to self-organizing maps, neural gas, elastic maps, various types of principal curves and principal trees, and so on. For each type of approximators the measure of the approximator complexity was developed too. These measures are necessary to find the balance between accuracy and complexity and to define the optimal approximations of a given type. We propose a measure of complexity (geometrical complexity) which is applicable to approximators of several types and which allows comparing data approximations of different types.