Self-Organising Stochastic Encoders

TL;DR

This paper introduces stochastic vector quantisers (SVQs) that automatically discover independent subspaces in high-dimensional data, enabling adaptive, self-organising data processing without manual window sizing.

Contribution

The paper presents a novel stochastic encoder extending vector quantisation that self-organises to split data into independent subspaces, demonstrated through analytical and numerical solutions.

Findings

SVQs automatically split input space into independent subspaces.

Numerical solutions show emergence of specialized encoders for targets and waveforms.

SVQs exhibit rich self-organising behaviour discovering data structure.

Abstract

The processing of mega-dimensional data, such as images, scales linearly with image size only if fixed size processing windows are used. It would be very useful to be able to automate the process of sizing and interconnecting the processing windows. A stochastic encoder that is an extension of the standard Linde-Buzo-Gray vector quantiser, called a stochastic vector quantiser (SVQ), includes this required behaviour amongst its emergent properties, because it automatically splits the input space into statistically independent subspaces, which it then separately encodes. Various optimal SVQs have been obtained, both analytically and numerically. Analytic solutions which demonstrate how the input space is split into independent subspaces may be obtained when an SVQ is used to encode data that lives on a 2-torus (e.g. the superposition of a pair of uncorrelated sinusoids). Many numerical solutions have also been obtained, using both SVQs and chains of linked SVQs: (1) images of multiple independent targets (encoders for single targets emerge), (2) images of multiple correlated targets (various types of encoder for single and multiple targets emerge), (3) superpositions of various waveforms (encoders for the separate waveforms emerge - this is a type of independent component analysis (ICA)), (4) maternal and foetal ECGs (another example of ICA), (5) images of textures (orientation maps and dominance stripes emerge). Overall, SVQs exhibit a rich variety of self-organising behaviour, which effectively discovers the internal structure of the training data. This should have an immediate impact on "intelligent" computation, because it reduces the need for expert human intervention in the design of data processing algorithms.