Understanding information as well as its redundancy, or duplication, has been crucial in the development of many of our everyday items such mobile phones, the internet, the compact disc as well as ensuring the success of many space missions. Using information geometry tools, researchers at the University of Hertfordshire, led by Dr Daniel Polani have developed a new mathematically precise method of measuring information redundancy, as published in Physical Review E.
Most of us are familiar with the notion of "redundancy," where there is a duplication of concepts -- sometimes the duplication is for reasons of safety, but other times it is unintended. For example, critical machinery such as airplanes or satellites have "redundant" components built into systems to ensure continued operation in the event of some parts failing. Similarly, information or data can also be redundant. Sometimes, this redundancy is intentional, such as in the case of computer backups. However, on other occasions, the redundancy is an unintentional and unnecessary duplication, such as in saying "poodle dog" -- we know that we are referring to a dog whether we say "poodle" or we say "dog." Such unnecessary duplication can impact on data compression, data storage or unnecessarily increase the effort required to administrate data.
Dr Daniel Polani, Reader in Artificial Life in the University of Hertfordshire's School of Computer Science, said: "We often infer information on one variable based on the observations of another linked variable. For example, observing a person entering a house with a wet umbrella allows one to infer that there is a good likelihood that it is raining outside. Traditionally, this approach, called 'Mutual Information', was a good way to measure the degree of redundancy with respect to each of the two linked variables."
However, this simple approach fails when extended to three variables since they can interact in a very complicated way. A new approach was needed to measure redundancy for a system with three variables.
The new method developed by Dr Polani's team measures redundancy in a system with three variables. This new measure captures many of the intuitive properties of redundancy, with the added bonus of a novel information-geometric interpretation, which has not been done before. It measures how much the information in one variable lies "in the same direction" with respect to the other variable that you want to know more about.
This novel method of measuring redundancy has applications for researchers in a variety of different fields. One immediate use is to track how information flows through a system which promises to be a very valuable tool in neuroscience and the study of networks, agents and other complex scenarios where it is essential to trace the origin and the effects of information flow.
- Malte Harder, Christoph Salge, Daniel Polani. Bivariate measure of redundant information. Physical Review E, 2013; 87 (1) DOI: 10.1103/PhysRevE.87.012130
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