AGR Stats Colloquium: Averaging in the right way: how to combine data into a representative value

Host Institution:

La Trobe University

Title of Seminar:

Averaging in the right way: how to combine data into a representative value

Speaker's Name:

Professor G. Beliakov

Speaker's Institution:

Deakin University

Time and Date:

Friday 6 September, 12.00pm (AEST)

Seminar Abstract:

In this lecture I will talk about aggregating data, and specifically about averaging aggregation. Our aim is to define some sort of a representative value of the data, and the arithmetic mean is the simplest way to do this. But is it the right way? I will present many other means that do a similar job, and will talk about their properties and applicability. From the arithmetic mean I will move to fuzzy measures and integrals and discuss how these tools allow one to take into account dependencies (redundancy, complimentarity) between the inputs, and avoid double counting. I will then discuss penalty based aggregation, where the average value is found by minimising some sort of a penalty for lack of consensus. This construction is so general that it allows one to obtain all possible averaging functions through minimising a suitable penalty. Further on I will discuss some very recent developments in this area, including non-monotone averaging (and noise filtering).

Applications of averaging are abundant, from statistics to signal processing, voting, game theory, image processing, data analysis, decision making, and so on. In this lecture I will focus on image processing and multiattribute decision making problems.

Speaker Bio

Professor G. Beliakov has been with Deakin University since 1999, when he started as a lecturer after several postdoc positions in Australia and overseas. He is a Senior Member of IEEE and is an Associate Editor of two flagship journals in the area of fuzzy systems. His research focuses on computational mathematics, numerical data analysis, fuzzy systems and aggregation operators. He is an author of a monograph on aggregation functions, two edited volumes and over 150 refereed papers.

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