Event Details

An algebraic perspective on dimension reduction in statistics

Principal Component Analysis simplifies high dimensional data by means of an orthogonal projection onto a lower dimensional hyperplane. An orthogonal projection can be defined through the (Euclidean) scalar product or, equivalently, as the minimizer of the sum of squared distances between the data and their approximations. In order to transfer the PCA to extreme values, we just need to find the natural scalar product and/or the natural distance measure for extreme values. The talk gives an insight into a general approach, how scalar products and distances might be defined, when fundamental requirements for a standard scalar product are violated. We illustrate this approach by many examples and new perspectives on some well-known concepts.

Although the approach is heavily based on algebraic objects such as monoids and quasi-semi-rings, the talk will only deal with their properties, such as the validity of the associative law.