2020-02-10 new paper

**Genie+OWA: Robustifying Hierarchical Clustering with OWA-based Linkages**

Check out our (by Anna Cena and me) most recent paper
on the best hierarchical clustering algorithm in the world – Genie.
It is going to appear in *Information Sciences*;
doi:10.1016/j.ins.2020.02.025.

Abstract.We investigate the application of the Ordered Weighted Averaging (OWA) data fusion operator in agglomerative hierarchical clustering. The examined setting generalises the well-known single, complete and average linkage schemes. It allows to embody expert knowledge in the cluster merge process and to provide a much wider range of possible linkages. We analyse various families of weighting functions on numerous benchmark data sets in order to assess their influence on the resulting cluster structure. Moreover, we inspect the correction for the inequality of cluster size distribution -- similar to the one in the Genie algorithm. Our results demonstrate that by robustifying the procedure with the Genie correction, we can obtain a significant performance boost in terms of clustering quality. This is particularly beneficial in the case of the linkages based on the closest distances between clusters, including the single linkage and its "smoothed" counterparts. To explain this behaviour, we propose a new linkage process called three-stage OWA which yields further improvements. This way we confirm the intuition that hierarchical cluster analysis should rather take into account a few nearest neighbours of each point, instead of trying to adapt to their non-local neighbourhood.

2019-12-11 new paper

**DC optimization for constructing discrete Sugeno integrals and learning nonadditive measures**

We (Gleb Beliakov, Simon James and I) have another paper accepted
for publication – this time in the *Optimization* journal;
doi:10.1080/02331934.2019.1705300.

Abstract.Defined solely by means of order-theoretic operations meet (min) and join (max), weighted lattice polynomial functions are particularly useful for modeling data on an ordinal scale. A special case, the discrete Sugeno integral, defined with respect to a nonadditive measure (a capacity), enables accounting for the interdependencies between input variables.However until recently the problem of identifying the fuzzy measure values with respect to various objectives and requirements has not received a great deal of attention. By expressing the learning problem as the difference of convex functions, we are able to apply DC (difference of convex) optimization methods. Here we formulate one of the global optimization steps as a local linear programming problem and investigate the improvement under different conditions.

2019-12-01

**IEEE WCCI 2020 Special Session - Aggregation Structures: New Trends and Applications**

Call for contributions –
IEEE World Congress on Computational Intelligence (WCCI) 2020,
Glasgow, Scotland —
FUZZ-IEEE-6 Special Session on *Aggregation Structures: New Trends and Applications*;
for more details,
click here.

2019-11-14 new paper

**Robust fitting for the Sugeno integral with respect to general fuzzy measures**

The editor of *Information Sciences* have just let us know that a paper
by Gleb Beliakov, Simon James and me will be published in this outlet.

Abstract.The Sugeno integral is an expressive aggregation function with potential applications across a range of decision contexts. Its calculation requires only the lattice minimum and maximum operations, making it particularly suited to ordinal data and robust to scale transformations. However, for practical use in data analysis and prediction, we require efficient methods for learning the associated fuzzy measure. While such methods are well developed for the Choquet integral, the fitting problem is more difficult for the Sugeno integral because it is not amenable to being expressed as a linear combination of weights, and more generally due to plateaus and non-differentiability in the objective function. Previous research has hence focused on heuristic approaches or simplified fuzzy measures. Here we show that the problem of fitting the Sugeno integral to data such that the maximum absolute error is minimized can be solved using an efficient bilevel program. This method can be incorporated into algorithms that learn fuzzy measures with the aim of minimizing the median residual. This equips us with tools that make the Sugeno integral a feasible option in robust data regression and analysis. We provide experimental comparison with a genetic algorithms approach and an example in data analysis.

2019-09-23

2019-09-10 new paper

**Constrained Ordered Weighted averaging aggregation with multiple comonotone constraints**

Lucian Coroianu, Robert Fullér, Simon James and I got a paper accepted in the
*Fuzzy Sets and Systems* outlet. Abstract below.

Abstract.The constrained ordered weighted averaging (OWA) aggregation problem arises when we aim to maximize or minimize a convex combination of order statistics under linear inequality constraints that act on the variables with respect to their original sources. The standalone approach to optimizing the OWA under constraints is to consider all permutations of the inputs, which becomes quickly infeasible when there are more than a few variables, however in certain cases we can take advantage of the relationships amongst the constraints and the corresponding solution structures. For example, we can consider a land-use allocation satisfaction problem with an auxiliary aim of balancing land-types, whereby the response curves for each species are non-decreasing with respect to the land-types. This results in comonotone constraints, which allow us to drastically reduce the complexity of the problem.

In this paper, we show that if we have an arbitrary number of constraints that are comonotone (i.e., they share the same ordering permutation of the coefficients), then the optimal solution occurs for decreasing components of the solution. After investigating the form of the solution in some special cases and providing theoretical results that shed light on the form of the solution, we detail practical approaches to solving and give real-world examples.

2019-06-17 new PhD

My PhD student, Jan Lasek,
has successfully defended his doctoral thesis,
*New data-driven
rating systems for association football*.
:)

2019-06-08 new paper

**Aggregation on ordinal scales with the Sugeno integral for biomedical applications**

Gleb Beliakov, Simon James and I got another paper accepted for publication in
*Information Sciences*. This time we re-write a learning-to-aggregate
problem based on the Sugeno integral in a difference-of-convex objective setting.
The derived tool is particularly useful when working with ordinal data.

Abstract.The Sugeno integral is a function particularly suited to the aggregation of ordinal inputs. Defined with respect to a fuzzy measure, its ability to account for complementary and redundant relationships between variables brings much potential to the field of biomedicine, where it is common for measurements and patient information to be expressed qualitatively. However, practical applications require well-developed methods for identifying the Sugeno integral's parameters, and this task is not easily expressed using the standard optimisation approaches. Here we formulate the objective function as the difference of two convex functions, which enables the use of specialised numerical methods. Such techniques are compared with other global optimisation frameworks through a number of numerical experiments.