Mathematics Symposium: "Mathematics Awareness Month at UNO"
Naomi Kochi
An Algebraic Method to the Identification of Fuzzy Measures Based on Choquet Integrals
There are different nonlinear integrals that could be used as an aggregation
tool in information fusion and data mining, and the Choquet integral based on fuzzy
measures is one of them. The focus of this project is on the methods to identify
fuzzy measures based on the Choquet integral. An iterative method introduced by
Grabisch is discussed with some counterexamples. We also introduce an algebraic
method to identify fuzzy measures and present some experimental results on both
artificial and real-world data sets to show its effectiveness.
Bryan Johnson
Using statistics to analyze 'home field advantage' in college football
College football fans and announcers often speculate on which teams benefit
from a significant home-field advantage. In this talk, home-field advantage
is quantified for each of the 120 Division I FBS teams for the 2008/2009
season using both empirical and statistical methods. The relationship
between the quality of each team and its corresponding home-field advantage
is also investigated. The statistical analysis involved the fitting of a
Linear Regression Model using Bayesian techniques.
Jaime Lopez
Alternative Methods for Certain Monotonic Functions
This work covers the topic of providing alternative methods to the
approximation of derivatives of monotonic functions. It includes
several numerical examples on the rate of convergence for geometric
and arithmetic means for derivatives and compares them to classical
methods used in calculus. It covers certain criteria that must be
met to identify which method to use for several general types of functions.
Finally, it delves into the limitations on the usage of these methods
and when it becomes necessary to involve a more complex analysis if
it is desired to use the geometric mean.
Weiwei Zhang
On the uniqueness of the expression for the Choquet integral with linear core
The Choquet integral has been applied in data mining, such as nonlinear
multiregressions and nonlinear classifications. Adopting signed efficiency
measure in the Choquet integral makes the models more powerful. Another idea
for generalizing the above-mentioned models is to use a linear core in the
Choquet integral. This has been successfully used in nonlinear mulregression.
However, there is a uniqueness problem for presenting the Choquet integral
in classification models, such that and, therefore, it is difficult to explain
the exact contribution from each individual attributes, as well as their
combinations, towards the target. In this work, an additional restriction
on the parameters is given to guarantee the uniqueness of the explanation.
Jeremy Trageser
The Kauffman Bracket of a Family of Arboresceant Links
The Kauffman Bracket of a link is a strong invariant. However, many questions remain
on what it actually measures. We introduce a family of links that are associated to
a family of trees, called arboresceant links. From here we have a diagrammatic proof
that this family of links corresponds to a family of graphs that can be defined inductively.
This allows us to calculate the Kauffman Bracket for each link in the family.
Bo Guo
May We Assign Different Values of lambda -Parameter to Attributes for an Extended lambda -Measure?
The lambda -measure is one of the most important types of monotone measures in common use.
It can be adopted to describe a special style of interaction among attributes towards
a certain target. The value of the parameter lambda describes the strength of the interaction
among predictive attributes towards the target. A certain type of integral with respect to
a lambda-measure then can be used as an aggregation tool in information fusion. Recently, some
scholars proposed to extend the lambda-measure such that each attribute has own parameter lambda_i
( i = 1, 2 , ... , n , where n is the number of predictive attributes). However, according
to the extension they proposed, we find that all the lambda have to be the same and that the
last or the first lambda can not be used, which denies the authors' proposition.