An Effective Method for Identifying Clusters of Robot Strengths

by   Jen-Chieh Teng, et al.

In the analysis of qualification data from the FIRST Robotics Competition, the ratio of the number of observations to the number of parameters has been found to be quite small for the commonly used winning margin power rating (WMPR) model. This usually leads to imprecise estimates and inaccurate predictions in such a three-on-three game. With the finding of a clustering feature in estimated robot strengths, a more flexible model with latent clusters of robots was proposed to alleviate overparameterization of the WMPR model. Since its structure can be regarded as a dimension reduction of the parameter space in the WMPR model, the identification of clusters of robot strengths is naturally transformed into a model selection problem. Instead of comparing a huge number of competing models, we develop an effective method to estimate the number of clusters, clusters of robots, and robot strengths. The new method consists of two parts: (i) a combination of hierarchical and non-hierarchical classifications to determine candidate models; and (ii) variant goodness-of-fit criteria to select optimal models. Different from existing hierarchical classification systems, each step of ours is based on estimated robot strengths from a candidate model in the preceding non-hierarchical classification step. A great advantage of the designed non-hierarchical classification system is to examine the possibility of reassigning robots to other cluster sets of robots. To reduce the overestimation of clusters by the mean squared prediction error criteria, the corresponding BIC are established as alternatives for model selection. By assembling these essential elements into a coherent whole, a systematic procedure is presented to perform the estimation. In addition, we propose two indices to measure the nested relation between cluster sets of two models and monotonic association between robot strengths of two models.


Estimating Robot Strengths with Application to Selection of Alliance Members in FIRST Robotics Competitions

Since the inception of the FIRST Robotics Competition and its special pl...

Constrained Bayesian Hierarchical Models for Gaussian Data: A Model Selection Criterion Approach

Consider the setting where there are B>1 candidate statistical models, a...

Selection of the Number of Clusters in Functional Data Analysis

Identifying the number K of clusters in a dataset is one of the most dif...

A description length approach to determining the number of k-means clusters

We present an asymptotic criterion to determine the optimal number of cl...

Estimating the Number of Clusters via Normalized Cluster Instability

We improve existing instability-based methods for the selection of the n...

A model selection approach for clustering a multinomial sequence with non-negative factorization

We consider a problem of clustering a sequence of multinomial observatio...

Please sign up or login with your details

Forgot password? Click here to reset