Cluster Analysis Using N-gram Statistics for Daihinmin Programs and Performance Evaluations

2.1. N-gram Statistics

N-gram statistics comprise a linguistic model of the type and emergence ratio of n items of element strings appearing next to a sequence of words or letters. N-gram statistics are typically used to extract idioms and identify authors in the area of natural language processing. In addition, these statistics are widely applied to extensive areas of research. By utilizing them in game studies, we can extract procedures with different lengths and identify established procedures, such as behavioral choices unconsciously made by players, without placing constraints on the game.

In studies of perfect information games, n-gram statistics are used to automatically extract established patterns (Nakamura, 1997). For Daihinmin, for example, no clustering or other detailed analyses have been made to date.

2.2 .Cluster Analysis

In this study, we use three types of distance concepts to compute distances. We then use Ward’s method for clustering. The computation methods for each distance concept are defined below.

• Manhattan distance: Manhattan distance can be obtained by measuring the distance between two points along orthogonal coordinate axes. It is defined as Equation 1:

  
  (1)

• Euclidean distance: It is a distance that is applicable in Euclidean space. It is defined as Equation 2:

  
  (2)

• Chebyshev distance: This distance defines the greatest difference between two vectors in a dimension as the distance. It is designed as Equation 3:

  
  (3)

We use Ward’s method for hierarchical cluster analysis, which herein refers to the following.