Growing Neural Gas 알고리즘을 활용한 자기조직화지도

Abstract

다변량 자료를 분석하는 데 있어 관측 개체들에 대한 분포적 양상을 파악하는 것은 자료 특성의 이해에 큰 도움이 된다. 고차원의 자료에 대해 이러한 양상을 파악하기 어려운 이유는 서로 복잡하게 상관되어있는 여러 개의 변수를 포함하기 때문이다. 따라서 이러한 다변량 자료의 경우 자료를 시각적으로 표현하여 두 변수 간 관계 등의 단편적인 정보를 우선으로 파악하게 된다. 이러한 자료구조의 파악에 있어서 자기조직화지도는 대표적인 차원축소방법 중 하나로, 고차원 다변량 자료의 저차원 시각화기법이라 할 수 있다. 자기조직화지도는 다차원 공간에서 비선형적 관계를 갖는 주된 변수 간의 위상적, 계량적 특성을 저차원 공간에서 축약적으로 나타내는 것을 목표로 한다.

본 논문에서는 기존의 자기조직화지도가 가지고 있는 구조적인 문제인 고정된 격자 문제, 가장자리 효과 등을 해결하고자 초기 격자의 구조를 고정하지 않고 Growing Neural Gas 알고리즘을 활용하여 자기조직화지도가 기존과 다르게 유동적인 노드 수와 고정되지 않은 구조를 갖도록 하였고 이러한 경우에도 기존의 자기조직화지도와 유사한 결과를 낼 수 있는지 알아보고자 하였다.| In analyzing multivariate data, identifying the distribution patterns of the observations greatly helps to understand the characteristics of the data. The reason why this aspect of high-level data is difficult to understand is that it includes several variables that are complex and correlated. Thus, in the case of such multivariate data, fragmentary information, such as the relationship between two variables, is first identified by visual representation of the data. In the identification of this data structure, self-organization maps are one of the typical dimensional reduction methods, which can be called low-dimensional visualization techniques for high-dimensional multivariate data. Self-organization maps aim to abbreviate the topological and quantitative characteristics among the main variables having non-linear relationships in multi-dimensional space in low-dimensional space.

In this paper, in order to solve the structural problems of conventional self-organizing maps, such as fixed grid problems, border effects, the self-organizing maps were made to have flexible number of nodes and non-fixed structures without fixing the structure of the initial grid, and to see if they could produce similar results to the existing self-organizing maps.; In analyzing multivariate data, identifying the distribution patterns of the observations greatly helps to understand the characteristics of the data. The reason why this aspect of high-level data is difficult to understand is that it includes several variables that are complex and correlated. Thus, in the case of such multivariate data, fragmentary information, such as the relationship between two variables, is first identified by visual representation of the data. In the identification of this data structure, self-organization maps are one of the typical dimensional reduction methods, which can be called low-dimensional visualization techniques for high-dimensional multivariate data. Self-organization maps aim to abbreviate the topological and quantitative characteristics among the main variables having non-linear relationships in multi-dimensional space in low-dimensional space.

In this paper, in order to solve the structural problems of conventional self-organizing maps, such as fixed grid problems, border effects, the self-organizing maps were made to have flexible number of nodes and non-fixed structures without fixing the structure of the initial grid, and to see if they could produce similar results to the existing self-organizing maps.