Studying the correlation structure based on market geometry

Network methods can extract the structure of financial correlation matrices, and market geometry reconstructs the correlation relationship by constructing a vector set in the Euclidean space. This study uses a geometric perspective to analyse financial networks and examine the relationship between correlation structures and geometric conditions. Based on the concept of Euclidean space, we can naturally define geometric concepts such as stock vector and inner product between stocks. The analysis reveals that the structure of the financial correlation network is significantly affected by geometric conditions. We use stock market data to construct networks with different structures, such as a network with a hub node. We find that some stocks with small vector norms have an important effect on changes in network structure. In addition, we define a dimension to describe the correlation information included in the subspace of the market space and find that the dynamics of the dimension are related to the market state. This paper establishes a way to study network structure through market geometry, thereby providing a new method of correlation analysis.