Edges in topological maps have rich information such as shape, numbers of obstacles, locations of obstacles which can be used for a data association. However, no systematic approach on using the edge data for the data association has been reported. This paper proposes a systematic way of utilizing the edge data for data association. First, we explain a Local Generalized Voronoi Angle(LGA) to represent the edge data in 1-dimension. Second, we suggest a key factor extraction procedure from the LGA to reduce the number by 27-28 times for computational efficiency using the wavelet transformation. Finally we propose a way of data association using the key factors of the LGA. Simulations and experiments show that the proposed data association algorithm yields higher probability for similar edges in computationally efficient manner.