Context-flexible cartography with Siamese topological neural networks

Abstract

Abstract Cartography is a technique for creating maps, which are graphical representations of spatial information. Traditional cartography involves the creation of geographical data, such as locations of countries, geographical features of mountains, rivers, and oceans, and celestial objects. However, cartography has recently been utilized to display various data, such as antigenic signatures, graphically. Hence, it is natural to consider a new cartography that can flexibly deal with various data types. This study proposes a model of Siamese topological neural networks consisting of a pair of hierarchical neural networks, each with a low-dimensional internal layer for creating context-flexible maps. The proposed Siamese topological neural network transfers high-dimensional data with various contexts into their low-dimensional spatial representations on a map that humans can use to gain insights from the data. Here, it is enough to define a metric of difference between an arbitrary pair of data instances for training the proposed neural network. As the metric can be arbitrarily defined, the proposed neural network realizes context-flexible cartography useful for visual data analysis. This paper applies the proposed network for visualizing various demographic data.

Keywords

• Cartography
• Similarity learning
• Self-organizing maps
• Visualization
• Topological representation
• Dimensionality reduction