V-SOINN: A topology preserving visualization method for multidimensional data

Data visualization plays an important role in data analysis by displaying data to observers in an interpretable way. Visualizing multidimensional data requires projecting the data into a low-dimensional space that is visible to humans. In this paper, we propose a neural network model that can generate such projections while preserving the topology relationships within data points, which is named Visible Self Organizing Incremental Neural Network (V-SOINN). V-SOINN is able to construct a topology preserving visible network automatically and classify visible nodes to different classes in the low-dimensional space. The thought of topology preserving visualization stems from Self-Organizing Map (SOM). Compared to SOM, the main advantage of V-SOINN is that it does not need prior decision of network structure, including the number of nodes and grid in the output layer. V-SOINN can show the density distribution of datasets by using the activation counts of datasets. V-SOINN is able to depict the number of classes in the low-dimensional space as well. We perform experiments on artificial and real-world datasets, and V-SOINN outperforms PCA, MDS, t-SNE, Neural Gas and SOM on the datasets. Experiments show that V-SOINN can preserve the topology and V-SOINN can produce the correct classification result when the number of samples is small.