Geometric separability of mesoscale patterns in embedding representation and visualization of multidimensional data and complex networks
Fig 7
Empirical evidence on real complex multidimensional data.
The radar signal dataset is composed of 350 valid samples, 34 features, and three groups: good radar signal, bad radar signal type1 and bad radar signal type2. The complexity of this dataset is associated with the mix of hierarchical and similarity relations between the data samples. (a) Embedding of the radar signal dataset in the two-dimensional space by MCE algorithm. (b) The geometric separability of MCE representation is estimated of high quality (performance larger than 0.8) according to any type of measure, because MCE algorithm is able to produce a representation that accounts for hierarchical structure in the data. (c) t-SNE representation (p = 31 is the best perplexity setting, see text for details) suffers from the crowding problem because t-SNE algorithm does not well preserve hierarchical organization. (d) the geometric separability measures confirm that the representation of t-SNE is of less quality of MCE for what concerns the separability of the data group structure in the representation space. In (b,d) the values of the indices with a significant (p-value < 0.01) geometric separability are marked with a star, which means that these values are very unlikely to be obtained by chance.