Visualization of Tree-Structured Data Through Generative Topographic Mapping

N Gianniotis, Peter Tino

Research output: Contribution to journalArticle

22 Citations (Scopus)


In this paper, we present a probabilistic generative approach for constructing topographic maps of tree-structured data. Our model defines a low-dimensional manifold of local noise models, namely, (hidden) Markov tree models, induced by a smooth mapping from low-dimensional latent space. We contrast our approach with that of topographic map formation using recursive neural-based techniques, namely, the self-organizing map for structured data (SOMSD) (Hagenbuchner , 2003). The probabilistic nature of our model brings a number of benefits: 1) naturally defined cost function that drives the model optimization; 2) principled model comparison and testing for overfitting; 3) a potential for transparent interpretation of the map by inspecting the underlying local noise models; 4) natural accommodation of alternative local noise models implicitly expressing different notions of structured data similarity. Furthermore, in contrast with the recursive neural-based approaches, the smooth nature of the mapping from the latent space to the local model space allows for calculation of magnification factors--a useful tool for the detection of data clusters. We demonstrate our approach on three data sets: a toy data set, an artificially generated data set, and on a data set of images represented as quadtrees.
Original languageEnglish
Pages (from-to)1468-1493
Number of pages26
JournalIEEE Transactions on Neural Networks
Issue number8
Publication statusPublished - 1 Aug 2008


  • topographic mapping
  • structured data
  • hidden Markov tree model (HMTM)


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