Elements of information theory
Elements of information theory
Neural Networks
GTM: the generative topographic mapping
Neural Computation
A Combined Latent Class and Trait Model for the Analysis and Visualization of Discrete Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recursive self-organizing maps
Neural Networks - New developments in self-organizing maps
Botanical Visualization of Huge Hierarchies
INFOVIS '01 Proceedings of the IEEE Symposium on Information Visualization 2001 (INFOVIS'01)
A generative probabilistic approach to visualizing sets of symbolic sequences
Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining
Metric properties of structured data visualizations through generative probabilistic modeling
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Neurocomputing
Wavelet-based statistical signal processing using hidden Markovmodels
IEEE Transactions on Signal Processing
Computational methods for hidden Markov tree models-an application to wavelet trees
IEEE Transactions on Signal Processing
A self-organizing map for adaptive processing of structured data
IEEE Transactions on Neural Networks
Visualization of Tree-Structured Data Through Generative Topographic Mapping
IEEE Transactions on Neural Networks
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We propose a generative probabilistic approach to constructing topographic maps of sequences and tree-structured data. The model formulation specifies a low-dimensional manifold of local noise models on the structured data. The manifold of noise models is induced by a smooth mapping from a low dimensional Euclidean latent space to the parameter space of local noise models. In this paper, we consider noise models endowed with hidden Markovian state space structure, namely Hidden Markov Tree Models (HMTM) and Hidden Markov Models (HMM). Compared with recursive extensions of the traditional Self-Organizing Map that can be used to visualize sequential or tree-structured data, topographic maps formulated within this framework possess a number of advantages such as a well defined cost function that drives the model optimization, the ability to test for overfitting and the accommodation of alternative local noise models implicitly expressing different notions of structured data similarity. Additionally, using information geometry one can calculate magnification factors on the constructed topographic maps. Magnification factors are a useful tool for cluster detection in non-linear topographic map formulations. We demonstrate the framework on two artificial data sets and chorals by J.S. Bach represented as sequences, as well as on images represented as trees.