TY - GEN
T1 - Parametric embedding for class visualization
AU - Iwata, Tomoharu
AU - Saito, Kazumi
AU - Ueda, Naonori
AU - Stromsten, Sean
AU - Griffiths, Thomas L.
AU - Tenenbaum, Joshua B.
PY - 2005
Y1 - 2005
N2 - In this paper, we propose a new method, Parametric Embedding (PE), for visualizing the posteriors estimated over a mixture model. PE simultaneously embeds both objects and their classes in a low-dimensional space. PE takes as input a set of class posterior vectors for given data points, and tries to preserve the posterior structure in an embedding space by minimizing a sum of Kullback-Leibler divergences, under the assumption that samples are generated by a Gaussian mixture with equal covariances in the embedding space. PE has many potential uses depending on the source of the input data, providing insight into the classifier's behavior in supervised, semi-supervised and unsupervised settings. The PE algorithm has a computational advantage over conventional embedding methods based on pairwise object relations since its complexity scales with the product of the number of objects and the number of classes. We demonstrate PE by visualizing supervised categorization of web pages, semi-supervised categorization of digits, and the relations of words and latent topics found by an unsupervised algorithm, Latent Dirichlet Allocation.
AB - In this paper, we propose a new method, Parametric Embedding (PE), for visualizing the posteriors estimated over a mixture model. PE simultaneously embeds both objects and their classes in a low-dimensional space. PE takes as input a set of class posterior vectors for given data points, and tries to preserve the posterior structure in an embedding space by minimizing a sum of Kullback-Leibler divergences, under the assumption that samples are generated by a Gaussian mixture with equal covariances in the embedding space. PE has many potential uses depending on the source of the input data, providing insight into the classifier's behavior in supervised, semi-supervised and unsupervised settings. The PE algorithm has a computational advantage over conventional embedding methods based on pairwise object relations since its complexity scales with the product of the number of objects and the number of classes. We demonstrate PE by visualizing supervised categorization of web pages, semi-supervised categorization of digits, and the relations of words and latent topics found by an unsupervised algorithm, Latent Dirichlet Allocation.
UR - http://www.scopus.com/inward/record.url?scp=84899002783&partnerID=8YFLogxK
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M3 - Conference contribution
AN - SCOPUS:84899002783
SN - 0262195348
SN - 9780262195348
T3 - Advances in Neural Information Processing Systems
BT - Advances in Neural Information Processing Systems 17 - Proceedings of the 2004 Conference, NIPS 2004
PB - Neural information processing systems foundation
T2 - 18th Annual Conference on Neural Information Processing Systems, NIPS 2004
Y2 - 13 December 2004 through 16 December 2004
ER -