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Issue No. 10 - Oct. (2013 vol. 35)
ISSN: 0162-8828
pp: 2340-2356
Tingting Mu , Dept. of Electr. Eng. & Electron., Univ. of Liverpool, Liverpool, UK
J. Y. Goulermas , Dept. of Electr. Eng. & Electron., Univ. of Liverpool, Liverpool, UK
In this paper, we study the co-embedding problem of how to map different types of patterns into one common low-dimensional space, given only the associations (relation values) between samples. We conduct a generic analysis to discover the commonalities between existing co-embedding algorithms and indirectly related approaches and investigate possible factors controlling the shapes and distributions of the co-embeddings. The primary contribution of this work is a novel method for computing co--embeddings, termed the automatic co-embedding with adaptive shaping (ACAS) algorithm, based on an efficient transformation of the co-embedding problem. Its advantages include flexible model adaptation to the given data, an economical set of model variables leading to a parametric co-embedding formulation, and a robust model fitting criterion for model optimization based on a quantization procedure. The secondary contribution of this work is the introduction of a set of generic schemes for the qualitative analysis and quantitative assessment of the output of co-embedding algorithms, using existing labeled benchmark datasets. Experiments with synthetic and real-world datasets show that the proposed algorithm is very competitive compared to existing ones.
Vectors, Computational modeling, Algorithm design and analysis, Eigenvalues and eigenfunctions, Large scale integration, Adaptation models, Data models

Tingting Mu and J. Y. Goulermas, "Automatic Generation of Co-Embeddings from Relational Data with Adaptive Shaping," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 35, no. 10, pp. 2340-2356, 2013.
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