Abstract
Current methods capable of processing tensor objects in their natural higher-order structure have been introduced for real-valued tensors. Such techniques, however, are not suitable for processing binary tensors which arise in many real world problems, such as gait recognition, document analysis, or graph mining. To account for binary nature of the data, we propose a novel generalized multi-linear model for principal component analysis of binary tensors (GML-PCA). We compare the performance of GML-PCA with an existing model for real-valued tensor decomposition (TensorLSI) in two experiments. In the first experiment, synthetic binary tensors were compressed and consequently reconstructed, yielding the reconstruction error in terms of AUC. In the second experiment, we compare the ability to reveal biologically meaningful dominant trends in a real world large-scale dataset of DNA sequences represented through binary tensors. Both experiments show that our GML-PCA model is better suited for modeling binary tensors than the TensorLSI.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Lu, H., Plataniotis, K.N., Venetsanopoulos, A.N.: MPCA: Multilinear Principal Component Analysis of Tensor Objects. IEEE Trans. on Neural Networks 19, 18–39 (2008)
Cai, D., He, X., Han, J.: Tensor Space Model for Document Analysis. In: Proc. 29th Annu. ACM SIGIR Int. Conf. Research and Development in Information Retrieval, Seatlle, WA, pp. 625–626 (August 2006)
De Lathauwer, L., De Moor, B., Vandewalle, J.: A Multilinear Singular Value Decomposition. SIAM Journal on Matrix Analysis and Applications 21(4), 1253–1278 (2000)
Wang, H., Ahuja, N.: Compact Representation of Multidimensional Data Using Tensor Rank-One Decomposition. In: Proc. 17th Int. Conf. Pattern Recognition, Cambridge, UK, pp. 44–47 (August 2004)
Mažgut, J., Tiňo, P., Bodén, M., Yan, H.: Generalized Multi-Linear Principal Component Analysis of Binary Tensors. Technical Report CSRP-07-10, University of Birmingham, School of Computer Science, UK (2010), http://www.cs.bham.ac.uk/~pxt/PAPERS/bin_tensor_tr.pdf
Schein, A., Saul, L., Ungar, L.: A Generalized Linear Model for Principal Component Analysis of Binary Data. In: 9th Int. Workshop Artificial Intelligence and Statistics, Key West, FL (January 2003)
Cortes, C., Mohri, M.: AUC Optimization vs. Error Rate Minimization. In: Advances in Neural Information Processing Systems, Banff, AL, Canada, vol. 16, pp. 313–320 (July 2003)
Li, X., Zeng, J., Yan, H.: PCA-HPR: A Principle Component Analysis Model for Human Promoter Recognition. Bioinformation 2(9), 373–378 (2008)
Cross, S., Clark, V., Bird, A.: Isolation of CpG islands from large genomic clones. Nucleic Acids Res. 27(10), 2099–2107 (1999)
Bodén, M., Bailey, T.L.: Associating transcription factor-binding site motifs with target GO terms and target genes. Nucleic Acids Res. 36(12), 4108–4117 (2008)
Ashburner, M., Ball, C.A., Blake, J.A., Botstein, D., Butler, H., Cherry, J.M., Davis, A.P., Dolinski, K., Dwight, S.S., Eppig, J.T., Harris, M.A., Hill, D.P., Issel-Tarver, L., Kasarskis, A., Lewis, S., Matese, J.C., Richardson, J.E., Ringwald, M., Rubin, G.M., Sherlock, G.: Gene Ontology: tool for the unification of biology. The Gene Ontology Consortium. Nature Genetics 25(1), 25–29 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mažgut, J., Tiňo, P., Bodén, M., Yan, H. (2010). Multilinear Decomposition and Topographic Mapping of Binary Tensors. In: Diamantaras, K., Duch, W., Iliadis, L.S. (eds) Artificial Neural Networks – ICANN 2010. ICANN 2010. Lecture Notes in Computer Science, vol 6352. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15819-3_42
Download citation
DOI: https://doi.org/10.1007/978-3-642-15819-3_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15818-6
Online ISBN: 978-3-642-15819-3
eBook Packages: Computer ScienceComputer Science (R0)