A Multilinear Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
Compact Representation of Multidimensional Data Using Tensor Rank-One Decomposition
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 1 - Volume 01
Tensor space model for document analysis
SIGIR '06 Proceedings of the 29th annual international ACM SIGIR conference on Research and development in information retrieval
MPCA: Multilinear Principal Component Analysis of Tensor Objects
IEEE Transactions on Neural Networks
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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.