Multilinear Compressive Learning (MCL)

What is an Multilinear Compressive Learning?

Compressive Learning is an emerging topic that combines signal acquisition via compressive sensing and machine learning to perform inference tasks directly on a small number of measurements. Many data modalities naturally have a multi-dimensional or tensorial format, with each dimension or tensor mode representing different features such as the spatial and temporal information in video sequences or the spatial and spectral information in hyperspectral images. We propose Multilinear Compressive Learning, a framework that takes into account the tensorial nature of multi-dimensional signals in the acquisition step and builds the subsequent inference model on the structurally sensed measurements. Our theoretical complexity analysis shows that the proposed framework is more efficient compared to its vector-based counterpart in both memory and computation requirement. Moreover, it empirically outperforms the vector-based framework in object classification and face recognition tasks, and scales favorably when the dimensionalities of the original signals increase, making it highly efficient for high-dimensional multi-dimensional signals.

Multilinear Compressive Learning with Prior Knowledge

The key idea behind MCL is the assumption of the existence of a tensor subspace which can capture the essential features from the signal for the downstream learning task. Thus, the ability to find such a discriminative tensor subspace and optimize the system to project the signals onto that data manifold plays an important role in Multilinear Compressive Learning. We propose a novel solution to address both of the aforementioned requirements, i.e., How to find those tensor subspaces in which the signals of interest are highly separable? and How to optimize the sensing and feature synthesis components to transform the original signals to the data manifold found in the first question? In our proposal, the discovery of a high-quality data manifold is conducted by training a nonlinear compressive learning system on the inference task. Its knowledge of the data manifold of interest is then progressively transferred to the MCL components via multi-stage supervised training with the supervisory information encoding how the compressed measurements, the synthesized features, and the predictions should be like. The proposed knowledge transfer algorithm also comes with a semi-supervised adaption that enables compressive learning models to utilize unlabeled data effectively.

References

The list provided in the following may be incomplete. The complete list of papers related to this topic can be found in the lists of journal papers and conference papers.

• D.T. Tran, M. Gabbouj and A. Iosifidis, “Performance Indicator in Multilinear Compressive Learning”, IEEE Symposium Series on Computational Intelligence, Canberra, Austrarila (online), 2020

• D.T. Tran, M. Gabbouj and A. Iosifidis, "Multilinear Compressive Learning with Prior Knowledge", arXiv:2002.07203, 2020

• D.T. Tran, M. Yamac, A. Degerli, M. Gabbouj and A. Iosifidis, "Multilinear Compressive Learning", IEEE Transactions on Neural Networks and Learning Systems, 2020