Uploaded September 2020 | Updated September 2026, 2 weeks ago
This summer, due to Covid19, IMA Mathematics 2020 was transformed into a series of online events. Prof Danilo Mandic from Imperial College London, presented the second talk of the Week 4 IMA Mathematics 2020 Online Series. His talk was on 'Tensors, graphs, and deep networks: Convergence of concepts and ideas.'
Abstract
“The widespread use of multisensor technology and the emergence of big data sets have highlighted limitations of standard flat-view matrix models in terms of their expressiveness, and the necessity to move toward more versatile data analysis tools. This has also highlighted the limitations of the rigid nature of standard uniform sampling in time (for time series) and space (for images and sensor networks), both prohibitive to efficient modelling of data recorded on irregular domains. These, together with the computational bottleneck associated with the deep learning paradigm, are calling for a unifying framework for the analysis of big data acquired on non-uniform domains and at an affordable computational costs. This talk addresses the convergence of concepts of tensor decompositions and data analytics on graphs, and offers insights into how their joint treatment provides feasible means to mitigate the curse of dimensionality associated with both the big data and deep learning paradigms. We show that for data which exhibit underlying signal generation structure, this can lead to orders of magnitude savings in the storage and computational complexity (super-compression), together with natural data separability by virtue of multilinear tensor algebra. It is further shown how the concept of local neighbourhood, an intrinsic feature of data acquired on graphs, can be employed to both perform dimensionality reduction and perform cost-efficient clustering directly on the domains where data reside. Finally, as an example, the convergence of these two concepts is shown to both introduce physical meaning into the otherwise black-box nature of neural networks, and to offer enhanced interpretability throughout the processing chain and at an affordable computational cost."
The IMA Mathematics 2020 Online Series has been organised in collaboration with the Newton Gateway to Mathematics.
This summer, due to Covid19, IMA Mathematics 2020 was transformed into a series of online events. Prof Danilo Mandic from Imperial College London, presented the second talk of the Week 4 IMA Mathematics 2020 Online Series. His talk was on 'Tensors, graphs, and deep networks: Convergence of concepts and ideas.'
Abstract
“The widespread use of multisensor technology and the emergence of big data sets have highlighted limitations of standard flat-view matrix models in terms of their expressiveness, and the necessity to move toward more versatile data analysis tools. This has also highlighted the limitations of the rigid nature of standard uniform sampling in time (for time series) and space (for images and sensor networks), both prohibitive to efficient modelling of data recorded on irregular domains. These, together with the computational bottleneck associated with the deep learning paradigm, are calling for a unifying framework for the analysis of big data acquired on non-uniform domains and at an affordable computational costs. This talk addresses the convergence of concepts of tensor decompositions and data analytics on graphs, and offers insights into how their joint treatment provides feasible means to mitigate the curse of dimensionality associated with both the big data and deep learning paradigms. We show that for data which exhibit underlying signal generation structure, this can lead to orders of magnitude savings in the storage and computational complexity (super-compression), together with natural data separability by virtue of multilinear tensor algebra. It is further shown how the concept of local neighbourhood, an intrinsic feature of data acquired on graphs, can be employed to both perform dimensionality reduction and perform cost-efficient clustering directly on the domains where data reside. Finally, as an example, the convergence of these two concepts is shown to both introduce physical meaning into the otherwise black-box nature of neural networks, and to offer enhanced interpretability throughout the processing chain and at an affordable computational cost."
The IMA Mathematics 2020 Online Series has been organised in collaboration with the Newton Gateway to Mathematics.
