Timezone: »
The current availability of powerful computers and huge data sets is creating new opportunities in computational mathematics to bring together concepts and tools from tensor algebra, graph theory, machine learning and signal processing. In discrete mathematics, a tensor is merely a collection of points (nodes in a graph) which are arranged as a multiway arrray. The power of such tensors lies in the fact that they can represent entities as diverse as the users of social networks or financial market data, and that these can be transformed into low-dimensional signals which can be analyzed using data analytics tools. In this talk, we aim to provide a comprehensive introduction to advanced data analytics on graphs using tensor. We will then establish a relationship between tensors and graphs, in order to move beyond the standard regular sampling in time and space. This facilitates modelling in many important areas, including communication networks, computer science, linguistics, social sciences, biology, physics, chemistry, transport, town planning, financial systems, personal health and many others. The tensor and graph topologies will be revisited from a modern data analytics point of view, and we will then proceed to establish a taxonomy of graph tensor networks. With this as a basis, we show such a framework allows for even the most challenging machine learning tasks, such as clustering, being performed in an intuitive and physically meaningful way. Unique aspects of the multi-graph tensor networks (MGTN) framework will be outlined, such as their benefits for processing data acquired on irregular domains, their ability to finely-tune statistical learning procedures through local information processing, the concepts of random signals on graphs and tensors, learning of graph topology from data observed on graphs, and confluence with deep neural networksnd Big Data. Extensive examples are included to render the concepts more concrete and to facilitate a greater understanding of the underlying principles.
Author Information
Danilo Mandic (Imperial College London)
More from the Same Authors
-
2021 : Bayesian Tensor Networks »
Kriton Konstantinidis · Yao Lei Xu · Qibin Zhao · Danilo Mandic -
2021 : A Tensorized Spectral Attention Mechanism for Efficient Natural Language Processing »
Yao Lei Xu · Kriton Konstantinidis · Shengxi Li · Danilo Mandic -
2022 Spotlight: Lightning Talks 4B-4 »
Ziyue Jiang · Zeeshan Khan · Yuxiang Yang · Chenze Shao · Yichong Leng · Zehao Yu · Wenguan Wang · Xian Liu · Zehua Chen · Yang Feng · Qianyi Wu · James Liang · C.V. Jawahar · Junjie Yang · Zhe Su · Songyou Peng · Yufei Xu · Junliang Guo · Michael Niemeyer · Hang Zhou · Zhou Zhao · Makarand Tapaswi · Dongfang Liu · Qian Yang · Torsten Sattler · Yuanqi Du · Haohe Liu · Jing Zhang · Andreas Geiger · Yi Ren · Long Lan · Jiawei Chen · Wayne Wu · Dahua Lin · Dacheng Tao · Xu Tan · Jinglin Liu · Ziwei Liu · 振辉 叶 · Danilo Mandic · Lei He · Xiangyang Li · Tao Qin · sheng zhao · Tie-Yan Liu -
2022 Spotlight: BinauralGrad: A Two-Stage Conditional Diffusion Probabilistic Model for Binaural Audio Synthesis »
Yichong Leng · Zehua Chen · Junliang Guo · Haohe Liu · Jiawei Chen · Xu Tan · Danilo Mandic · Lei He · Xiangyang Li · Tao Qin · sheng zhao · Tie-Yan Liu -
2022 Poster: BinauralGrad: A Two-Stage Conditional Diffusion Probabilistic Model for Binaural Audio Synthesis »
Yichong Leng · Zehua Chen · Junliang Guo · Haohe Liu · Jiawei Chen · Xu Tan · Danilo Mandic · Lei He · Xiangyang Li · Tao Qin · sheng zhao · Tie-Yan Liu -
2021 : A Tensorized Spectral Attention Mechanism for Efficient Natural Language Processing »
Yao Lei Xu · Kriton Konstantinidis · Shengxi Li · Danilo Mandic -
2021 : Bayesian Tensor Networks »
Kriton Konstantinidis · Yao Lei Xu · Qibin Zhao · Danilo Mandic -
2021 : Danilo P. Mandic »
Danilo Mandic -
2020 Poster: Reciprocal Adversarial Learning via Characteristic Functions »
Shengxi Li · Zeyang Yu · Min Xiang · Danilo Mandic -
2020 Spotlight: Reciprocal Adversarial Learning via Characteristic Functions »
Shengxi Li · Zeyang Yu · Min Xiang · Danilo Mandic -
2011 Poster: A Multilinear Subspace Regression Method Using Orthogonal Tensors Decompositions »
Qibin Zhao · Cesar F Caiafa · Danilo Mandic · Liqing Zhang · Tonio Ball · Andreas Schulze-bonhage · Andrzej S CICHOCKI -
2011 Spotlight: A Multilinear Subspace Regression Method Using Orthogonal Tensors Decompositions »
Qibin Zhao · Cesar F Caiafa · Danilo Mandic · Liqing Zhang · Tonio Ball · Andreas Schulze-bonhage · Andrzej S CICHOCKI