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Both recent and long term advances in data acquisition and storage technology have led to the genesis of the so-called ’big data era’. The proliferation of social and scientific databases of increasing size has lead to a need for algorithms that can efficiently process, analyze, and, even generate this data. However, due to the large number of observations (volume), and the number of variables observed (dimension), many classical approaches from traditional signal processing and statistics are not computationally feasible in this regime. The field of Geometric Data Processing has been developed as a way to exploit inherent coherence in data to design new algorithms based on motivation from both differential and discrete geometry.In this talk, we will explore techniques for exploiting the geometric structure of data to analyze and generate geometric, as well as general data. First, we will use ideas from parallel transport on manifolds to generalize convolution and convolutional neural networks to deformable manifolds. We will show that this allows us to analyze signals based on the intrinsic dimension, and separate intrinsic and extrinsic information which can be usefull for analysis and generation of novel synthetic data. Afterwards, we will conclude by proposing a novel auto-regressive model for capturing the intrinsic geometry and topology of data which also allows us to devleop univeral generation theorems for neural networks.

zoom info available https://sites.google.com/view/maddd After the seminar, Naoki Saito will make a presentation on the UCD4IDS plan for this academic year.