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Organizing Committee
Abstract
WiSDM 2019 is a research collaboration workshop targeted toward people working in data science and mathematics. This program will bring together researchers at all stages of their careers, from graduate students to senior researchers, to collaborate on problems in data science.
Data science is typically characterized as work at the intersection of mathematics, computer science, statistics, and an application domain. The scientific focus will be on cutting-edge problems in network analysis for gene detection, group dynamics, graph clustering, novel statistical and topological learning algorithms, tensor product decompositions, reconciliation of assurance of anonymity and privacy with utility measures for data transfer and analytics, as well as efficient and accurate completion, inference and fusion methods for large data and correlations.
Applications are now open. Applicants should rank their top 3 choices of projects in their personal statement. Project descriptions can be found below.
Application deadline extended to March 31, 2019.
Data science is typically characterized as work at the intersection of mathematics, computer science, statistics, and an application domain. The scientific focus will be on cutting-edge problems in network analysis for gene detection, group dynamics, graph clustering, novel statistical and topological learning algorithms, tensor product decompositions, reconciliation of assurance of anonymity and privacy with utility measures for data transfer and analytics, as well as efficient and accurate completion, inference and fusion methods for large data and correlations.
Applications are now open. Applicants should rank their top 3 choices of projects in their personal statement. Project descriptions can be found below.
Application deadline extended to March 31, 2019.
Group Leads
UCLA
George Mason University
University of Alberta
Tufts University
UCLA
Icahn School of Medicine at Mount Sinai
Rutgers University
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Projects
Project 1: Graph regularization of high dimensional data
Andrea Bertozzi (UCLA), Yifei Lou (The University of Texas at Dallas)
There has been a large volume of mathematical models to process signals and/or images that are defined on a regular domain. As for irregular or unsorted data graph modeling often provides a flexible representation to capture the underlying structures. However, some key notions in image processing, such as translation, convolution, and dilation, are not straightforward on graphs. This project aims to develop a graph-regularized framework in data analysis, to address key challenges regarding both theoretical and computational aspects in graph representation, and to demonstrate its capacity in various applications. More specifically, given a graph, the graph Fourier transform is defined in terms of the eigenvectors of graph Laplacian. As a result, aforementioned image processing operators can be carried out on the graph frequency domain. This approach offers a possible way to process data on the graph, but computational efficiency remains an open question. The project will be supplemented with prototypical applications in data science, such as social networks, electric power grids, and hyperspectral imaging.
Project 2: Tensor Tools for Multiway Data Analysis
Misha Kilmer (Tufts University)
Many problems in scientific settings involve operators or data that are inherently multidimensional: consider the storage of digital video data referenced by frame number, color band, and spatial dimensions; data on gene responses to different chemical combinations; discrete PDE snapshot data according to three spatial dimensions and a time dimension. It makes sense to treat multiway (aka tensor) data in its natural format. However, it is in this regime that traditional results from linear algebra break down, necessitating the development of new constructs and algorithms to treat multiway data.
Recent work has shown that with the right tensor tools, processing data in tensor format rather than matrix format can definitively provide additional structural information that allows for better compression and analysis of the data, for example in facial recognition. However, different data sets involve different structural characteristics, and some tensor decompositions are better suited than others to reveal the corresponding latent features. On the other hand, for large datasets, the computational time for the decompositions must also be a consideration.
In this project, participants with learn about some of the state-of-the-art tensor techniques from both a mathematical and computational viewpoint for compressing and mining of multiway data. Particular attention will be given to one such approach using tensor-tensor products whose associated algebraic framework permits a computationally efficient extension of linear algebraic and data analytic concepts such as PCA, dictionary learning, clustering and neural nets. In addition to investigating the use of some of these tensor algorithms on real data, we will also consider open questions in the theoretical understanding of the data analysis tools built on this new mathematical framework.
Recent work has shown that with the right tensor tools, processing data in tensor format rather than matrix format can definitively provide additional structural information that allows for better compression and analysis of the data, for example in facial recognition. However, different data sets involve different structural characteristics, and some tensor decompositions are better suited than others to reveal the corresponding latent features. On the other hand, for large datasets, the computational time for the decompositions must also be a consideration.
In this project, participants with learn about some of the state-of-the-art tensor techniques from both a mathematical and computational viewpoint for compressing and mining of multiway data. Particular attention will be given to one such approach using tensor-tensor products whose associated algebraic framework permits a computationally efficient extension of linear algebraic and data analytic concepts such as PCA, dictionary learning, clustering and neural nets. In addition to investigating the use of some of these tensor algorithms on real data, we will also consider open questions in the theoretical understanding of the data analysis tools built on this new mathematical framework.
