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geometry_topology_data_science_spring_2024 [2024/05/12 18:24] – [Week 22] Diaaeldin Tahageometry_topology_data_science_spring_2024 [2025/03/01 08:54] (current) – [Organization] Diaaeldin Taha
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 ===== Organization ===== ===== Organization =====
  
-  * **The Organizers**: Alvaro Diaz, Marzieh Eidi, Celia Hacker, Guillermo Restrepo, Daniel Spitz, Diaaeldin Taha, Francesca Tombari+  * **The Organizers**: Marzieh Eidi, Diaaeldin Taha
   * **MPI Seminar Page**: [[https://www.mis.mpg.de/events/series/mathematical-methods-in-data-science|Mathematical Methods in Data Science]]   * **MPI Seminar Page**: [[https://www.mis.mpg.de/events/series/mathematical-methods-in-data-science|Mathematical Methods in Data Science]]
   * **Contact**: To contact the organizers, email the lab at ''lab [at] mis [dot] mpg [dot] de''.   * **Contact**: To contact the organizers, email the lab at ''lab [at] mis [dot] mpg [dot] de''.
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 ^ Week        ^ Date       ^ Time         ^ Location   ^ Speaker              ^ Title                                   ^ ^ Week        ^ Date       ^ Time         ^ Location   ^ Speaker              ^ Title                                   ^
 ^ Week 19     | Fri 10.05  | 09:00–10:30  | E1 05      | Justin Curry         | “To Predict is NOT to Explain” | ^ Week 19     | Fri 10.05  | 09:00–10:30  | E1 05      | Justin Curry         | “To Predict is NOT to Explain” |
-^ Week 20     | Fri 17.05  | 09:00–10:30  | ---        | ---                  | [[https://www.mis.mpg.de/events/series/combinatorial-algebraic-geometry-from-physics|CAG Conference]] - **NO MEETING**| +^ Week 20     | Fri 17.05  | ---  | ---        | ---                  | [[https://www.mis.mpg.de/events/series/combinatorial-algebraic-geometry-from-physics|CAG Conference]] - **NO MEETING**| 
-^ Week 21     | Fri 24.05  | 09:00–10:30  | G3 10      | Celia Hacker         | TBA                                     | +^ Week 21     | Fri 24.05  | 09:00–10:30  | G3 10      | Celia Hacker         | What are Graph Neural Networks? |
-|             |  | TBA          | TBA        | Francesca Tombari    | TDA Course 01/06                        |+
 ^ Week 22     | Fri 31.05  | 09:00–10:30  | G3 10      | Jeff Philips         | The Geometry of Kernel Methods and Kernel Range Spaces | ^ Week 22     | Fri 31.05  | 09:00–10:30  | G3 10      | Jeff Philips         | The Geometry of Kernel Methods and Kernel Range Spaces |
-|             |  | TBA          | G3 10      | Francesca Tombari    | TDA Course 02/06                        | +^ Week 23     | Fri 07.06  | 09:00–10:30  | E1 05      | Simon Telen | Chebyshev varieties | 
-^ Week 23     | Fri 07.06  | 09:00–10:30  | E1 05      | Simon Telen | TBA                                     | +^ Week 24     | Fri 14.06  | 09:00–10:30  | G3 10      | Parvaneh Joharinad | Mathematical Foundations of Dimensionality Reduction |
-|             |  | ---          | ---        | Francesca Tombari    | **NO COURSE**                           | +
-^ Week 24     | Fri 14.06  | 09:00–10:30  | G3 10      | Parvaneh Joharinad | TBA                                     | +
-|             |  | TBA          | G3 10      | Francesca Tombari    | TDA Course 03/06                        |+
 ^ Week 25     | Fri 21.06  | 09:00–10:30  | E1 05      | Bei Wang             | Topology-Preserving Data Compression | ^ Week 25     | Fri 21.06  | 09:00–10:30  | E1 05      | Bei Wang             | Topology-Preserving Data Compression |
-|             |  | TBA          | TBA        | Francesca Tombari    | TDA Course 04/06                        | 
 ^ Week 26     | Fri 28.06  | ---          | ---        | ---                  | [[https://scads.ai/education/summer-schools/summer-school-2024/|ScaDS Summer School]] - **NO MEETING** | ^ Week 26     | Fri 28.06  | ---          | ---        | ---                  | [[https://scads.ai/education/summer-schools/summer-school-2024/|ScaDS Summer School]] - **NO MEETING** |
-|             |  | TBA          | TBA        | Francesca Tombari    | TDA Course 05/06                        | +^ Week 27     | Fri 05.07  | 09:00–10:30  | E1 05      | Marzieh Eidi | Quantitative and Qualitative Mathematical Data Analysis | 
-^ Week 27     | Fri 05.07  | 09:00–10:30  | E1 05      | Marzieh Eidi | TBA                                     | +^ Week 28     | Fri 12.07  | 09:00–10:30  | E1 05      | Karel Devriendt | Spanning Trees, Effective Resistances and Curvature on Graphs |
-|             |  | TBA          | TBA        | Francesca Tombari    | TDA Course 06/06                        | +
-^ Week 28     | Fri 12.07  | 09:00–10:30  | E1 05      | Karel Devriendt | TBA                                     | +
-^ Week 29     | Fri 19.07  | 09:00–10:30  | E2 10      | SPEAKER TBA          | TBA                                     | +
-^ Week 30     | Fri 26.07  | 09:00–10:30  | E1 05      | SPEAKER TBA          | TBA                                     |+
  
 ===== Abstracts ===== ===== Abstracts =====
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 ==== Week 20 ==== ==== Week 20 ====
 +
 +[[https://www.mis.mpg.de/events/series/combinatorial-algebraic-geometry-from-physics|CAG Conference]] - **NO MEETING**
  
 ==== Week 21 ==== ==== Week 21 ====
 +
 +**Speaker**: Celia Hacker (Max Planck Institute for Mathematics in the Science, Germany)
 +
 +**Coordinates**: [[https://www.mis.mpg.de/events/event/what-are-graph-neural-networks|Fri 24.05, 9–10:30 AM, G3 10]]
 +
 +**Title**: What are graph neural networks?
 +
 +**Abstract**: Graph structured data appears in many different context and with this comes the need for tools to analyse them. One of the most common tools to study data sets of graphs are graph neural networks (GNNs). However, to many of us GNNs remain a black box that magically perform predictions about graphs. In this lecture we will learn about the basics of GNNs, possible generalizations and research directions. 
 +
  
 ==== Week 22 ==== ==== Week 22 ====
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 **Speaker**: [[https://users.cs.utah.edu/~jeffp/|Jeff Philips]] (University of Utah, USA) **Speaker**: [[https://users.cs.utah.edu/~jeffp/|Jeff Philips]] (University of Utah, USA)
  
-Jeff Phillips is a Professor in the School of Computing at the University of Utah.  He founded the [[https://datascience.utah.edu/|Utah Center for Data Science]], and directs the [[https://www.cs.utah.edu/undergraduate/academic-programs/undergraduate-academic-program-overview/data-science/|Data Science academic program]] there.  He works on geometric data analysis, algorithms for big data, and how these intersect with data science.  His book, [[https://mathfordata.github.io/|Mathematical Foundations for Data Analysis]], was published by Springer-Nature in 2021. +**Coordinates**: [[https://www.mis.mpg.de/events/event/the-geometry-of-kernel-methods-and-kernel-range-spaces|Fri 31.05, 9–10:30 AM,  MiS G3 10]]
- +
-**Coordinates**: Fri 31.05, 9–10:30 AM,  MiS G3 10+
  
 **Title**: The Geometry of Kernel Methods and Kernel Range Spaces **Title**: The Geometry of Kernel Methods and Kernel Range Spaces
  
 **Abstract**: I will start by overviewing kernel methods in machine learning, and how the simple kernel trick allows one to effortlessly turn intuitive linear methods into non-linear ones.  While these methods can seem mysterious, I’ll try to give insight into the geometry that arises, especially in kernel SVM.  This will lead into kernel range spaces, which describes all the ways one can inspection a data set with a kernel.  From there I will discuss approximation of these with coresets, and just approximating the spaces themselves which leads to surprising results in high dimensions. **Abstract**: I will start by overviewing kernel methods in machine learning, and how the simple kernel trick allows one to effortlessly turn intuitive linear methods into non-linear ones.  While these methods can seem mysterious, I’ll try to give insight into the geometry that arises, especially in kernel SVM.  This will lead into kernel range spaces, which describes all the ways one can inspection a data set with a kernel.  From there I will discuss approximation of these with coresets, and just approximating the spaces themselves which leads to surprising results in high dimensions.
 +
 +**Speaker Bio**: Jeff Phillips is a Professor in the School of Computing at the University of Utah.  He founded the [[https://datascience.utah.edu/|Utah Center for Data Science]], and directs the [[https://www.cs.utah.edu/undergraduate/academic-programs/undergraduate-academic-program-overview/data-science/|Data Science academic program]] there.  He works on geometric data analysis, algorithms for big data, and how these intersect with data science.  His book, [[https://mathfordata.github.io/|Mathematical Foundations for Data Analysis]], was published by Springer-Nature in 2021.
 +
 ==== Week 23 ==== ==== Week 23 ====
 +
 +**Speaker**: [[https://simontelen.webnode.page/|Simon Telen]] (Max Planck Institute for Mathematics in the Science, Germany)
 +
 +**Coordinates**: [[https://www.mis.mpg.de/events/event/chebyshev-varieties|Fri 07.06, 9–10:30 AM, MiS E1 05]]
 +
 +**Title**: Chebyshev Varieties
 +
 +**Abstract**: Chebyshev varieties are algebraic varieties parametrized by Chebyshev polynomials. They arise naturally when solving polynomial equations expressed in the Chebyshev basis. More precisely, when passing from monomials to Chebyshev polynomials, Chebyshev varieties replace toric varieties. I will introduce these objects, discuss their defining equations and present key properties. Via examples, I will motivate their use in practical computations. This is joint work with Zaïneb Bel-Afia and Chiara Meroni.
  
 ==== Week 24 ==== ==== Week 24 ====
 +
 +**Speaker**: Parvaneh Joharinad (Max Planck Institute for Mathematics in the Science, Germany)
 +
 +**Coordinates**: [[https://www.mis.mpg.de/events/event/mathematical-foundations-of-dimensionality-reduction|Fri 14.06, 9–10:30 AM, G3 10]]
 +
 +**Title**: Mathematical Foundations of Dimensionality Reduction
 +
 +**Abstract**: Dimensionality reduction is a crucial technique in data analysis and machine learning, enabling the simplification of complex high-dimensional datasets while preserving their intrinsic structures. In this talk we will present the mathematical footings of several prominent dimensionality reduction methods: Principal Component Analysis (PCA), Isomap, Laplace Eigenmaps, etc. We will explore the specific optimization objectives and the role of weight assignments within k-neighborhood graphs for each method. By examining the theoretical frameworks and optimization processes, we aim to provide a comprehensive understanding of how these techniques transform metric relationships within data into meaningful lower dimensional representations.  Insights into the mathematical principles that drive these algorithms highlight their unique approaches to capturing and preserving data structures.
  
 ==== Week 25 ==== ==== Week 25 ====
  
-**Speaker**: [[https://www.sci.utah.edu/~beiwang/|Bei Wang]] (University of Utah)+**Speaker**: [[https://www.sci.utah.edu/~beiwang/|Bei Wang]] (University of Utah, USA)
  
-**Coordinates**: Fri 21.06, 9–10:30 AM, MiS E1 05+**Coordinates**: [[https://www.mis.mpg.de/events/event/topology-preserving-data-compression|Fri 21.06, 9–10:30 AM, MiS E1 05]]
  
 **Title**: Topology-Preserving Data Compression **Title**: Topology-Preserving Data Compression
  
 **Abstract**: Existing error-bounded lossy compression techniques control the pointwise error during compression to guarantee the integrity of the decompressed data. However, they typically do not explicitly preserve the topological features in data. When performing post hoc analysis with decompressed data using topological methods, preserving topology in the compression process to obtain topologically consistent and correct scientific insights is desirable. In this talk, we will discuss a couple of lossy compression methods that preserve the topological features in 2D and 3D scalar fields. Specifically, we aim to preserve the types and locations of local extrema as well as the level set relations among critical points captured by contour trees in the decompressed data. This talk is based on joint works with Lin Yan, Xin Liang, Hanqi Guo, and Nathan Gorski. **Abstract**: Existing error-bounded lossy compression techniques control the pointwise error during compression to guarantee the integrity of the decompressed data. However, they typically do not explicitly preserve the topological features in data. When performing post hoc analysis with decompressed data using topological methods, preserving topology in the compression process to obtain topologically consistent and correct scientific insights is desirable. In this talk, we will discuss a couple of lossy compression methods that preserve the topological features in 2D and 3D scalar fields. Specifically, we aim to preserve the types and locations of local extrema as well as the level set relations among critical points captured by contour trees in the decompressed data. This talk is based on joint works with Lin Yan, Xin Liang, Hanqi Guo, and Nathan Gorski.
 +
 +**Speaker Bio**: Dr. Bei Wang Phillips is an Associate Professor in the School of Computing and a faculty member in the Scientific Computing and Imaging (SCI) Institute, University of Utah. She obtained her Ph.D. in Computer Science from Duke University. Her research focuses on topological data analysis, data visualization, and computational topology. She works on combining topological, geometric, statistical, data mining, and machine learning techniques with visualization to study large and complex data for information exploration and scientific discovery. Some of her current research activities involve the analysis and visualization of high-dimensional point clouds, scalar fields, vector fields, tensor fields, networks, and multivariate ensembles. Dr. Phillips is a DOE Early Career Research Program (ECRP) awardee in 2020 and an NSF CAREER awardee in 2022. Her research has been supported by multiple awards from NSF, NIH, and DOE.
  
 ==== Week 26 ==== ==== Week 26 ====
 +
 +[[https://scads.ai/education/summer-schools/summer-school-2024/|ScaDS Summer School]] - **NO MEETING**
  
 ==== Week 27 ==== ==== Week 27 ====
 +
 +**Speaker**: [[https://sites.google.com/view/marzieheidi|Marzieh Eidi]] (ScaDS.AI, Germany)
 +
 +**Coordinates**: [[https://www.mis.mpg.de/events/event/quantitative-and-qualitative-mathematical-data-analysis-examples-differences-and-connections|Fri 05.07, 9–10:30 AM, MiS E1 05]]
 +
 +**Title**: Quantitative and Qualitative Mathematical Data Analysis: Examples, differences, and connections.
 +
 +**Abstract**: In this talk, I am going to present a hopefully intuitive (and less technical) overview of some powerful geometric, topological and stochastic methods for analyzing the shape, and structure of complex data. These methods are becoming more and more popular in complex network analysis and machine learning. After presenting some of the main applications, I will present the idea of how these methods are connected, and in particular, what is a connection between geometry and topology, and how we can consider topology as a fluid geometry? And what are some of the main applications of this dynamic viewpoint?
 +
  
 ==== Week 28 ==== ==== Week 28 ====
  
-==== Week 29 ====+**Speaker**: [[https://sites.google.com/view/kareldevriendt/|Karel Devriendt]] (Max Planck Institute for Mathematics in the Science, Germany) 
 + 
 +**Coordinates**: [[https://www.mis.mpg.de/events/event/diversity-measures-for-data-in-metric-spaces|Fri 12.07, 9–10:30 AM, MiS E1 05]] 
 + 
 +**Title**: Spanning Trees, Effective Resistances and Curvature on Graphs
  
-==== Week 30 ====+**Abstract**: Kirchhoff's celebrated matrix tree theorem expresses the number of spanning trees of a graph as the maximal minor of the Laplacian matrix of the graph. In modern language, this determinantal counting formula reflects the fact that spanning trees form a regular matroid. In this talk, I will discuss some consequences of this perspective for the study of a related quantity from electrical circuit theory: the effective resistance. I will give a new characterization of effective resistances in terms of a certain polytope and discuss applications to recent work on discrete notions of curvature based on the effective resistance.
  • geometry_topology_data_science_spring_2024.1715538244.txt.gz
  • Last modified: 2024/05/12 18:24
  • by Diaaeldin Taha