ATDA2019: Applications of Topological Data Analysis

The emergent area of Topological data analysis (TDA) aims to uncover hidden structure in a wide variety of data sets, combining methods from algebraic topology and other tools of pure mathematics to study the shape of data. Though the pure mathematical foundation of TDA is a major research topic on its own, TDA has been applied to a wide variety of real world problems, among which image compression, cancer research, and shape or pattern recognition are only a few of the many examples.

As TDA is generally not a well-known topic to the data mining and machine learning community, this workshop aims to address the flow of information between the different communities. By illustrating some of its recent and new applications, we will discuss the potential of TDA to active researchers within the fields of data science and machine learning. Furthermore, this workshop provides new and young TDA researchers a chance to present their work to a new community in an interesting and creative way, emphasizing the many possible applications of TDA in real-world data sets.

Topics of interest to the workshop include, but are not limited to, the following:

• TDA and applications in biology, economics, computer science, medicine, physics, geology, . . .
• TDA in machine learning
• Clustering
• Computational topology
• Manifold learning
• Mapper
• Mode estimation
• (Nonlinear) dimensionality reduction
• Pattern recognition
• Persistent (local) homology
• Persistent diagrams
• Ridge estimation
• Shape recognition
• Simplicial complexes
• Skeletonization
• Visualization