The CUNY Data Science and Applied Topology Reading Group is joint between the Mathematics and Computer Science programmes. We meet Fridays 11.45 -- 12.45 in GC 3209. You can contact us at cunygc@appliedtopology.nyc.

Our plan is to primarily read and discuss seminal papers in data science, in applied topology and in topological data analysis. Each seminar one participant takes the responsibility to present a paper and prepare items for discussion. We expect occasionally to be able to invite external speakers.

## Schedule

Current schedule can be found here.

We will be sending out announcements through a mailing list; you can subscribe here.

## Organizers

- Mikael Vejdemo-Johansson, Computer Science Programme, CUNY Graduate Center; Department of Mathematics, CUNY College of Staten Island
- Azita Mayeli, Mathematics Programme, CUNY Graduate Center; Department of Mathematics, CUNY Queensborough Community College

## Suggested papers

We have compiled a list of papers that might be interesting to present.

# Schedule

### Semester introduction

TBA

### Algebra of Persistence and Cohomology (cont...)

We will be reading Chapters 3.5 - 3.7 in the TDA Book.

Email mvejdemojohansson@gc.cuny.edu if you want access to the book.

### Algebra of Persistence and Cohomology

We will be reading Chapters 3.5 - 3.7 in the TDA Book.

Email mvejdemojohansson@gc.cuny.edu if you want access to the book.

### Fibers of Failure - using Mapper to classify prediction failures

The Mapper algorithm is able to produce intrinsic topological models of arbitrary data in high dimensions. Through a statistical adaptation of the Nerve lemma, the algorithm can be seen to reproduce the topology and parts of the geometry of the data source under assumptions of dense sampling and good parameter choices. In this talk, we will describe how by careful choice of the Mapper model parameters, the resulting topological model can be guaranteed to separate input values to the predictive process for prediction error, grouping high-error and low-error regions separately. This approach produces a diagnostic process where local failure modes can be classified, feeding into either a model development process or a local correction term to improve predictive performance. We have successfully applied this approach to temperature prediction in steel furnaces.

### Fibres of Faiure

The Mapper algorithm is able to produce intrinsic topological models of arbitrary data in high dimensions. Through a statistical adaptation of the Nerve lemma, the algorithm can be seen to reproduce the topology and parts of the geometry of the data source under assumptions of dense sampling and good parameter choices. In this talk, we will describe how by careful choice of the Mapper model parameters, the resulting topological model can be guaranteed to separate input values to the predictive process for prediction error, grouping high-error and low-error regions separately. This approach produces a diagnostic process where local failure modes can be classified, feeding into either a model development process or a local correction term to improve predictive performance. We have successfully applied this approach to temperature prediction in steel furnaces.

### Inaugural meeting

For our spring inaugural meeting MVJ will refresh our memory on the basics, and we will discuss paper assignments and focus interests for our active seminar participants.

### Persistent Cohomology and human motion

TBD: Discuss persistent cohomology, circular coordinates and applications to motion capture.

### Inaugural meeting

For an inaugural meeting we will discuss paper assignments and focus interests for our active seminar participants. There will be pizza and brownies.