Summer@ICERM 2017: Topological Data Analysis
(June 19 - August 11, 2017)
Imagine spending eight-weeks on the beautiful Brown University campus in historic Providence, RI, working in a small team setting to solve mathematical research problems developed by faculty experts in their fields.
Imagine creating career-building connections between peers, near peers (graduate students and postdocs), and academic professionals.
Imagine spending your summer in a fun, memorable, and intellectually stimulating environment.
Now, imagine having this experience with support for travel within the U.S., room and board paid, plus a $3,000 stipend*.
The 2017 Summer@ICERM program is designed for a select group of 16-20 undergraduate scholars. The program will give undergraduates an opportunity for exposure and research in the methods of “Applied Topology” in the study of complex data sets.
The program will offer mini-courses for students at the beginning of the program:
- Persistent Homology from the Computational Viewpoint;
- Distances Between Metric Spaces and Applications; and
- Topological Time Series Analysis.
The faculty advisors will then present several research projects that are highly interdisciplinary and represent areas where topological data analysis stands to have a deep and meaningful impact:
- Shape Classification;
- Action Recognition;
- Feature Recognition from Persistent Diagrams;
- Local Persistence Diagrams;
- Configuration Spaces;
- Künneth Formula for Persistent Homology;
- Classification of Music Data Streams: Music Information Retrieval; and
- Analysis of Hippocampal Networks.
Tackling these projects will require a combination of analytical and computational approaches, and students will be expected to gain intuition into some of these problems via analysis, computer experimentation, and visualization.
Throughout the eight-week program, students will work on their assigned projects in groups of two to four, supervised by faculty advisors and aided by teaching assistants. Students will meet daily, attend mini-courses, learn how to write reports in LaTeX, give weekly team talks about their findings, attend professional development seminars, and write up their research into a poster and/or paper by the end of the program.
ICERM provides an excellent research environment, and the students and their faculty and TA mentors will have access to shared offices and collaborative space throughout the institute. They also will have access to ICERM’s computer facilities and specialized software. ICERM staff will provide logistical support for students and will help build community through fun activities and events.
The Data Science Initiative, a hub at Brown University for research and education in the foundational methodologies, domain applications, and societal impacts of data science, is pleased to support this Summer@ICERM program through faculty and postdoctoral mentorship, and undergraduate support.
- $3,000 stipend
- Travel support within U.S.
- Dormitory housing
- Meal plan
- Fun events
The main ideas of PH will be introduced via a tutorial combining theoretical concepts with their software implementation. The Matlab frontend of javaplex will be used for all demostrations, tutorials, and all applications. The package is freely available from http://appliedtopology.github. io/javaplex/ and it is readily distributed together with an excellent tutorial that guides students both though the landscape of theoretical ideas and their immediate computational implementation. We envision covering both simplicial homology (with eld coecients) and its computation at the same time: we will be complementing standard denitions with the basic methods from linear algebra for reducing matrices and eectively nding bases for homology. These methods are readily implemented by javaplex. We will then introduce functoriality and progress to the concept of persistent homology and its computation.
The main ideas behind the construction and applications of the Gromov-Hausdor distance will be presented in a series of lectures.
Time series are ubiquitous in today's data rich world, so naturally their analysis is a fundamental object of study. In recent years, tools from the growing eld of topological data analysis have been adapted to the analysis of time series data. In short, time series can be transformed into high-dimensional point clouds (via delay-embeddings) and their shape can be probed via persistent homology to quantify characteristics such as periodicity, quasiperiodicity, existence of motifs, presence of dynamic chaos, etc [13, 14]. This mini-course we will cover some of the theory behind topological time series analysis, and will explore applications ranging from biology to music analysis.