An introduction to Topological Data Analysis

An introduction to Topological Data Analysis

Presentación:

Big Data analysis is becoming one of the hottest topics in current research in applicable mathematics. Information extracted from Big datasets plays a key role in the understanding of complex processes in a wide range of fields such as biomedicine, e-commerce, and industry.

The need of methods that can handle with big data sets more efficiently and exploit the extra information that high dimensional data offer has lead to a revolution in analytical data sciences. Besides machine and statistical learning, geometry and topology are very natural tools to apply in this direction, since geometry can be regarded as the study of distance functions, and what one often works with are distance functions on large finite sets of data.

Topological Data Analysis (TDA) is a recent field whose aim is to uncover, understand and exploit the topological and geometric structure underlying complex and possibly high dimensional data. It proposes new well-founded mathematical theories and computational tools that can be used independently or in combination with other data analysis and statistical learning techniques. Interestingly, TDA set of tools for dimensional reduction and visualisation of high dimensional data have shown a big potential to unlock relationships that would be considered as noise by traditional statistical approaches as traditional clustering.

TDA has been attracting a lot of interest during the recent years but it still appears difficult to access for data scientists with low expertise in topology or geometry. The goal of this course is to make the fundamentals of TDA accessible to a large audience (with a minimal mathematical background). For that purpose, the focus will be put on the practical aspects of the field rather than very theoretical considerations. The course will be organized around the following topics that play a central role in TDA.

  1. Mapper as a topological tool for data exploration and visualization.
  2. Persistent homology: an introduction (simplicial complexes, filtrations, homology,...).
  3. Applications of persistent homology in TDA: clustering, topological signatures, statistical aspects,...
  4. Distance-to-Measure and geometric inference.

Destinatarios:

El curso An introduction to Topological Data Analysis está dirigido a estadísticos profesionales o académicos, así como investigadores de cualquier ámbito con unos mínimos conocimientos matemáticos que deseen introducirse en esta técnica.
 - Para aprovechar las sesiones prácticas es recomendable que los participantes tengan conocimientos básicos del software R.
 - No son necesarios conocimientos avanzados en matemáticas.
 - Todos los conceptos técnicos se introduciran en el mismo curso.

Requisitos:

Para la realización de este curso es imprescindible traer ordenador personal.

Idioma:

Inglés.

Profesorado:

Frédéric Chazal - INRIA - DataShape team

    Frédéric Chazal is Director of Research at the INRIA Saclay Center in Paris and the head of the INRIA DataShape team. He was a student at Ecole Normale Superieure de Cachan and he got a PhD in Mathematics in 1997 at Burgundy University. Frédéric’s main current research interests are in Topological and Geometric Data Analysis, including Statistical Methods and Inference, functional maps and spectral methods for the analysis of geometric data (images, 3D shapes,...), geometric inference and geometric learning. He is author of more than 60 peer reviewed papers in scientific journals, and he is also member to a number of editorial boards of international journals.

http://geometrica.saclay.inria.fr/team/Fred.Chazal/

Bertrand Michel - Université Pierre et Marie Curie - DataShape team

    Bertrand Michel is Assistant Professor at University Pierre and Marie Curie, LSTA and member of the INRIA DataShape team. He got a Phd in Applied Mathematics at University Paris Sud Orsay (2008) and a habilitation thesis at University Pierre and Marie Curie (2015). Bertrand’s main research interests are in Topological and Geometric Data Analysis, Statistical Methods and Inference, spectral methods for the analysis of geometric data, statistical learning and model selection. He is author of more than 10 scientific publications in international peer reviewed journals.

http://www.lsta.upmc.fr/michelb.html

Albert Ruiz - UAB - Mathematics Department, Algebraic Topology group

    Albert Ruiz is associate professor at the Mathematics Department of the Universitat Autònoma de Barcelona. He got his undergraduate in the Universitat de Barcelona and his PhD in Algebraic Topology in the UAB (2001). He spent one year at the Université Paris XIII (2002-2003) as a post-doc and he has been visitor at Institut Interfacultaire Bernoulli (2005), Mittag Leffler Institute (2006), Paris XIII (2010), Copenhagen University (2011) and Kyoto University (2015). His main research interest is the study of groups from a p-local point of view, with more than 10 publications on this area and 1 advised PhD thesis. He is also interested in applied topology: topological robotics and topological data analysis.

http://mat.uab.cat/~albert

Raquel Iniesta - King’s College London - Department of Medical and Molecular genetics - Statistical Genetics Unit

    Raquel Iniesta is Post Doctoral researcher at the Department of medical and molecular genetics, King’s College London University. She got her PhD in Statistical Genetics at the Catalan Institute of Oncology - Universitat Autònoma de Barcelona (2010). Raquel’s current main research interests are in computational statistics & machine learning, Topological Data Analysis, High-dimensional data modeling, Bioinformatics, Genetics and Pharmacogenetics of complex diseases (Cancer, Schizophrenia, Major Depression, Hypertension). She is author of more than 20 scientific publications in international peer reviewed journals.

http://kclpure.kcl.ac.uk/portal/raquel.iniesta.html

Detalles de organización:

El curso An introduction to Topological Data Analysis se impartirá los días 6, 7 y 8 de junio de 2016 de 9:30 a 13:30.

La duración total del curso es de 12 horas.

La realización del curso está sujeta a un número mínimo de participantes.

La preinscripción se podrá formalizar vía el Servei d'Estadística rellendando el formulario de preinscripción que encontrareis a la web. Una vez recibido vuestro formulario, os confirmaremos mediante un correo electrónico si tenéis plaza asignada o bien si estáis en lista de espera.

Cuotas de inscripción (2016):

Concepto Quantitat Importe
    Externo Esfera UAB
Inscripción
(antes del 22 de mayo)
1 asist 380,00 €  380,00 €  230,00 €
Inscripción
(después del 22 de mayo)
1 asist 530,00 €  530,00 €  380,00 €

Tarifa UAB: Se podrán acoger a esta tarifa todos los interesados que pertenezcan a la comunidad universitaria (PAS, profesores, estudiantes), así como los estudiantes de otras universidades que lo acrediten enviándonos una copia de la matrícula del curso vigente. En caso de desear factura se deberán inscribir con otra tarifa.

(*) Descuentos especiales para personas en situación de paro. Presentando copia del documento de alta o de renovación de la solicitud de ocupación emitido por la Oficina de trabajo de la Generalitat de Catalunya.

(*) Descuentos especiales para grupos de personas procedentes de la misma empresa/institución.

(*) Todos los estudiantes de cualquier titulación en matemáticas/estadística pueden acogerse a la tarifa Last Minute, en caso que quedan plazas disponibles la semana antes del inicio del curso (Tarifa Last Minute: Sin factura; Precio Curso 100 €). Solicitar esta tarifa no garantiza poder realizar el curso hasta la semana antes del inicio.

Detalles de pago:

Una vez formalizada la preinscripción, recibiréis un correo electrónico informando de los detalles para realizar el pago de la inscripción.

Las personas interesadas en solicitar la factura a nombre de una empresa, deberán de hacer constar al justificante del pago de su cuota el nombre de su entidad y NO el del propio asistente al curso. Una vez se haya efectuado el pago del curso, y si no hay ningún motivo de fuerza mayor, no se devolverá el dinero de la inscripción.

Antes de efectuar el pago, esperad a recibir nuestra confirmación de la reserva de la plaza para el curso.

Programa del curso:

The course will be organized around the following topics that play a central role in TDA.

  • Mapper is a topological tool for data exploration and visualization.
  • Persistent homology: an introduction (simplicial complexes, filtrations, homology,...).
  • Applications of persistent homology in TDA: clustering, topological signatures, statistical aspects,...
  • Distance-to-Measure and geometric inference.

Practical sessions will be organized to illustrate the concepts and help the audience to become familiar with the tools of TDA.

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