in many area of medical research, a relation analysis between one response variable and some explanatory variables is desirable. regression is the most common tool in this situation. if we have some assumptions for such normality for response variable, we could use it. in this paper we propose a nonparametric regression that does not have normality assumption for response variable and we focus ...

In this work we study how to apply topological data analysis to create a method suitable to classify EEGs of patients affected by epilepsy. The topological space constructed from the collection of EEGs signals is analyzed by Persistent Entropy acting as a global topological feature for discriminating between healthy and epileptic signals. The Physionet data-set has been used for testing the cla...

This paper explores the new and growing field of topological data analysis (TDA). TDA is a data analysis method that provides information about the ’shape’ of data. The paper describes what types of shapes TDA detects and why these shapes having meaning. Additionally, concepts from algebraic topology, the mathematics behind TDA, will be discussed. Specifically, the concepts of persistent homolo...

We provide an analysis of the turbo decoding algorithm (TDA) in a setting involving Gaussian densities. In this context, we are able to show that the algorithm converges and that somewhat surprisingly though the density generated by the TDA may differ significantly from the desired posterior density, the means of these two densities coincide.

This talk fits into the general topic of 'stratification learning,' wherein one tries to make inferences about data based on some assumption that it is sampled from a mixture of manifolds glued together in some nicely-structured way. The theoretical tool of persistent local homology (PLH), now more than five years old, provides a useful way to understand the local singularity structure of the i...

Scientific data is often in the form of a finite set of noisy points, sampled from an unknown space, and embedded in a high-dimensional space. Topological data analysis focuses on recovering the topology of the sampled space. In this chapter, we look at methods for constructing combinatorial representations of point sets, as well as theories and algorithms for effective computation of robust to...