Research Statement Statistical Topological Data Analysis
نویسنده
چکیده
My most significant recent work is in the field of applied topology. While the early development of topology was firmly rooted in applications, many of its later advances have been driven by purely mathematical motivations. More recently there is a growing awareness that some of its powerful tools may be just what is needed to help address outstanding problems in diverse modern applications. I have also worked on problems in algebraic topology and algebra.
منابع مشابه
Statistical Inference for Topological Data Analysis PhD Thesis Proposal
Topological Data Analysis (TDA) is an emerging area of research at the intersection of algebraic topology and computational geometry, aimed at describing, summarizing and analyzing possibly high-dimensional data using low-dimensional algebraic representations. Recent advances in computational topology have made it possible to actually compute topological invariants from data. These novel types ...
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Computational topology is an exciting new area which is emerging at the intersection of theoretical computer science and mathematics. Algorithmic techniques in topology are far from new, but the increasing use of computational geometry in many disciplines has led to an explosion of new results in both computer science and mathematics. There is currently great demand for algorithms which can mak...
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We define a new topological summary for data that we call the persistence landscape. In contrast to the standard topological summaries, the barcode and the persistence diagram, it is easy to combine with statistical analysis, and its associated computations are much faster. This summary obeys a Strong Law of Large Numbers and a Central Limit Theorem. Under certain finiteness conditions, this al...
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Introduction: Graph theoretical analysis of functional Magnetic Resonance Imaging (fMRI) data has provided new measures of mapping human brain in vivo. Of all methods to measure the functional connectivity between regions, Linear Correlation (LC) calculation of activity time series of the brain regions as a linear measure is considered the most ubiquitous one. The strength of the dependence obl...
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Data is ubiquitous in today’s society: we track our locations with GPS; we record the number of steps each day using pedometers; we digitally record daily life with pictures and videos; etc. To interpret and to understand the data requires both technical theory to find important features of the data and application expertise to interpret those features. My research is primarily in the technical...
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تاریخ انتشار 2013