DIMENSION
The Role of Dimension in Metric Embedding
| Coordinatore | BEN-GURION UNIVERSITY OF THE NEGEV
Organization address
address: Office of the President - Main Campus contact info |
| Nazionalità Coordinatore | Israel [IL] |
| Totale costo | 100˙000 € |
| EC contributo | 100˙000 € |
| Programma | FP7-PEOPLE
Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) |
| Code Call | FP7-PEOPLE-2011-CIG |
| Funding Scheme | MC-CIG |
| Anno di inizio | 2012 |
| Periodo (anno-mese-giorno) | 2012-10-01 - 2016-09-30 |
Partecipanti
| # | ||||
|---|---|---|---|---|
| 1 |
BEN-GURION UNIVERSITY OF THE NEGEV
Organization address
address: Office of the President - Main Campus contact info |
IL (BEER SHEVA) | coordinator | 100˙000.00 |
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Obiettivo del progetto (Objective)
'We are currently witnessing the generation of massive amounts of data that require analysis, particularly in application areas such as computational biology, text mining, networking and web applications. Many of these computational tasks can be performed efficiently in low dimensional Euclidean space. In this research proposal, I will set out to investigate fundamental questions in the field of metric embedding, which could provide tools and algorithms for handling arbitrary metric data. The dimension of the host space will play a major role, as it is crucial for the efficiency of algorithms in normed spaces and as it enables compact representation. In particular, I plan to investigate questions such as: How well do certain classes of metric spaces embed into Euclidean space of bounded dimension? What are the bounds on dimension reduction, in several normed spaces and for particular subsets of Euclidean space? Of particular interest is the class of metrics known as doubling-metrics; in some sense, these are metrics with low intrinsic dimension. While there has been much research, in several communities, on these metrics, we still do not understand the dimensionality required for embedding these metrics into normed spaces. I plan to achieve better understanding of the above questions by using newly developed embedding techniques, in combination with tools from probability theory and functional analysis. Answering these questions will enrich the knowledge of the European Mathematics and Computer Science communities and supply its researchers with new tools and insights for developing improved algorithms for various computational tasks.'