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This book introduces the basic methodologies for successful data
analytics. Matrix optimization and approximation are explained in
detail and extensively applied to dimensionality reduction by
principal component analysis and multidimensional scaling.
Diffusion maps and spectral clustering are derived as powerful
tools. The methodological overlap between data science and machine
learning is emphasized by demonstrating how data science is used
for classification as well as supervised and unsupervised learning.
This contributed volume contains articles written by the plenary
and invited speakers from the second international MATHEON Workshop
2015 that focus on applications of compressed sensing. Article
authors address their techniques for solving the problems of
compressed sensing, as well as connections to related areas like
detecting community-like structures in graphs, curbatures on
Grassmanians, and randomized tensor train singular value
decompositions. Some of the novel applications covered include
dimensionality reduction, information theory, random matrices,
sparse approximation, and sparse recovery. This book is aimed at
both graduate students and researchers in the areas of applied
mathematics, computer science, and engineering, as well as other
applied scientists exploring the potential applications for the
novel methodology of compressed sensing. An introduction to the
subject of compressed sensing is also provided for researchers
interested in the field who are not as familiar with it.
The chapters in this volume highlight the state-of-the-art of
compressed sensing and are based on talks given at the third
international MATHEON conference on the same topic, held from
December 4-8, 2017 at the Technical University in Berlin. In
addition to methods in compressed sensing, chapters provide
insights into cutting edge applications of deep learning in data
science, highlighting the overlapping ideas and methods that
connect the fields of compressed sensing and deep learning.
Specific topics covered include: Quantized compressed sensing
Classification Machine learning Oracle inequalities Non-convex
optimization Image reconstruction Statistical learning theory This
volume will be a valuable resource for graduate students and
researchers in the areas of mathematics, computer science, and
engineering, as well as other applied scientists exploring
potential applications of compressed sensing.
This volume contains revised versions of 43 papers presented during
the 21st Annual Conference of the Gesellschaft fur Klassifikation
(GfKl), the German Classification Society. The conference took
place at the University of Pots- dam (Germany) in March 1997; the
local organizer was Prof. 1. Balderjahn, Chair of Business
Administration and Marketing at Potsdam. The scientific program of
the conference included 103 plenary and con- tributed papers,
software and book presentations as well as special (tutorial)
courses. Researchers and practitioners interested in data analysis
and clus- tering methods, information sciences and database
techniques, and in the main topic of the conference: data highways
and their importance for classifi- cation and data analysis, had
the opportunity to discuss recent developments and to establish
cross-disciplinary cooperation in these fields. The conference owed
much to its sponsors - Berliner Volksbank - Daimler Benz AG -
Deutsche Telekom AG Direktion Potsdam - Dresdner Bank AG Filiale
Potsdam - Henkel KGaA - Landeszentralbank in Berlin und Brandenburg
- Ministerium fur Wissenschaft, Forschung und Kultur des Landes
Brandenburg - Sci con GmbH - Siemens AG - Universitat Potsdam -
Unternehmensgruppe Roland Ernst who helped in many ways. Their
generous support is gratefully acknowl- edged. In the present
proceedings volume, selected and peer-reviewed papers are presented
in six chapters as follows.
This book introduces the basic methodologies for successful data
analytics. Matrix optimization and approximation are explained in
detail and extensively applied to dimensionality reduction by
principal component analysis and multidimensional scaling.
Diffusion maps and spectral clustering are derived as powerful
tools. The methodological overlap between data science and machine
learning is emphasized by demonstrating how data science is used
for classification as well as supervised and unsupervised learning.
This contributed volume contains articles written by the plenary
and invited speakers from the second international MATHEON Workshop
2015 that focus on applications of compressed sensing. Article
authors address their techniques for solving the problems of
compressed sensing, as well as connections to related areas like
detecting community-like structures in graphs, curbatures on
Grassmanians, and randomized tensor train singular value
decompositions. Some of the novel applications covered include
dimensionality reduction, information theory, random matrices,
sparse approximation, and sparse recovery. This book is aimed at
both graduate students and researchers in the areas of applied
mathematics, computer science, and engineering, as well as other
applied scientists exploring the potential applications for the
novel methodology of compressed sensing. An introduction to the
subject of compressed sensing is also provided for researchers
interested in the field who are not as familiar with it.
Das vorliegende Buch entstand aus einer Reihe von Vorlesungen, die
wir an der Rheinisch-Westfcilischen Technischen Hochschule Aachen,
der European Business School, der Universitat Oldenburg und der
Universitat Augsburg seit 1984 ge- halt en haben. Diese Vorlesungen
wandten sich vor allem an Informatikstudenten und
Mathematikstudenten mit Nebenfach Informatik mit dem Ziel,
stochastische Grundbegriffe unter besonderer Beriicksichtigung
Informatik-spezifischer Aspekte zu vermitteln. Unter den
zahlreichen Einsatzfeldern stochastischer Methoden in der
Informatik seien hier beispielhaft genannt: Die
Average-Case-Analyse von Algorithmen, die stochastische
Automatentheorie, Anwendungen im Bereich des CAD (Bezier-Kurven und
-Flii.chen), stochastische Informationstheorie und
Codierungstheorie, Rechnernetze und Leistungsbewer- tung von
Rechnersystemen (Warteschlangenprobleme), Bildverarbeitung (Compu-
tertomographie), automatische Spracherkennung
(Hidden-Markov-Modelle), Ex- pertensysteme (effiziente Bereclmung
von bedingten Wahrscheinlichkeiten), kiinst- liche Intelligenz
(Neuronale Netze), stochastische Optimierungs- und Suchverfah- ren
(Simulated Annealing), stochastische Simulation, probabilistische
Algorithmen u.v.a .. Die zum Verstiindnis benotigten theoretischen
Grundlagen, die erfahrungsgemiill haufig weit iiber den in
einfiihrenden Veranstaltungen angebotenen Stoff hinausge- hen, sind
dementsprechend vielfci.ltig und reichen von einfachen
kombinatorischen Uberlegungen bei einigen Problemen der
Average-Case-Analyse von Algorithmen bis hin zu tiefliegenden
Satzen der axiomatischen Wahrscheinlichkeitstheorie, etwa bei den
Markoff-Ketten und -Prozessen oder der Theorie der Punktprozesse im
Bereich der Bildverarbeitung.
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