7 research outputs found
Sliced average variance estimation for multivariate time series
Supervised dimension reduction for time series is challenging as there may be temporal dependence between the response y and the predictors . Recently a time series version of sliced inverse regression, TSIR, was suggested, which applies approximate joint diagonalization of several supervised lagged covariance matrices to consider the temporal nature of the data. In this paper, we develop this concept further and propose a time series version of sliced average variance estimation, TSAVE. As both TSIR and TSAVE have their own advantages and disadvantages, we consider furthermore a hybrid version of TSIR and TSAVE. Based on examples and simulations we demonstrate and evaluate the differences between the three methods and show also that they are superior to apply their iid counterparts to when also using lagged values of the explaining variables as predictors
A review of second-order blind identification methods
Second-order source separation (SOS) is a data analysis tool which can be used for revealing hidden structures in multivariate time series data or as a tool for dimension reduction. Such methods are nowadays increasingly important as more and more high-dimensional multivariate time series data are measured in numerous fields of applied science. Dimension reduction is crucial, as modeling such high-dimensional data with multivariate time series models is often impractical as the number of parameters describing dependencies between the component time series is usually too high. SOS methods have their roots in the signal processing literature, where they were first used to separate source signals from an observed signal mixture. The SOS model assumes that the observed time series (signals) is a linear mixture of latent time series (sources) with uncorrelated components. The methods make use of the second-order statistics-hence the name "second-order source separation." In this review, we discuss the classical SOS methods and their extensions to more complex settings. An example illustrates how SOS can be performed.This article is categorized under:Statistical Models > Time Series ModelsStatistical and Graphical Methods of Data Analysis > Dimension ReductionData: Types and Structure > Time Series, Stochastic Processes, and Functional Dat
Computational Methods for Cognitive and Cooperative Robotics
In the last decades design methods in control engineering made substantial progress in
the areas of robotics and computer animation. Nowadays these methods incorporate the
newest developments in machine learning and artificial intelligence. But the problems
of flexible and online-adaptive combinations of motor behaviors remain challenging for
human-like animations and for humanoid robotics. In this context, biologically-motivated
methods for the analysis and re-synthesis of human motor programs provide new insights
in and models for the anticipatory motion synthesis.
This thesis presents the authorâs achievements in the areas of cognitive and developmental robotics, cooperative and humanoid robotics and intelligent and machine learning methods in computer graphics. The first part of the thesis in the chapter âGoal-directed Imitation for Robotsâ considers imitation learning in cognitive and developmental robotics.
The work presented here details the authorâs progress in the development of hierarchical
motion recognition and planning inspired by recent discoveries of the functions of mirror-neuron cortical circuits in primates. The overall architecture is capable of âlearning for
imitationâ and âlearning by imitationâ. The complete system includes a low-level real-time
capable path planning subsystem for obstacle avoidance during arm reaching. The learning-based path planning subsystem is universal for all types of anthropomorphic robot arms, and is capable of knowledge transfer at the level of individual motor acts.
Next, the problems of learning and synthesis of motor synergies, the spatial and spatio-temporal combinations of motor features in sequential multi-action behavior, and the
problems of task-related action transitions are considered in the second part of the thesis
âKinematic Motion Synthesis for Computer Graphics and Roboticsâ. In this part, a new
approach of modeling complex full-body human actions by mixtures of time-shift invariant
motor primitives in presented. The online-capable full-body motion generation architecture
based on dynamic movement primitives driving the time-shift invariant motor synergies
was implemented as an online-reactive adaptive motion synthesis for computer graphics
and robotics applications.
The last chapter of the thesis entitled âContraction Theory and Self-organized Scenarios
in Computer Graphics and Roboticsâ is dedicated to optimal control strategies in multi-agent scenarios of large crowds of agents expressing highly nonlinear behaviors. This last
part presents new mathematical tools for stability analysis and synthesis of multi-agent
cooperative scenarios.In den letzten Jahrzehnten hat die Forschung in den Bereichen der Steuerung und Regelung
komplexer Systeme erhebliche Fortschritte gemacht, insbesondere in den Bereichen
Robotik und Computeranimation. Die Entwicklung solcher Systeme verwendet heutzutage
neueste Methoden und Entwicklungen im Bereich des maschinellen Lernens und der
kĂŒnstlichen Intelligenz. Die flexible und echtzeitfĂ€hige Kombination von motorischen Verhaltensweisen
ist eine wesentliche Herausforderung fĂŒr die Generierung menschenĂ€hnlicher
Animationen und in der humanoiden Robotik. In diesem Zusammenhang liefern biologisch
motivierte Methoden zur Analyse und Resynthese menschlicher motorischer Programme
neue Erkenntnisse und Modelle fĂŒr die antizipatorische Bewegungssynthese.
Diese Dissertation prÀsentiert die Ergebnisse der Arbeiten des Autors im Gebiet der
kognitiven und Entwicklungsrobotik, kooperativer und humanoider Robotersysteme sowie
intelligenter und maschineller Lernmethoden in der Computergrafik. Der erste Teil der
Dissertation im Kapitel âZielgerichtete Nachahmung fĂŒr Roboterâ behandelt das Imitationslernen
in der kognitiven und Entwicklungsrobotik. Die vorgestellten Arbeiten beschreiben
neue Methoden fĂŒr die hierarchische Bewegungserkennung und -planung, die durch
Erkenntnisse zur Funktion der kortikalen Spiegelneuronen-Schaltkreise bei Primaten inspiriert
wurden. Die entwickelte Architektur ist in der Lage, âdurch Imitation zu lernenâ
und âzu lernen zu imitierenâ. Das komplette entwickelte System enthĂ€lt ein echtzeitfĂ€higes
Pfadplanungssubsystem zur Hindernisvermeidung wĂ€hrend der DurchfĂŒhrung von Armbewegungen.
Das lernbasierte Pfadplanungssubsystem ist universell und fĂŒr alle Arten von
anthropomorphen Roboterarmen in der Lage, Wissen auf der Ebene einzelner motorischer
Handlungen zu ĂŒbertragen.
Im zweiten Teil der Arbeit âKinematische Bewegungssynthese fĂŒr Computergrafik und
Robotikâ werden die Probleme des Lernens und der Synthese motorischer Synergien, d.h.
von rÀumlichen und rÀumlich-zeitlichen Kombinationen motorischer Bewegungselemente
bei Bewegungssequenzen und bei aufgabenbezogenen Handlungs ĂŒbergĂ€ngen behandelt.
Es wird ein neuer Ansatz zur Modellierung komplexer menschlicher Ganzkörperaktionen
durch Mischungen von zeitverschiebungsinvarianten Motorprimitiven vorgestellt. Zudem
wurde ein online-fĂ€higer Synthesealgorithmus fĂŒr Ganzköperbewegungen entwickelt, der
auf dynamischen Bewegungsprimitiven basiert, die wiederum auf der Basis der gelernten
verschiebungsinvarianten Primitive konstruiert werden. Dieser Algorithmus wurde fĂŒr
verschiedene Probleme der Bewegungssynthese fĂŒr die Computergrafik- und Roboteranwendungen
implementiert.
Das letzte Kapitel der Dissertation mit dem Titel âKontraktionstheorie und selbstorganisierte
Szenarien in der Computergrafik und Robotikâ widmet sich optimalen Kontrollstrategien
in Multi-Agenten-Szenarien, wobei die Agenten durch eine hochgradig nichtlineare
Kinematik gekennzeichnet sind. Dieser letzte Teil prÀsentiert neue mathematische Werkzeuge
fĂŒr die StabilitĂ€tsanalyse und Synthese von kooperativen Multi-Agenten-Szenarien
On the use of joint diagonalization in blind signal processing
Blind source separation (BSS) tries to decompose a given multivariate data set into the product of a mixing matrix and a source vector, both of which are unknown. The sources can be recovered if we pose additional constraints to this model. One class of BSS algorithms is given by algebraic BSS, which recovers the mixing structure by jointly diagonalizing various source condition matrices corresponding to different source models. We review classical BSS algorithms such as FOBI, JADE, AMUSE, SOBI, TDSEP and SONS within this framework; combination of the respective source conditions can then yield additional algorithms as implemented e.g. by JADETD. Extensions to dependent component analysis models such as spatiotemporal or multidimensional BSS are discussed