Combining blind source extraction with joint approximate diagonalization: Thin algorithms for ICA

In this paper a multivariate contrast function is proposed for the blind signal extraction of a subset of the indepen dent components from a linear mixture. This contrast com bines the robustness of the joint approximate diagonaliza tion techniques with the flexibility of the methods for blind signal extraction. Its maximization leads to hierarchical and simultaneous ICA extraction algorithms which are respec tively based on the thin QR and thin SVD factorizations. The interesting similarities and differences with other exist ing contrasts and algorithms are commented.Comisión Interministerial de Ciencia y Tecnología (CICYT). España TIC2001-0751-C04-0

Coherency and sharpness measures by using ICA algorithms. An investigation for Alzheimer’s disease discrimination

In this paper, we present a comprehensive study of different Independent Component Analysis (ICA) algorithms for the calculation of coherency and sharpness of electroencephalogram (EEG) signals, in order to investigate the possibility of early detection of Alzheimer’s disease (AD). We found that ICA algorithms can help in the artifact rejection and noise reduction, improving the discriminative property of features in high frequency bands (specially in high alpha and beta ranges). In addition to different ICA algorithms, the optimum number of selected components is investigated, in order to help decision processes for future works

Initialization method for speech separation algorithms that work in the time-frequency domain

This article addresses the problem of the unsupervised separa tion of speech signals in realistic scenarios. An initialization procedure is proposed for independent component analysis (ICA) algorithms that work in the time-frequency domain and require the prewhitening of the observations. It is shown that the proposed method drastically reduces the permuted solu tions in that domain and helps to reduce the execution time of the algorithms. Simulations confirm these advantages for several ICA instantaneous algo rithms and the effectiveness of the proposed technique in emulated reverber ant environments.Ministerio de Ciencia y tecnología (España) TEC2008-0625

Fast and accurate methods of independent component analysis: A survey

summary:This paper presents a survey of recent successful algorithms for blind separation of determined instantaneous linear mixtures of independent sources such as natural speech or biomedical signals. These algorithms rely either on non-Gaussianity, nonstationarity, spectral diversity, or on a combination of them. Performance of the algorithms will be demonstrated on separation of a linear instantaneous mixture of audio signals (music, speech) and on artifact removal in electroencephalogram (EEG)

Efficient feature reduction and classification methods

Durch die steigende Anzahl verfügbarer Daten in unterschiedlichsten Anwendungsgebieten nimmt der Aufwand vieler Data-Mining Applikationen signifikant zu. Speziell hochdimensionierte Daten (Daten die über viele verschiedene Attribute beschrieben werden) können ein großes Problem für viele Data-Mining Anwendungen darstellen. Neben höheren Laufzeiten können dadurch sowohl für überwachte (supervised), als auch nicht überwachte (unsupervised) Klassifikationsalgorithmen weitere Komplikationen entstehen (z.B. ungenaue Klassifikationsgenauigkeit, schlechte Clustering-Eigenschaften, …). Dies führt zu einem Bedarf an effektiven und effizienten Methoden zur Dimensionsreduzierung. Feature Selection (die Auswahl eines Subsets von Originalattributen) und Dimensionality Reduction (Transformation von Originalattribute in (Linear)-Kombinationen der Originalattribute) sind zwei wichtige Methoden um die Dimension von Daten zu reduzieren. Obwohl sich in den letzten Jahren vielen Studien mit diesen Methoden beschäftigt haben, gibt es immer noch viele offene Fragestellungen in diesem Forschungsgebiet. Darüber hinaus ergeben sich in vielen Anwendungsbereichen durch die immer weiter steigende Anzahl an verfügbaren und verwendeten Attributen und Features laufend neue Probleme. Das Ziel dieser Dissertation ist es, verschiedene Fragenstellungen in diesem Bereich genau zu analysieren und Verbesserungsmöglichkeiten zu entwickeln. Grundsätzlich, werden folgende Ansprüche an Methoden zur Feature Selection und Dimensionality Reduction gestellt: Die Methoden sollten effizient (bezüglich ihres Rechenaufwandes) sein und die resultierenden Feature-Sets sollten die Originaldaten möglichst kompakt repräsentieren können. Darüber hinaus ist es in vielen Anwendungsgebieten wichtig, die Interpretierbarkeit der Originaldaten beizubehalten. Letztendlich sollte der Prozess der Dimensionsreduzierung keinen negativen Effekt auf die Klassifikationsgenauigkeit haben - sondern idealerweise, diese noch verbessern. Offene Problemstellungen in diesem Bereich betreffen unter anderem den Zusammenhang zwischen Methoden zur Dimensionsreduzierung und der resultierenden Klassifikationsgenauigkeit, wobei sowohl eine möglichst kompakte Repräsentation der Daten, als auch eine hohe Klassifikationsgenauigkeit erzielt werden sollen. Wie bereits erwähnt, ergibt sich durch die große Anzahl an Daten auch ein erhöhter Rechenaufwand, weshalb schnelle und effektive Methoden zur Dimensionsreduzierung entwickelt werden müssen, bzw. existierende Methoden verbessert werden müssen. Darüber hinaus sollte natürlich auch der Rechenaufwand der verwendeten Klassifikationsmethoden möglichst gering sein. Des Weiteren ist die Interpretierbarkeit von Feature Sets zwar möglich, wenn Feature Selection Methoden für die Dimensionsreduzierung verwendet werden, im Fall von Dimensionality Reduction sind die resultierenden Feature Sets jedoch meist Linearkombinationen der Originalfeatures. Daher ist es schwierig zu überprüfen, wie viel Information einzelne Originalfeatures beitragen. Im Rahmen dieser Dissertation konnten wichtige Beiträge zu den oben genannten Problemstellungen präsentiert werden: Es wurden neue, effiziente Initialisierungsvarianten für die Dimensionality Reduction Methode Nonnegative Matrix Factorization (NMF) entwickelt, welche im Vergleich zu randomisierter Initialisierung und im Vergleich zu State-of-the-Art Initialisierungsmethoden zu einer schnelleren Reduktion des Approximationsfehlers führen. Diese Initialisierungsvarianten können darüber hinaus mit neu entwickelten und sehr effektiven Klassifikationsalgorithmen basierend auf NMF kombiniert werden. Um die Laufzeit von NMF weiter zu steigern wurden unterschiedliche Varianten von NMF Algorithmen auf Multi-Prozessor Systemen vorgestellt, welche sowohl Task- als auch Datenparallelismus unterstützen und zu einer erheblichen Reduktion der Laufzeit für NMF führen. Außerdem wurde eine effektive Verbesserung der Matlab Implementierung des ALS Algorithmus vorgestellt. Darüber hinaus wurde eine Technik aus dem Bereich des Information Retrieval -- Latent Semantic Indexing -- erfolgreich als Klassifikationsalgorithmus für Email Daten angewendet. Schließlich wurde eine ausführliche empirische Studie über den Zusammenhang verschiedener Feature Reduction Methoden (Feature Selection und Dimensionality Reduction) und der resultierenden Klassifikationsgenauigkeit unterschiedlicher Lernalgorithmen präsentiert. Der starke Einfluss unterschiedlicher Methoden zur Dimensionsreduzierung auf die resultierende Klassifikationsgenauigkeit unterstreicht dass noch weitere Untersuchungen notwendig sind um das komplexe Zusammenspiel von Dimensionsreduzierung und Klassifikation genau analysieren zu können.The sheer volume of data today and its expected growth over the next years are some of the key challenges in data mining and knowledge discovery applications. Besides the huge number of data samples that are collected and processed, the high dimensional nature of data arising in many applications causes the need to develop effective and efficient techniques that are able to deal with this massive amount of data. In addition to the significant increase in the demand of computational resources, those large datasets might also influence the quality of several data mining applications (especially if the number of features is very high compared to the number of samples). As the dimensionality of data increases, many types of data analysis and classification problems become significantly harder. This can lead to problems for both supervised and unsupervised learning. Dimensionality reduction and feature (subset) selection methods are two types of techniques for reducing the attribute space. While in feature selection a subset of the original attributes is extracted, dimensionality reduction in general produces linear combinations of the original attribute set. In both approaches, the goal is to select a low dimensional subset of the attribute space that covers most of the information of the original data. During the last years, feature selection and dimensionality reduction techniques have become a real prerequisite for data mining applications. There are several open questions in this research field, and due to the often increasing number of candidate features for various application areas (e.\,g., email filtering or drug classification/molecular modeling) new questions arise. In this thesis, we focus on some open research questions in this context, such as the relationship between feature reduction techniques and the resulting classification accuracy and the relationship between the variability captured in the linear combinations of dimensionality reduction techniques (e.\,g., PCA, SVD) and the accuracy of machine learning algorithms operating on them. Another important goal is to better understand new techniques for dimensionality reduction, such as nonnegative matrix factorization (NMF), which can be applied for finding parts-based, linear representations of nonnegative data. This ``sum-of-parts'' representation is especially useful if the interpretability of the original data should be retained. Moreover, performance aspects of feature reduction algorithms are investigated. As data grow, implementations of feature selection and dimensionality reduction techniques for high-performance parallel and distributed computing environments become more and more important. In this thesis, we focus on two types of open research questions: methodological advances without any specific application context, and application-driven advances for a specific application context. Summarizing, new methodological contributions are the following: The utilization of nonnegative matrix factorization in the context of classification methods is investigated. In particular, it is of interest how the improved interpretability of NMF factors due to the non-negativity constraints (which is of central importance in various problem settings) can be exploited. Motivated by this problem context two new fast initialization techniques for NMF based on feature selection are introduced. It is shown how approximation accuracy can be increased and/or how computational effort can be reduced compared to standard randomized seeding of the NMF and to state-of-the-art initialization strategies suggested earlier. For example, for a given number of iterations and a required approximation error a speedup of 3.6 compared to standard initialization, and a speedup of 3.4 compared to state-of-the-art initialization strategies could be achieved. Beyond that, novel classification methods based on the NMF are proposed and investigated. We can show that they are not only competitive in terms of classification accuracy with state-of-the-art classifiers, but also provide important advantages in terms of computational effort (especially for low-rank approximations). Moreover, parallelization and distributed execution of NMF is investigated. Several algorithmic variants for efficiently computing NMF on multi-core systems are studied and compared to each other. In particular, several approaches for exploiting task and/or data-parallelism in NMF are studied. We show that for some scenarios new algorithmic variants clearly outperform existing implementations. Last, but not least, a computationally very efficient adaptation of the implementation of the ALS algorithm in Matlab 2009a is investigated. This variant reduces the runtime significantly (in some settings by a factor of 8) and also provides several possibilities to be executed concurrently. In addition to purely methodological questions, we also address questions arising in the adaptation of feature selection and classification methods to two specific application problems: email classification and in silico screening for drug discovery. Different research challenges arise in the contexts of these different application areas, such as the dynamic nature of data for email classification problems, or the imbalance in the number of available samples of different classes for drug discovery problems. Application-driven advances of this thesis comprise the adaptation and application of latent semantic indexing (LSI) to the task of email filtering. Experimental results show that LSI achieves significantly better classification results than the widespread de-facto standard method for this special application context. In the context of drug discovery problems, several groups of well discriminating descriptors could be identified by utilizing the ``sum-of-parts`` representation of NMF. The number of important descriptors could be further increased when applying sparseness constraints on the NMF factors

Generalized linear-in-parameter models : theory and audio signal processing applications

This thesis presents a mathematically oriented perspective to some basic concepts of digital signal processing. A general framework for the development of alternative signal and system representations is attained by defining a generalized linear-in-parameter model (GLM) configuration. The GLM provides a direct view into the origins of many familiar methods in signal processing, implying a variety of generalizations, and it serves as a natural introduction to rational orthonormal model structures. In particular, the conventional division between finite impulse response (FIR) and infinite impulse response (IIR) filtering methods is reconsidered. The latter part of the thesis consists of audio oriented case studies, including loudspeaker equalization, musical instrument body modeling, and room response modeling. The proposed collection of IIR filter design techniques is submitted to challenging modeling tasks. The most important practical contribution of this thesis is the introduction of a procedure for the optimization of rational orthonormal filter structures, called the BU-method. More generally, the BU-method and its variants, including the (complex) warped extension, the (C)WBU-method, can be consider as entirely new IIR filter design strategies.reviewe