Unsupervised Learning of Latent Structure from Linear and Nonlinear Measurements

University of Minnesota Ph.D. dissertation. June 2019. Major: Electrical Engineering. Advisor: Nicholas Sidiropoulos. 1 computer file (PDF); xii, 118 pages.The past few decades have seen a rapid expansion of our digital world. While early dwellers of the Internet exchanged simple text messages via email, modern citizens of the digital world conduct a much richer set of activities online: entertainment, banking, booking for restaurants and hotels, just to name a few. In our digitally enriched lives, we not only enjoy great convenience and efficiency, but also leave behind massive amounts of data that offer ample opportunities for improving these digital services, and creating new ones. Meanwhile, technical advancements have facilitated the emergence of new sensors and networks, that can measure, exchange and log data about real world events. These technologies have been applied to many different scenarios, including environmental monitoring, advanced manufacturing, healthcare, and scientific research in physics, chemistry, bio-technology and social science, to name a few. Leveraging the abundant data, learning-based and data-driven methods have become a dominating paradigm across different areas, with data analytics driving many of the recent developments. However, the massive amount of data also bring considerable challenges for analytics. Among them, the collected data are often high-dimensional, with the true knowledge and signal of interest hidden underneath. It is of great importance to reduce data dimension, and transform the data into the right space. In some cases, the data are generated from certain generative models that are identifiable, making it possible to reduce the data back to the original space. In addition, we are often interested in performing some analysis on the data after dimensionality reduction (DR), and it would be helpful to be mindful about these subsequent analysis steps when performing DR, as latent structures can serve as a valuable prior. Based on this reasoning, we develop two methods, one for the linear generative model case, and the other one for the nonlinear case. In a related setting, we study parameter estimation under unknown nonlinear distortion. In this case, the unknown nonlinearity in measurements poses a severe challenge. In practice, various mechanisms can introduce nonlinearity in the measured data. To combat this challenge, we put forth a nonlinear mixture model, which is well-grounded in real world applications. We show that this model is in fact identifiable up to some trivial indeterminancy. We develop an efficient algorithm to recover latent parameters of this model, and confirm the effectiveness of our theory and algorithm via numerical experiments

An investigation of the utility of monaural sound source separation via nonnegative matrix factorization applied to acoustic echo and reverberation mitigation for hands-free telephony

In this thesis we investigate the applicability and utility of Monaural Sound Source Separation (MSSS) via Nonnegative Matrix Factorization (NMF) for various problems related to audio for hands-free telephony. We first investigate MSSS via NMF as an alternative acoustic echo reduction approach to existing approaches such as Acoustic Echo Cancellation (AEC). To this end, we present the single-channel acoustic echo problem as an MSSS problem, in which the objective is to extract the users signal from a mixture also containing acoustic echo and noise. To perform separation, NMF is used to decompose the near-end microphone signal onto the union of two nonnegative bases in the magnitude Short Time Fourier Transform domain. One of these bases is for the spectral energy of the acoustic echo signal, and is formed from the in- coming far-end user’s speech, while the other basis is for the spectral energy of the near-end speaker, and is trained with speech data a priori. In comparison to AEC, the speaker extraction approach obviates Double-Talk Detection (DTD), and is demonstrated to attain its maximal echo mitigation performance immediately upon initiation and to maintain that performance during and after room changes for similar computational requirements. Speaker extraction is also shown to introduce distortion of the near-end speech signal during double-talk, which is quantified by means of a speech distortion measure and compared to that of AEC. Subsequently, we address Double-Talk Detection (DTD) for block-based AEC algorithms. We propose a novel block-based DTD algorithm that uses the available signals and the estimate of the echo signal that is produced by NMF-based speaker extraction to compute a suitably normalized correlation-based decision variable, which is compared to a fixed threshold to decide on doubletalk. Using a standard evaluation technique, the proposed algorithm is shown to have comparable detection performance to an existing conventional block-based DTD algorithm. It is also demonstrated to inherit the room change insensitivity of speaker extraction, with the proposed DTD algorithm generating minimal false doubletalk indications upon initiation and in response to room changes in comparison to the existing conventional DTD. We also show that this property allows its paired AEC to converge at a rate close to the optimum. Another focus of this thesis is the problem of inverting a single measurement of a non- minimum phase Room Impulse Response (RIR). We describe the process by which percep- tually detrimental all-pass phase distortion arises in reverberant speech filtered by the inverse of the minimum phase component of the RIR; in short, such distortion arises from inverting the magnitude response of the high-Q maximum phase zeros of the RIR. We then propose two novel partial inversion schemes that precisely mitigate this distortion. One of these schemes employs NMF-based MSSS to separate the all-pass phase distortion from the target speech in the magnitude STFT domain, while the other approach modifies the inverse minimum phase filter such that the magnitude response of the maximum phase zeros of the RIR is not fully compensated. Subjective listening tests reveal that the proposed schemes generally produce better quality output speech than a comparable inversion technique

An investigation of the utility of monaural sound source separation via nonnegative matrix factorization applied to acoustic echo and reverberation mitigation for hands-free telephony

In this thesis we investigate the applicability and utility of Monaural Sound Source Separation (MSSS) via Nonnegative Matrix Factorization (NMF) for various problems related to audio for hands-free telephony. We first investigate MSSS via NMF as an alternative acoustic echo reduction approach to existing approaches such as Acoustic Echo Cancellation (AEC). To this end, we present the single-channel acoustic echo problem as an MSSS problem, in which the objective is to extract the users signal from a mixture also containing acoustic echo and noise. To perform separation, NMF is used to decompose the near-end microphone signal onto the union of two nonnegative bases in the magnitude Short Time Fourier Transform domain. One of these bases is for the spectral energy of the acoustic echo signal, and is formed from the in- coming far-end user’s speech, while the other basis is for the spectral energy of the near-end speaker, and is trained with speech data a priori. In comparison to AEC, the speaker extraction approach obviates Double-Talk Detection (DTD), and is demonstrated to attain its maximal echo mitigation performance immediately upon initiation and to maintain that performance during and after room changes for similar computational requirements. Speaker extraction is also shown to introduce distortion of the near-end speech signal during double-talk, which is quantified by means of a speech distortion measure and compared to that of AEC. Subsequently, we address Double-Talk Detection (DTD) for block-based AEC algorithms. We propose a novel block-based DTD algorithm that uses the available signals and the estimate of the echo signal that is produced by NMF-based speaker extraction to compute a suitably normalized correlation-based decision variable, which is compared to a fixed threshold to decide on doubletalk. Using a standard evaluation technique, the proposed algorithm is shown to have comparable detection performance to an existing conventional block-based DTD algorithm. It is also demonstrated to inherit the room change insensitivity of speaker extraction, with the proposed DTD algorithm generating minimal false doubletalk indications upon initiation and in response to room changes in comparison to the existing conventional DTD. We also show that this property allows its paired AEC to converge at a rate close to the optimum. Another focus of this thesis is the problem of inverting a single measurement of a non- minimum phase Room Impulse Response (RIR). We describe the process by which percep- tually detrimental all-pass phase distortion arises in reverberant speech filtered by the inverse of the minimum phase component of the RIR; in short, such distortion arises from inverting the magnitude response of the high-Q maximum phase zeros of the RIR. We then propose two novel partial inversion schemes that precisely mitigate this distortion. One of these schemes employs NMF-based MSSS to separate the all-pass phase distortion from the target speech in the magnitude STFT domain, while the other approach modifies the inverse minimum phase filter such that the magnitude response of the maximum phase zeros of the RIR is not fully compensated. Subjective listening tests reveal that the proposed schemes generally produce better quality output speech than a comparable inversion technique

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

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

Dissémination de l’information et dynamique des opinions dans les réseaux sociaux

Our aim in this Ph. D. thesis is to study the diffusion of information as well as the opinion dynamics of users in social networks. Information diffusion models explore the paths taken by information being transmitted through a social network in order to understand and analyze the relationships between users in such network, leading to a better comprehension of human relations and dynamics. This thesis is based on both sides of information diffusion: first by developing mathematical theories and models to study the relationships between people and information, and in a second time by creating tools to better exploit the hidden patterns in these relationships. The theoretical tools developed in this thesis are opinion dynamics models and information diffusion models, where we study the information flow from users in social networks, and the practical tools developed in this thesis are a novel community detection algorithm and a novel trend detection algorithm. We start by introducing an opinion dynamics model in which agents interact with each other about several distinct opinions/contents. In our framework, agents do not exchange all their opinions with each other, they communicate about randomly chosen opinions at each time. We show, using stochastic approximation algorithms, that under mild assumptions this opinion dynamics algorithm converges as time increases, whose behavior is ruled by how users choose the opinions to broadcast at each time. We develop next a community detection algorithm which is a direct application of this opinion dynamics model: when agents broadcast the content they appreciate the most. Communities are thus formed, where they are defined as groups of users that appreciate mostly the same content. This algorithm, which is distributed by nature, has the remarkable property that the discovered communities can be studied from a solid mathematical standpoint. In addition to the theoretical advantage over heuristic community detection methods, the presented algorithm is able to accommodate weighted networks, parametric and nonparametric versions, with the discovery of overlapping communities a byproduct with no mathematical overhead. In a second part, we define a general framework to model information diffusion in social networks. The proposed framework takes into consideration not only the hidden interactions between users, but as well the interactions between contents and multiple social networks. It also accommodates dynamic networks and various temporal effects of the diffusion. This framework can be combined with topic modeling, for which several estimation techniques are derived, which are based on nonnegative tensor factorization techniques. Together with a dimensionality reduction argument, this techniques discover, in addition, the latent community structure of the users in the social networks. At last, we use one instance of the previous framework to develop a trend detection algorithm designed to find trendy topics in a social network. We take into consideration the interaction between users and topics, we formally define trendiness and derive trend indices for each topic being disseminated in the social network. These indices take into consideration the distance between the real broadcast intensity and the maximum expected broadcast intensity and the social network topology. The proposed trend detection algorithm uses stochastic control techniques in order calculate the trend indices, is fast and aggregates all the information of the broadcasts into a simple one-dimensional process, thus reducing its complexity and the quantity of necessary data to the detection. To the best of our knowledge, this is the first trend detection algorithm that is based solely on the individual performances of topicsLa dissémination d'information explore les chemins pris par l'information qui est transmise dans un réseau social, afin de comprendre et modéliser les relations entre les utilisateurs de ce réseau, ce qui permet une meilleur compréhension des relations humaines et leurs dynamique. Même si la priorité de ce travail soit théorique, en envisageant des aspects psychologiques et sociologiques des réseaux sociaux, les modèles de dissémination d'information sont aussi à la base de plusieurs applications concrètes, comme la maximisation d'influence, la prédication de liens, la découverte des noeuds influents, la détection des communautés, la détection des tendances, etc. Cette thèse est donc basée sur ces deux facettes de la dissémination d'information: nous développons d'abord des cadres théoriques mathématiquement solides pour étudier les relations entre les personnes et l'information, et dans un deuxième moment nous créons des outils responsables pour une exploration plus cohérente des liens cachés dans ces relations. Les outils théoriques développés ici sont les modèles de dynamique d'opinions et de dissémination d'information, où nous étudions le flot d'informations des utilisateurs dans les réseaux sociaux, et les outils pratiques développés ici sont un nouveau algorithme de détection de communautés et un nouveau algorithme de détection de tendances dans les réseaux sociau

Advances in knowledge discovery and data mining Part II

19th Pacific-Asia Conference, PAKDD 2015, Ho Chi Minh City, Vietnam, May 19-22, 2015, Proceedings, Part II</p