Raman spectroscopy provides a powerful means of chemical identification in a variety of fields, partly because of its non-contact nature and the speed at which measurements can be taken. The development of powerful, inexpensive lasers and sensitive charge-coupled device (CCD) detectors has led to widespread use of commercial and scientific Raman systems. However, relatively little work has been done developing physics-based probabilistic models for Raman measurement systems and crafting inference algorithms within the framework of statistical estimation and detection theory. The objective of this thesis is to develop algorithms and performance bounds for the identification of chemicals from their Raman spectra. First, a Poisson measurement model based on the physics of a dispersive Raman device is presented. The problem is then expressed as one of deterministic parameter estimation, and several methods are analyzed for computing the maximum-likelihood (ML) estimates of the mixing coefficients under our data model. The performance of these algorithms is compared against the Cramer-Rao lower bound (CRLB). Next, the Raman detection problem is formulated as one of multiple hypothesis detection (MHD), and an approximation to the optimal decision rule is presented. The resulting approximations are related to the minimum description length (MDL) approach to inference. In our simulations, this method is seen to outperform two common general detection approaches, the spectral unmixing approach and the generalized likelihood ratio test (GLRT). The MHD framework is applied naturally to both the detection of individual target chemicals and to the detection of chemicals from a given class. The common, yet vexing, scenario is then considered in which chemicals are present that are not in the known reference library. A novel variation of nonnegative matrix factorization (NMF) is developed to address this problem. Our simulations indicate that this algorithm gives better estimation performance than the standard two-stage NMF approach and the fully supervised approach when there are chemicals present that are not in the library. Finally, estimation algorithms are developed that take into account errors that may be present in the reference library. In particular, an algorithm is presented for ML estimation under a Poisson errors-in-variables (EIV) model. It is shown that this same basic approach can also be applied to the nonnegative total least squares (NNTLS) problem. Most of the techniques developed in this thesis are applicable to other problems in which an object is to be identified by comparing some measurement of it to a library of known constituent signatures.

Reducing interference noise in a noisy speech recording has been a challenging task for many years yet has a variety of applications, for example, in handsfree mobile communications, in speech recognition, and in hearing aids. Traditional single-channel noise reduction schemes, such as Wiener filtering, do not work satisfactorily in the presence of non-stationary background noise. Alternatively, supervised approaches, where the noise type is known in advance, lead to higher-quality enhanced speech signals. This dissertation proposes supervised and unsupervised single-channel noise reduction algorithms. We consider two classes of methods for this purpose: approaches based on nonnegative matrix factorization (NMF) and methods based on hidden Markov models (HMM).  The contributions of this dissertation can be divided into three main (overlapping) parts. First, we propose NMF-based enhancement approaches that use temporal dependencies of the speech signals. In a standard NMF, the important temporal correlations between consecutive short-time frames are ignored. We propose both continuous and discrete state-space nonnegative dynamical models. These approaches are used to describe the dynamics of the NMF coefficients or activations. We derive optimal minimum mean squared error (MMSE) or linear MMSE estimates of the speech signal using the probabilistic formulations of NMF. Our experiments show that using temporal dynamics in the NMF-based denoising systems improves the performance greatly. Additionally, this dissertation proposes an approach to learn the noise basis matrix online from the noisy observations. This relaxes the assumption of an a-priori specified noise type and enables us to use the NMF-based denoising method in an unsupervised manner. Our experiments show that the proposed approach with online noise basis learning considerably outperforms state-of-the-art methods in different noise conditions.  Second, this thesis proposes two methods for NMF-based separation of sources with similar dictionaries. We suggest a nonnegative HMM (NHMM) for babble noise that is derived from a speech HMM. In this approach, speech and babble signals share the same basis vectors, whereas the activation of the basis vectors are different for the two signals over time. We derive an MMSE estimator for the clean speech signal using the proposed NHMM. The objective evaluations and performed subjective listening test show that the proposed babble model and the final noise reduction algorithm outperform the conventional methods noticeably. Moreover, the dissertation proposes another solution to separate a desired source from a mixture with arbitrarily low artifacts.  Third, an HMM-based algorithm to enhance the speech spectra using super-Gaussian priors is proposed. Our experiments show that speech discrete Fourier transform (DFT) coefficients have super-Gaussian rather than Gaussian distributions even if we limit the speech data to come from a specific phoneme. We derive a new MMSE estimator for the speech spectra that uses super-Gaussian priors. The results of our evaluations using the developed noise reduction algorithm support the super-Gaussianity hypothesis. / <p>QC 20130916</p>

Nous proposons dans cette thèse trois contributions principales aux méthodes d'apprentissage de dictionnaire. La première est un critère de parcimonie par groupes adapté à la NMF lorsque la mesure de distorsion choisie est la divergence d'Itakura-Saito. Dans la plupart des signaux de musique on peut trouver de longs intervalles où seulement une source est active (des soli). Le critère de parcimonie par groupe que nous proposons permet de trouver automatiquement de tels segments et d'apprendre un dictionnaire adapté à chaque source. Ces dictionnaires permettent ensuite d'effectuer la tâche de séparation dans les intervalles où les sources sont mélangés. Ces deux tâches d'identification et de séparation sont effectuées simultanément en une seule passe de l'algorithme que nous proposons. Notre deuxième contribution est un algorithme en ligne pour apprendre le dictionnaire à grande échelle, sur des signaux de plusieurs heures. L'espace mémoire requis par une NMF estimée en ligne est constant alors qu'il croit linéairement avec la taille des signaux fournis dans la version standard, ce qui est impraticable pour des signaux de plus d'une heure. Notre troisième contribution touche à l'interaction avec l'utilisateur. Pour des signaux courts, l'apprentissage aveugle est particulièrement dificile, et l'apport d'information spécifique au signal traité est indispensable. Notre contribution est similaire à l'inpainting et permet de prendre en compte des annotations temps-fréquences. Elle repose sur l'observation que la quasi-totalité du spectrogramme peut etre divisé en régions spécifiquement assignées à chaque source. Nous décrivons une extension de NMF pour prendre en compte cette information et discutons la possibilité d'inférer cette information automatiquement avec des outils d'apprentissage statistique simples. / In this thesis we provide three main contributions to blind source separation methods based on NMF. Our first contribution is a group-sparsity inducing penalty specifically tailored for Itakura-Saito NMF. In many music tracks, there are whole intervals where only one source is active at the same time. The group-sparsity penalty we propose allows to blindly indentify these intervals and learn source specific dictionaries. As a consequence, those learned dictionaries can be used to do source separation in other parts of the track were several sources are active. These two tasks of identification and separation are performed simultaneously in one run of group-sparsity Itakura-Saito NMF. Our second contribution is an online algorithm for Itakura-Saito NMF that allows to learn dictionaries on very large audio tracks. Indeed, the memory complexity of a batch implementation NMF grows linearly with the length of the recordings and becomes prohibitive for signals longer than an hour. In contrast, our online algorithm is able to learn NMF on arbitrarily long signals with limited memory usage. Our third contribution deals user informed NMF. In short mixed signals, blind learning becomes very hard and sparsity do not retrieve interpretable dictionaries. Our contribution is very similar in spirit to inpainting. It relies on the empirical fact that, when observing the spectrogram of a mixture signal, an overwhelming proportion of it consists in regions where only one source is active. We describe an extension of NMF to take into account time-frequency localized information on the absence/presence of each source. We also investigate inferring this information with tools from machine learning.

La séparation aveugle de source consiste à estimer les signaux de sources uniquement à partir des mélanges observés. Le problème peut être séparé en deux catégories en fonction du modèle de mélange: mélanges instantanés, où le retard et la réverbération (effet multi-chemin) ne sont pas pris en compte, et des mélanges convolutives qui sont plus généraux mais plus compliqués. De plus, le bruit additif au niveaux des capteurs et le réglage sous-déterminé, où il y a moins de capteurs que les sources, rendent le problème encore plus difficile.Dans cette thèse, tout d'abord, nous avons étudié le lien entre deux méthodes existantes pour les mélanges instantanés: analyse des composants indépendants (ICA) et analyse des composant parcimonieux (SCA). Nous avons ensuite proposé une nouveau formulation qui fonctionne dans les cas déterminés et sous-déterminés, avec et sans bruit. Les évaluations numériques montrent l'avantage des approches proposées.Deuxièmement, la formulation proposés est généralisés pour les mélanges convolutifs avec des signaux de parole. En intégrant un nouveau modèle d'approximation, les algorithmes proposés fonctionnent mieux que les méthodes existantes, en particulier dans des scénarios bruyant et / ou de forte réverbération.Ensuite, on prend en compte la technique de décomposition morphologique et l'utilisation de parcimonie structurée qui conduit à des algorithmes qui peuvent mieux exploiter les structures des signaux audio. De telles approches sont testées pour des mélanges convolutifs sous-déterminés dans un scénario non-aveugle.Enfin, en bénéficiant du modèle NMF (factorisation en matrice non-négative), nous avons combiné l'hypothèse de faible-rang et de parcimonie et proposé de nouvelles approches pour les mélanges convolutifs sous-déterminés. Les expériences illustrent la bonne performance des algorithmes proposés pour les signaux de musique, en particulier dans des scénarios de forte réverbération. / Blind source separation (BSS) consists of estimating the source signals only from the observed mixtures. The problem can be divided into two categories according to the mixing model: instantaneous mixtures, where delay and reverberation (multi-path effect) are not taken into account, and convolutive mixtures which are more general but more complicated. Moreover, the additive noise at the sensor level and the underdetermined setting, where there are fewer sensors than the sources, make the problem even more difficult.In this thesis, we first studied the link between two existing methods for instantaneous mixtures: independent component analysis (ICA) and sparse component analysis (SCA). We then proposed a new formulation that works in both determined and underdetermined cases, with and without noise. Numerical evaluations show the advantage of the proposed approaches.Secondly, the proposed formulation is generalized for convolutive mixtures with speech signals. By integrating a new approximation model, the proposed algorithms work better than existing methods, especially in noisy and/or high reverberation scenarios.Then, we take into account the technique of morphological decomposition and the use of structured sparsity which leads to algorithms that can better exploit the structures of audio signals. Such approaches are tested for underdetermined convolutive mixtures in a non-blind scenario.At last, being benefited from the NMF model, we combined the low-rank and sparsity assumption and proposed new approaches for under-determined convolutive mixtures. The experiments illustrate the good performance of the proposed algorithms for music signals, especially in strong reverberation scenarios.

Nous sommes intéressé par la reconstitution et la prédiction des séries temporelles multivariées à partir des données partiellement observées et/ou agrégées.La motivation du problème vient des applications dans la gestion du réseau électrique.Nous envisageons des outils capables de résoudre le problème d'estimation de plusieurs domaines.Après investiguer le krigeage, qui est une méthode de la litérature de la statistique spatio-temporelle, et une méthode hybride basée sur le clustering des individus, nous proposons un cadre général de reconstitution et de prédiction basé sur la factorisation de matrice nonnégative.Ce cadre prend en compte de manière intrinsèque la corrélation entre les séries temporelles pour réduire drastiquement la dimension de l'espace de paramètres.Une fois que le problématique est formalisé dans ce cadre, nous proposons deux extensions par rapport à l'approche standard.La première extension prend en compte l'autocorrélation temporelle des individus.Cette information supplémentaire permet d'améliorer la précision de la reconstitution.La deuxième extension ajoute une composante de régression dans la factorisation de matrice nonnégative.Celle-ci nous permet d'utiliser dans l'estimation du modèle des variables exogènes liées avec la consommation électrique, ainsi de produire des facteurs plus interprétatbles, et aussi améliorer la reconstitution.De plus, cette méthod nous donne la possibilité d'utiliser la factorisation de matrice nonnégative pour produire des prédictions.Sur le côté théorique, nous nous intéressons à l'identifiabilité du modèle, ainsi qu'à la propriété de la convergence des algorithmes que nous proposons.La performance des méthodes proposées en reconstitution et en prédiction est testé sur plusieurs jeux de données de consommation électrique à niveaux d'agrégation différents. / We are interested in the recovery and prediction of multiple time series from partially observed and/or aggregate data.Motivated by applications in electricity network management, we investigate tools from multiple fields that are able to deal with such data issues.After examining kriging from spatio-temporal statistics and a hybrid method based on the clustering of individuals, we propose a general framework based on nonnegative matrix factorization.This frameworks takes advantage of the intrisic correlation between the multivariate time series to greatly reduce the dimension of the parameter space.Once the estimation problem is formalized in the nonnegative matrix factorization framework, two extensions are proposed to improve the standard approach.The first extension takes into account the individual temporal autocorrelation of each of the time series.This increases the precision of the time series recovery.The second extension adds a regression layer into nonnegative matrix factorization.This allows exogenous variables that are known to be linked with electricity consumption to be used in estimation, hence makes the factors obtained by the method to be more interpretable, and also increases the recovery precision.Moreover, this method makes the method applicable to prediction.We produce a theoretical analysis on the framework which concerns the identifiability of the model and the convergence of the algorithms that are proposed.The performance of proposed methods to recover and forecast time series is tested on several multivariate electricity consumption datasets at different aggregation level.

Factor models attribute stock returns to a linear combination of factors. A model with great explanatory power (R2) can be used to estimate the systematic risk of an investment. One of the most important factors is the industry which the company of the stock operates in. In commercial risk models this factor is often determined with a manually constructed stock classification scheme such as GICS. We present Natural Language Industry Scheme (NLIS), an automatic and multivalued classification scheme based on topic modeling. The topic modeling is performed on transcripts of company earnings calls and identifies a number of topics analogous to industries. We use non-negative matrix factorization (NMF) on a term-document matrix of the transcripts to perform the topic modeling. When set to explain returns of the MSCI USA index we find that NLIS consistently outperforms GICS, often by several hundred basis points. We attribute this to NLIS’ ability to assign a stock to multiple industries. We also suggest that the proportions of industry assignments for a given stock could correspond to expected future revenue sources rather than current revenue sources. This property could explain some of NLIS’ success since it closely relates to theoretical stock pricing. / Faktormodeller förklarar aktieprisrörelser med en linjär kombination av faktorer. En modell med hög förklaringsgrad (R2) kan användas föratt skatta en investerings systematiska risk. En av de viktigaste faktorerna är aktiebolagets industritillhörighet. I kommersiella risksystem bestäms industri oftast med ett aktieklassifikationsschema som GICS, publicerat av ett finansiellt institut. Vi presenterar Natural Language Industry Scheme (NLIS), ett automatiskt klassifikationsschema baserat på topic modeling. Vi utför topic modeling på transkript av aktiebolags investerarsamtal. Detta identifierar ämnen, eller topics, som är jämförbara med industrier. Topic modeling sker genom icke-negativmatrisfaktorisering (NMF) på en ord-dokumentmatris av transkripten. När NLIS används för att förklara prisrörelser hos MSCI USA-indexet finner vi att NLIS överträffar GICS, ofta med 2-3 procent. Detta tillskriver vi NLIS förmåga att ge flera industritillhörigheter åt samma aktie. Vi föreslår också att proportionerna hos industritillhörigheterna för en aktie kan motsvara förväntade inkomstkällor snarare än nuvarande inkomstkällor. Denna egenskap kan också vara en anledning till NLIS framgång då den nära relaterar till teoretisk aktieprissättning.

Cette thèse considère l'apprentissage de motifs récurrents dans la perception multimodale. Elle s'attache à développer des modèles robotiques de ces facultés telles qu'observées chez l'enfant, et elle s'inscrit en cela dans le domaine de la robotique développementale.Elle s'articule plus précisément autour de deux thèmes principaux qui sont d'une part la capacité d'enfants ou de robots à imiter et à comprendre le comportement d'humains, et d'autre part l'acquisition du langage. A leur intersection, nous examinons la question de la découverte par un agent en développement d'un répertoire de motifs primitifs dans son flux perceptuel. Nous spécifions ce problème et établissons son lien avec ceux de l'indétermination de la traduction décrit par Quine et de la séparation aveugle de source tels qu'étudiés en acoustique.Nous en étudions successivement quatre sous-problèmes et formulons une définition expérimentale de chacun. Des modèles d'agents résolvant ces problèmes sont également décrits et testés. Ils s'appuient particulièrement sur des techniques dites de sacs de mots, de factorisation de matrices et d'apprentissage par renforcement inverse. Nous approfondissons séparément les trois problèmes de l'apprentissage de sons élémentaires tels les phonèmes ou les mots, de mouvements basiques de danse et d'objectifs primaires composant des tâches motrices complexes. Pour finir nous étudions le problème de l'apprentissage d'éléments primitifs multimodaux, ce qui revient à résoudre simultanément plusieurs des problèmes précédents. Nous expliquons notamment en quoi cela fournit un modèle de l'ancrage de mots acoustiques / This thesis focuses on learning recurring patterns in multimodal perception. For that purpose it develops cognitive systems that model the mechanisms providing such capabilities to infants; a methodology that fits into thefield of developmental robotics.More precisely, this thesis revolves around two main topics that are, on the one hand the ability of infants or robots to imitate and understand human behaviors, and on the other the acquisition of language. At the crossing of these topics, we study the question of the how a developmental cognitive agent can discover a dictionary of primitive patterns from its multimodal perceptual flow. We specify this problem and formulate its links with Quine's indetermination of translation and blind source separation, as studied in acoustics.We sequentially study four sub-problems and provide an experimental formulation of each of them. We then describe and test computational models of agents solving these problems. They are particularly based on bag-of-words techniques, matrix factorization algorithms, and inverse reinforcement learning approaches. We first go in depth into the three separate problems of learning primitive sounds, such as phonemes or words, learning primitive dance motions, and learning primitive objective that compose complex tasks. Finally we study the problem of learning multimodal primitive patterns, which corresponds to solve simultaneously several of the aforementioned problems. We also details how the last problems models acoustic words grounding.

非負値行列因子分解(NMF)は，全要素が非負であるデータ行列に対する行列分解法である．本論文では，実在するデータ行列に頻繁に見られる特徴や解釈容易性の向上を考慮に入れ，探索的にデータ分析を行うためのNMFの拡張について論じている．具体的には，零過剰行列や外れ値を含む行列を扱うための確率分布やダイバージェンス，さらには分解結果である因子行列の数や因子行列への直交制約について述べている． / Nonnegative matrix factorization (NMF) is a matrix decomposition technique to analyze nonnegative data matrices, which are matrices of which all elements are nonnegative. In this thesis, we discuss extensions of NMF for exploratory data analysis considering common features of a real nonnegative data matrix and an easy interpretation. In particular, we discuss probability distributions and divergences for zero-inflated data matrix and data matrix with outliers, two-factor vs. three-factor, and orthogonal constraint to factor matrices. / 博士(文化情報学) / Doctor of Culture and Information Science / 同志社大学 / Doshisha University