bioNMF: a versatile tool for non-negative matrix factorization in biology

Medical imaging has become an absolutely essential diagnostic tool for clinical practices; at present, pathologies can be detected with an earliness never before known. Its use has not only been relegated to the field of radiology but also, increasingly, to computer-based imaging processes prior to surgery. Motion analysis, in particular, plays an important role in analyzing activities or behaviors of live objects in medicine. This short paper presents several low-cost hardware implementation approaches for the new generation of tablets and/or smartphones for estimating motion compensation and segmentation in medical images. These systems have been optimized for breast cancer diagnosis using magnetic resonance imaging technology with several advantages over traditional X-ray mammography, for example, obtaining patient information during a short period. This paper also addresses the challenge of offering a medical tool that runs on widespread portable devices, both on tablets and/or smartphones to aid in patient diagnostics.

Non-negative matrix decomposition approaches to frequency domain analysis of music audio signals

On étudie l’application des algorithmes de décomposition matricielles tel que la Factorisation Matricielle Non-négative (FMN), aux représentations fréquentielles de signaux audio musicaux. Ces algorithmes, dirigés par une fonction d’erreur de reconstruction, apprennent un ensemble de fonctions de base et un ensemble de coef- ficients correspondants qui approximent le signal d’entrée. On compare l’utilisation de trois fonctions d’erreur de reconstruction quand la FMN est appliquée à des gammes monophoniques et harmonisées: moindre carré, divergence Kullback-Leibler, et une mesure de divergence dépendente de la phase, introduite récemment. Des nouvelles méthodes pour interpréter les décompositions résultantes sont présentées et sont comparées aux méthodes utilisées précédemment qui nécessitent des connaissances du domaine acoustique. Finalement, on analyse la capacité de généralisation des fonctions de bases apprises par rapport à trois paramètres musicaux: l’amplitude, la durée et le type d’instrument. Pour ce faire, on introduit deux algorithmes d’étiquetage des fonctions de bases qui performent mieux que l’approche précédente dans la majorité de nos tests, la tâche d’instrument avec audio monophonique étant la seule exception importante.

Linear Hyperspectral Unmixing Using L0-norm Approximations and Nonnegative Matrix Factorization

Spectral unmixing (SU) is a technique to characterize mixed pixels of the hyperspectral images measured by remote sensors. Most of the existing spectral unmixing algorithms are developed using the linear mixing models. Since the number of endmembers/materials present at each mixed pixel is normally scanty compared with the number of total endmembers (the dimension of spectral library), the problem becomes sparse. This thesis introduces sparse hyperspectral unmixing methods for the linear mixing model through two different scenarios. In the first scenario, the library of spectral signatures is assumed to be known and the main problem is to find the minimum number of endmembers under a reasonable small approximation error. Mathematically, the corresponding problem is called the $\ell_0$-norm problem which is NP-hard problem. Our main study for the first part of thesis is to find more accurate and reliable approximations of $\ell_0$-norm term and propose sparse unmixing methods via such approximations. The resulting methods are shown considerable improvements to reconstruct the fractional abundances of endmembers in comparison with state-of-the-art methods such as having lower reconstruction errors. In the second part of the thesis, the first scenario (i.e., dictionary-aided semiblind unmixing scheme) will be generalized as the blind unmixing scenario that the library of spectral signatures is also estimated. We apply the nonnegative matrix factorization (NMF) method for proposing new unmixing methods due to its noticeable supports such as considering the nonnegativity constraints of two decomposed matrices. Furthermore, we introduce new cost functions through some statistical and physical features of spectral signatures of materials (SSoM) and hyperspectral pixels such as the collaborative property of hyperspectral pixels and the mathematical representation of the concentrated energy of SSoM for the first few subbands. Finally, we introduce sparse unmixing methods for the blind scenario and evaluate the efficiency of the proposed methods via simulations over synthetic and real hyperspectral data sets. The results illustrate considerable enhancements to estimate the spectral library of materials and their fractional abundances such as smaller values of spectral angle distance (SAD) and abundance angle distance (AAD) as well.

Automatic musical instrument recognition for multimedia indexing

Trabalho apresentado no âmbito do Mestrado em Engenharia Informática, como requisito parcial para obtenção do grau de Mestre em Engenharia Informática

Modeling High-Dimensional Audio Sequences with Recurrent Neural Networks

Cette thèse étudie des modèles de séquences de haute dimension basés sur des réseaux de neurones récurrents (RNN) et leur application à la musique et à la parole. Bien qu'en principe les RNN puissent représenter les dépendances à long terme et la dynamique temporelle complexe propres aux séquences d'intérêt comme la vidéo, l'audio et la langue naturelle, ceux-ci n'ont pas été utilisés à leur plein potentiel depuis leur introduction par Rumelhart et al. (1986a) en raison de la difficulté de les entraîner efficacement par descente de gradient. Récemment, l'application fructueuse de l'optimisation Hessian-free et d'autres techniques d'entraînement avancées ont entraîné la recrudescence de leur utilisation dans plusieurs systèmes de l'état de l'art. Le travail de cette thèse prend part à ce développement. L'idée centrale consiste à exploiter la flexibilité des RNN pour apprendre une description probabiliste de séquences de symboles, c'est-à-dire une information de haut niveau associée aux signaux observés, qui en retour pourra servir d'à priori pour améliorer la précision de la recherche d'information. Par exemple, en modélisant l'évolution de groupes de notes dans la musique polyphonique, d'accords dans une progression harmonique, de phonèmes dans un énoncé oral ou encore de sources individuelles dans un mélange audio, nous pouvons améliorer significativement les méthodes de transcription polyphonique, de reconnaissance d'accords, de reconnaissance de la parole et de séparation de sources audio respectivement. L'application pratique de nos modèles à ces tâches est détaillée dans les quatre derniers articles présentés dans cette thèse. Dans le premier article, nous remplaçons la couche de sortie d'un RNN par des machines de Boltzmann restreintes conditionnelles pour décrire des distributions de sortie multimodales beaucoup plus riches. Dans le deuxième article, nous évaluons et proposons des méthodes avancées pour entraîner les RNN. Dans les quatre derniers articles, nous examinons différentes façons de combiner nos modèles symboliques à des réseaux profonds et à la factorisation matricielle non-négative, notamment par des produits d'experts, des architectures entrée/sortie et des cadres génératifs généralisant les modèles de Markov cachés. Nous proposons et analysons également des méthodes d'inférence efficaces pour ces modèles, telles la recherche vorace chronologique, la recherche en faisceau à haute dimension, la recherche en faisceau élagué et la descente de gradient. Finalement, nous abordons les questions de l'étiquette biaisée, du maître imposant, du lissage temporel, de la régularisation et du pré-entraînement.

Understanding Subsystems in Biology through Dimensionality Reduction, Graph Partitioning and Analytical Modeling

Biological systems exhibit rich and complex behavior through the orchestrated interplay of a large array of components. It is hypothesized that separable subsystems with some degree of functional autonomy exist; deciphering their independent behavior and functionality would greatly facilitate understanding the system as a whole. Discovering and analyzing such subsystems are hence pivotal problems in the quest to gain a quantitative understanding of complex biological systems. In this work, using approaches from machine learning, physics and graph theory, methods for the identification and analysis of such subsystems were developed. A novel methodology, based on a recent machine learning algorithm known as non-negative matrix factorization (NMF), was developed to discover such subsystems in a set of large-scale gene expression data. This set of subsystems was then used to predict functional relationships between genes, and this approach was shown to score significantly higher than conventional methods when benchmarking them against existing databases. Moreover, a mathematical treatment was developed to treat simple network subsystems based only on their topology (independent of particular parameter values). Application to a problem of experimental interest demonstrated the need for extentions to the conventional model to fully explain the experimental data. Finally, the notion of a subsystem was evaluated from a topological perspective. A number of different protein networks were examined to analyze their topological properties with respect to separability, seeking to find separable subsystems. These networks were shown to exhibit separability in a nonintuitive fashion, while the separable subsystems were of strong biological significance. It was demonstrated that the separability property found was not due to incomplete or biased data, but is likely to reflect biological structure.

Characterization of a dual-energy X-ray absorptiometry system for soft tissues assessment and their correlations with metabolic state

Il crescente utilizzo di sistemi di analisi high-throughput per lo studio dello stato fisiologico e metabolico del corpo, ha evidenziato che una corretta alimentazione e una buona forma fisica siano fattori chiave per la salute. L'aumento dell'età media della popolazione evidenzia l'importanza delle strategie di contrasto delle patologie legate all'invecchiamento. Una dieta sana è il primo mezzo di prevenzione per molte patologie, pertanto capire come il cibo influisce sul corpo umano è di fondamentale importanza. In questo lavoro di tesi abbiamo affrontato la caratterizzazione dei sistemi di imaging radiografico Dual-energy X-ray Absorptiometry (DXA). Dopo aver stabilito una metodologia adatta per l'elaborazione di dati DXA su un gruppo di soggetti sani non obesi, la PCA ha evidenziato alcune proprietà emergenti dall'interpretazione delle componenti principali in termini delle variabili di composizione corporea restituite dalla DXA. Le prime componenti sono associabili ad indici macroscopici di descrizione corporea (come BMI e WHR). Queste componenti sono sorprendentemente stabili al variare dello status dei soggetti in età, sesso e nazionalità. Dati di analisi metabolica, ottenuti tramite Magnetic Resonance Spectroscopy (MRS) su campioni di urina, sono disponibili per circa mille anziani (provenienti da cinque paesi europei) di età compresa tra i 65 ed i 79 anni, non affetti da patologie gravi. I dati di composizione corporea sono altresì presenti per questi soggetti. L'algoritmo di Non-negative Matrix Factorization (NMF) è stato utilizzato per esprimere gli spettri MRS come combinazione di fattori di base interpretabili come singoli metaboliti. I fattori trovati sono stabili, quindi spettri metabolici di soggetti sono composti dallo stesso pattern di metaboliti indipendentemente dalla nazionalità. Attraverso un'analisi a singolo cieco sono stati trovati alti valori di correlazione tra le variabili di composizione corporea e lo stato metabolico dei soggetti. Ciò suggerisce la possibilità di derivare la composizione corporea dei soggetti a partire dal loro stato metabolico.

Marine mammal species detection and classification

Thesis (Ph.D.)--University of Washington, 2016-04

Optimización de la factorización de matrices no negativas en Bioinformática

En los últimos años se ha incrementado el interés de la comunidad científica en la Factorización de matrices no negativas (Non-negative Matrix Factorization, NMF). Este método permite transformar un conjunto de datos de grandes dimensiones en una pequeña colección de elementos que poseen semántica propia en el contexto del análisis. En el caso de Bioinformática, NMF suele emplearse como base de algunos métodos de agrupamiento de datos, que emplean un modelo estadístico para determinar el número de clases más favorable. Este modelo requiere de una gran cantidad de ejecuciones de NMF con distintos parámetros de entrada, lo que representa una enorme carga de trabajo a nivel computacional. La mayoría de las implementaciones de NMF han ido quedando obsoletas ante el constante crecimiento de los datos que la comunidad científica busca analizar, bien sea porque los tiempos de cómputo llegan a alargarse hasta convertirse en inviables, o porque el tamaño de esos datos desborda los recursos del sistema. Por ello, esta tesis doctoral se centra en la optimización y paralelización de la factorización NMF, pero no solo a nivel teórico, sino con el objetivo de proporcionarle a la comunidad científica una nueva herramienta para el análisis de datos de origen biológico. NMF expone un alto grado de paralelismo a nivel de datos, de granularidad variable; mientras que los métodos de agrupamiento mencionados anteriormente presentan un paralelismo a nivel de cómputo, ya que las diversas instancias de NMF que se ejecutan son independientes. Por tanto, desde un punto de vista global, se plantea un modelo de optimización por capas donde se emplean diferentes tecnologías de alto rendimiento...

Multivariate Techniques in Biomechanical Analysis

This work outlines the theoretical advantages of multivariate methods in biomechanical data, validates the proposed methods and outlines new clinical findings relating to knee osteoarthritis that were made possible by this approach. New techniques were based on existing multivariate approaches, Partial Least Squares (PLS) and Non-negative Matrix Factorization (NMF) and validated using existing data sets. The new techniques developed, PCA-PLS-LDA (Principal Component Analysis – Partial Least Squares – Linear Discriminant Analysis), PCA-PLS-MLR (Principal Component Analysis – Partial Least Squares –Multiple Linear Regression) and Waveform Similarity (based on NMF) were developed to address the challenging characteristics of biomechanical data, variability and correlation. As a result, these new structure-seeking technique revealed new clinical findings. The first new clinical finding relates to the relationship between pain, radiographic severity and mechanics. Simultaneous analysis of pain and radiographic severity outcomes, a first in biomechanics, revealed that the knee adduction moment’s relationship to radiographic features is mediated by pain in subjects with moderate osteoarthritis. The second clinical finding was quantifying the importance of neuromuscular patterns in brace effectiveness for patients with knee osteoarthritis. I found that brace effectiveness was more related to the patient’s unbraced neuromuscular patterns than it was to mechanics, and that these neuromuscular patterns were more complicated than simply increased overall muscle activity, as previously thought.

On S-matrix factorization of the Landau-Lifshitz model

We consider the three-particle scattering S-matrix for the Landau-Lifshitz model by directly computing the set of the Feynman diagrams up to the second order. We show, following the analogous computations for the non-linear Schrdinger model [1, 2], that the three-particle S-matrix is factorizable in the first non-trivial order.

Mathematical approach for predicting non-negative tristimulus values using the CAT02 chromatic adaptation transform

It has been reported that for certain colour samples, the chromatic adaptation transform CAT02 imbedded in the CIECAM02 colour appearance model predicts corresponding colours with negative tristimulus values (TSVs), which can cause problems in certain applications. To overcome this problem, a mathematical approach is proposed for modifying CAT02. This approach combines a non-negativity constraint for the TSVs of corresponding colours with the minimization of the colour differences between those values for the corresponding colours obtained by visual observations and the TSVs of the corresponding colours predicted by the model, which is a constrained non-linear optimization problem. By solving the non-linear optimization problem, a new matrix is found. The performance of the CAT02 transform with various matrices including the original CAT02 matrix, and the new matrix are tested using visual datasets and the optimum colours. Test results show that the CAT02 with the new matrix predicted corresponding colours without negative TSVs for all optimum colours and the colour matching functions of the two CIE standard observers under the test illuminants considered. However, the accuracy with the new matrix for predicting the visual data is approximately 1 CIELAB colour difference unit worse compared with the original CAT02. This indicates that accuracy has to be sacrificed to achieve the non-negativity constraint for the TSVs of the corresponding colours.

Cost sharing solutions defined by non-negative eigenvectors

The problem of sharing a cost M among n individuals, identified by some characteristic ci∈R+,ci∈R+, appears in many real situations. Two important proposals on how to share the cost are the egalitarian and the proportional solutions. In different situations a combination of both distributions provides an interesting approach to the cost sharing problem. In this paper we obtain a family of (compromise) solutions associated to the Perron’s eigenvectors of Levinger’s transformations of a characteristics matrix A. This family includes both the egalitarian and proportional solutions, as well as a set of suitable intermediate proposals, which we analyze in some specific contexts, as claims problems and inventory cost games.

Local non-negative initial data scalar characterization of the Kerr solution

For any vacuum initial data set, we define a local, non-negative scalar quantity which vanishes at every point of the data hypersurface if and only if the data are Kerr initial data. Our scalar quantity only depends on the quantities used to construct the vacuum initial data set which are the Riemannian metric defined on the initial data hypersurface and a symmetric tensor which plays the role of the second fundamental form of the embedded initial data hypersurface. The dependency is algorithmic in the sense that given the initial data one can compute the scalar quantity by algebraic and differential manipulations, being thus suitable for an implementation in a numerical code. The scalar could also be useful in studies of the non-linear stability of the Kerr solution because it serves to measure the deviation of a vacuum initial data set from the Kerr initial data in a local and algorithmic way.

Product autoregressive models for non-negative variables

When variables in time series context are non-negative, such as for volatility, survival time or wave heights, a multiplicative autoregressive model of the type Xt = Xα t−1Vt , 0 ≤ α < 1, t = 1, 2, . . . may give the preferred dependent structure. In this paper, we study the properties of such models and propose methods for parameter estimation. Explicit solutions of the model are obtained in the case of gamma marginal distribution