Quadratic Discriminant Analysis Revisited

In this thesis, we revisit quadratic discriminant analysis (QDA), a standard classification method. Specifically, we investigate the parameter estimation and dimension reduction problems for QDA. Traditionally, the parameters of QDA are estimated generatively; that is the parameters are estimated by maximizing the joint likelihood of observations and their labels. In practice, classical QDA, though computationally efficient, often underperforms discriminative classifiers, such as SVM, Boosting methods, and logistic regression. Motivated by recent research on hybrid generative/discriminative learning, we propose to estimate the parameters of QDA by minimizing a convex combination of negative joint log-likelihood and negative conditional log-likelihood of observations and their labels. For this purpose, we propose an iterative majorize-minimize (MM) algorithm for classifiers of which conditional distributions are from the exponential family; in each iteration of the MM algorithm, a convex optimization problem needs to be solved. To solve the convex problem specially derived for QDA, we propose a block-coordinate descent algorithm that sequentially updates the parameters of QDA; in each update, we present a trust region method for solving optimal estimations, of which we have closed form solutions in each iteration. Numerical experiments show: 1) the hybrid approach to QDA is competitive with, and in some cases significant better than other approaches to QDA, SVM with polynomial kernel ($d=2$) and logistic regression with linear and quadratic features; 2) in many cases, our optimization method converges faster to equal or better optimums than the conjugate gradient method used in the literature. Dimension reduction methods are commonly used to extract more compact features in the hope to build more efficient and possibly more robust classifiers. It is well known that Fisher\u27s discriminant analysis generates optimal lower dimensional features for linear discriminant analysis. However, ...for QDA, where so far there has been no universally accepted dimension-reduction technique in the literature\u27\u27, though considerable efforts have been made. To construct a dimension reduction method for QDA, we generalize the Fukunaga-Koontz transformation, and propose novel affine feature extraction (AFE) methods for binary QDA. The proposed AFE methods have closed-form solutions and thus can be solved efficiently. We show that 1) the AFE methods have desired geometrical, statistical and information-theoretical properties; and 2) the AFE methods generalize dimension reduction methods for LDA and QDA with equal means. Numerical experiments show that the new proposed AFE method is competitive with, and in some cases significantly better than some commonly used linear dimension reduction techniques for QDA in the literature

Scalable Tools for Information Extraction and Causal Modeling of Neural Data

Systems neuroscience has entered in the past 20 years into an era that one might call "large scale systems neuroscience". From tuning curves and single neuron recordings there has been a conceptual shift towards a more holistic understanding of how the neural circuits work and as a result how their representations produce neural tunings. With the introduction of a plethora of datasets in various scales, modalities, animals, and systems; we as a community have witnessed invaluable insights that can be gained from the collective view of a neural circuit which was not possible with small scale experimentation. The concurrency of the advances in neural recordings such as the production of wide field imaging technologies and neuropixels with the developments in statistical machine learning and specifically deep learning has brought system neuroscience one step closer to data science. With this abundance of data, the need for developing computational models has become crucial. We need to make sense of the data, and thus we need to build models that are constrained up to the acceptable amount of biological detail and probe those models in search of neural mechanisms. This thesis consists of sections covering a wide range of ideas from computer vision, statistics, machine learning, and dynamical systems. But all of these ideas share a common purpose, which is to help automate neuroscientific experimentation process in different levels. In chapters 1, 2, and 3, I develop tools that automate the process of extracting useful information from raw neuroscience data in the model organism C. elegans. The goal of this is to avoid manual labor and pave the way for high throughput data collection aiming at better quantification of variability across the population of worms. Due to its high level of structural and functional stereotypy, and its relative simplicity, the nematode C. elegans has been an attractive model organism for systems and developmental research. With 383 neurons in males and 302 neurons in hermaphrodites, the positions and function of neurons is remarkably conserved across individuals. Furthermore, C. elegans remains the only organism for which a complete cellular, lineage, and anatomical map of the entire nervous system has been described for both sexes. Here, I describe the analysis pipeline that we developed for the recently proposed NeuroPAL technique in C. elegans. Our proposed pipeline consists of atlas building (chapter 1), registration, segmentation, neural tracking (chapter 2), and signal extraction (chapter 3). I emphasize that categorizing the analysis techniques as a pipeline consisting of the above steps is general and can be applied to virtually every single animal model and emerging imaging modality. I use the language of probabilistic generative modeling and graphical models to communicate the ideas in a rigorous form, therefore some familiarity with those concepts could help the reader navigate through the chapters of this thesis more easily. In chapters 4 and 5 I build models that aim to automate hypothesis testing and causal interrogation of neural circuits. The notion of functional connectivity (FC) has been instrumental in our understanding of how information propagates in a neural circuit. However, an important limitation is that current techniques do not dissociate between causal connections and purely functional connections with no mechanistic correspondence. I start chapter 4 by introducing causal inference as a unifying language for the following chapters. In chapter 4 I define the notion of interventional connectivity (IC) as a way to summarize the effect of stimulation in a neural circuit providing a more mechanistic description of the information flow. I then investigate which functional connectivity metrics are best predictive of IC in simulations and real data. Following this framework, I discuss how stimulations and interventions can be used to improve fitting and generalization properties of time series models. Building on the literature of model identification and active causal discovery I develop a switching time series model and a method for finding stimulation patterns that help the model to generalize to the vicinity of the observed neural trajectories. Finally in chapter 5 I develop a new FC metric that separates the transferred information from one variable to the other into unique and synergistic sources. In all projects, I have abstracted out concepts that are specific to the datasets at hand and developed the methods in the most general form. This makes the presented methods applicable to a broad range of datasets, potentially leading to new findings. In addition, all projects are accompanied with extensible and documented code packages, allowing theorists to repurpose the modules for novel applications and experimentalists to run analysis on their datasets efficiently and scalably. In summary my main contribution in this thesis are the following: 1) Building the first atlases of hermaphrodite and male C. elegans and developing a generic statistical framework for constructing atlases for a broad range of datasets. 2) Developing a semi-automated analysis pipeline for neural registration, segmentation, and tracking in C. elegans. 3) Extending the framework of non-negative matrix factorization to datasets with deformable motion and developing algorithms for joint tracking and signal demixing from videos of semi-immobilized C. elegans. 4) Defining the notion of interventional connectivity (IC) as a way to summarize the effect of stimulation in a neural circuit and investigating which functional connectivity metrics are best predictive of IC in simulations and real data. 5) Developing a switching time series model and a method for finding stimulation patterns that help the model to generalize to the vicinity of the observed neural trajectories. 6) Developing a new functional connectivity metric that separates the transferred information from one variable to the other into unique and synergistic sources. 7) Implementing extensible, well documented, open source code packages for each of the above contributions

Nuclear Magnetic Resonance Spectroscopy

Nuclear Magnetic Resonance (NMR) spectroscopy is a nondestructive technique that can be used to characterize a wide variety of systems. Sustained development of both methodology and instrumentation have allowed NMR to evolve as a powerful technology, with applications in pure sciences, medicine, drug development, and important branches of industry. NMR provides precise structural information down to each atom and bond in a molecule, and is the only method for the determination of structures of molecules in a solution. This book compiles a series of articles describing the application of NMR in a variety of interesting scientific challenges. The articles illustrate the versatility and flexibility of NMR

Earth Resources: A continuing bibliography with indexes, Issue 4

This bibliography lists 651 reports, articles, and other documents introduced into the NASA scientific and technical information system between October 1974 and December 1974. Emphasis is placed on the use of remote sensing and geophysical instrumentation in spacecraft and aircraft to survey and inventory natural resources and urban areas. Subject matter is grouped according to agriculture and forestry, environmental changes and cultural resources, geodesy and cartography, geology and mineral resources, hydrology and water management, data processing and distribution systems, instrumentation and sensors, and economic analysis

Advances in Possibilistic Clustering with Application to Hyperspectral Image Processing

Η ομαδοποίηση δεδομένων είναι μια εδραιωμένη μεθοδολογία ανάλυσης δεδομένων που έχει χρησιμοποιηθεί εκτενώς σε διάφορα πεδία εφαρμογών κατά τη διάρκεια των τελευταίων δεκαετιών. Η παρούσα διατριβή εστιάζει κυρίως στην ευρύτερη οικογένεια των αλγορίθμων βελτιστοποίησης κόστους και πιο συγκεκριμένα στους αλγόριθμους ομαδοποίησης με βάση τα ενδεχόμενα (Possibilistic c-Means, PCM). Συγκεκριμένα, αφού εκτίθενται τα αδύνατα σημεία τους, προτείνονται νέοι (batch και online) PCM αλγόριθμοι που αποτελούν επεκτάσεις των προηγουμένων και αντιμετωπίζουν τα αδύνατα σημεία των πρώτων. Οι προτεινόμενοι αλγόριθμοι ομαδοποίησης βασίζονται κυρίως στην υιοθέτηση των εννοιών (α) της προσαρμοστικότητας παραμέτρων (parameter adaptivity), οι οποίες στους κλασσικούς PCM αλγορίθμους παραμένουν σταθερές κατά την εκτέλεσή τους και (β) της αραιότητας (sparsity). Αυτά τα χαρακτηριστικά προσδίδουν νέα δυναμική στους προτεινόμενους αλγορίθμους οι οποίοι πλέον: (α) είναι (κατ' αρχήν) σε θέση να προσδιορίσουν τον πραγματικό αριθμό των φυσικών ομάδων που σχηματίζονται από τα δεδομένα, (β) είναι ικανοί να αποκαλύψουν την υποκείμενη δομή ομαδοποίησης, ακόμη και σε δύσκολες περιπτώσεις, όπου οι φυσικές ομάδες βρίσκονται κοντά η μία στην άλλη ή/και έχουν σημαντικές διαφορές στις διακυμάνσεις ή/και στις πυκνότητές τους και (γ) είναι εύρωστοι στην παρουσία θορύβου και ακραίων σημείων. Επίσης, δίνονται θεωρητικά αποτελέσματα σχετικά με τη σύγκλιση των προτεινόμενων αλγορίθμων, τα οποία βρίσκουν επίσης εφαρμογή και στους κλασσικούς PCM αλγορίθμους. Η δυναμική των προτεινόμενων αλγορίθμων αναδεικνύεται μέσω εκτεταμένων πειραμάτων, τόσο σε συνθετικά όσο και σε πραγματικά δεδομένα. Επιπλέον, οι αλγόριθμοι αυτοί έχουν εφαρμοστεί με επιτυχία στο ιδιαίτερα απαιτητικό πρόβλημα της ομαδοποίησης σε υπερφασματικές εικόνες. Τέλος, αναπτύχθηκε και μια μέθοδος επιλογής χαρακτηριστικών κατάλληλη για υπερφασματικές εικόνες.Clustering is a well established data analysis methodology that has been extensively used in various fields of applications during the last decades. The main focus of the present thesis is on a well-known cost-function optimization-based family of clustering algorithms, called Possibilistic C-Means (PCM) algorithms. Specifically, the shortcomings of PCM algorithms are exposed and novel batch and online PCM schemes are proposed to cope with them. These schemes rely on (i) the adaptation of certain parameters which remain fixed during the execution of the original PCMs and (ii) the adoption of sparsity. The incorporation of these two characteristics renders the proposed schemes: (a) capable, in principle, to reveal the true number of physical clusters formed by the data, (b) capable to uncover the underlying clustering structure even in demanding cases, where the physical clusters are closely located to each other and/or have significant differences in their variances and/or densities, and (c) immune to the presence of noise and outliers. Moreover, theoretical results concerning the convergence of the proposed algorithms, also applicable to the classical PCMs, are provided. The potential of the proposed methods is demonstrated via extensive experimentation on both synthetic and real data sets. In addition, they have been successfully applied on the challenging problem of clustering in HyperSpectral Images (HSIs). Finally, a feature selection technique suitable for HSIs has also been developed

Large space structures and systems in the space station era: A bibliography with indexes

Bibliographies and abstracts are listed for 1219 reports, articles, and other documents introduced into the NASA scientific and technical information system between July 1, 1990 and December 31, 1990. The purpose is to provide helpful information to the researcher, manager, and designer in technology development and mission design according to system, interactive analysis and design, structural and thermal analysis and design, structural concepts and control systems, electronics, advanced materials, assembly concepts, propulsion, and solar power satellite systems

Understanding and measuring the complex relationship between natural disasters and violence against children

Background:Violence against children is thought to increase after natural disasters, but evidence is limited. Methodological questions of how to measure possible associations are similarly unanswered. This thesis addresses these gaps by analyzing the relationship between natural disasters and violence against children, with emphasis on the 2010 Haitian earthquake,and by advancing design-based approaches for inference. Methods:The thesis is comprised of four related studies: (i) a systematic review and meta-analysis of the association between natural disasters and violence against children; (ii) a systematic review of pathways to violence; (iii) a matched-pairs analysis of violence against girls and boys after internal displacement from the 2010 Haitian earthquake; and (iv) a simulation comparing bias reduction properties and accuracy of matching designs,with sexual violence against girls displaced to a camp as the motivating example. The first two components synthesize background literature, the third component is empirical, and the fourth is methodological. Results: Themeta-analysis found no clear association or directional effect, albeit with a limited number of studies that exhibited methodological weaknesses. Further systematic review identified five pathways to violence. In delving into one aspect of exposure, internal displacement from the 2010 Haitian earthquake was not associated with long-term violence. Sensitivity analysis, however, indicated that sexual violence against girls and physical violence perpetrated by authority figures against boys were sensitive to Unobserved covariates. Full matching incorporating an instrumental variable can mitigate measured and unmeasured biases to increase the accuracy of inference. Conclusion:This thesis begins to elucidate and quantify the relationship between natural disasters and violence against children. The findings identify gaps in knowledge and pathways to violence for future study. Additional high-quality research is needed to unpack the complex relationship. The methods piloted in this thesis present promising tools, particularly after rapid-onset natural disasters and in resource scarce settings