A methodological approach for algorithmic composition systems' parameter spaces aesthetic exploration

Algorithmic composition is the process of creating musical material by means of formal methods. As a consequence of its design, algorithmic composition systems are (explicitly or implicitly) described in terms of parameters. Thus, parameter space exploration plays a key role in learning the system's capabilities. However, in the computer music field, this task has received little attention. This is due in part, because the produced changes on the human perception of the outputs, as a response to changes on the parameters, could be highly nonlinear, therefore models with strongly predictable outputs are needed. The present work describes a methodology for the human perceptual (or aesthetic) exploration of generative systems' parameter spaces. As the systems' outputs are intended to produce an aesthetic experience on humans, audition plays a central role in the process. The methodology starts from a set of parameter combinations which are perceptually evaluated by the user. The sampling process of such combinations depends on the system under study and possible on heuristic considerations. The evaluated set is processed by a compaction algorithm able to generate linguistic rules describing the distinct perceptions (classes) of the user evaluation. The semantic level of the extracted rules allows for interpretability, while showing great potential in describing high and low-level musical entities. As the resulting rules represent discrete points in the parameter space, further possible extensions for interpolation between points are also discussed. Finally, some practical implementations and paths for further research are presented.Peer ReviewedPostprint (author's final draft

Charting perceptual spaces with fuzzy rules

Algorithmic music nowadays performs domain specific tasks for which classical algorithms do not offer optimal solutions or require user's expertise. Among these tasks is the extraction of models from data that offer an understanding of the underlying behavior, providing a quick and easy to use way to explore the data for first (sometimes on-the-fly) insights. Learning rules from examples is an approach often used to achieve this goal. However, together with the aforementioned requirements algorithmic composition needs to create new material so that it is perceived as consistent with the material of the data. In addition, the input data sets are usually small because the human is the bottleneck when generating them. In this contribution we present a fuzzy rule induction algorithm focused on generalizing a set of data, complying with the previous requirements, that offers good results for small data sets. For its evaluation -in a field where there are no benchmarks available - data sets obtained during user tests were used. The visual representation offered by the fuzzy chart helps to reduce the cognitive complexity of the devices used in algorithmic music. The results obtained show that this approach is promising for future developments.Peer ReviewedPostprint (author's final draft

Modeling perceptual categories of parametric musical systems

In computer music fields, such as algorithmic composition and live coding, the aural exploration of parameter combinations is the process through which systems’ capabilities are learned and the material for different musical tasks is selected and classified. Despite its importance, few models of this process have been proposed. Here, a rule extraction algorithm is presented. It works with data obtained during a user auditory exploration of parameters, in which specific perceptual categories are searched. The extracted rules express complex, but general relationships, among parameter values and categories. Its formation is controlled by functions that govern the data grouping. These are given by the user through heuristic considerations. The rules are used to build two more general models: a set of “extended or Inference Rules” and a fuzzy classifier which allow the user to infer unheard combinations of parameters consistent with the preselected categories from the extended rules and between the limits of the explored parameter space, respectively. To evaluate the models, user tests were performed. The constructed models allow to reduce complexity in operating the systems, by providing a set of “presets” for different categories, and extend compositional capacities through the inferred combinations, alongside a structured representation of the information.Peer ReviewedPostprint (author's final draft

On-the-fly synthesizer programming with rule learning

This manuscript explores automatic programming of sound synthesis algorithms within the context of the performative artistic practice known as live coding. Writing source code in an improvised way to create music or visuals became an instrument the moment affordable computers were able to perform real-time sound synthesis with languages that keep their interpreter running. Ever since, live coding has dealt with real time programming of synthesis algorithms. For that purpose, one possibility is an algorithm that automatically creates variations out of a few presets selected by the user. However, the need for real-time feedback and the small size of the data sets (which can even be collected mid-performance) are constraints that make existing automatic sound synthesizer programmers and learning algorithms unfeasible. Also, the design of such algorithms is not oriented to create variations of a sound but rather to find the synthesizer parameters that match a given one. Other approaches create representations of the space of possible sounds, allowing the user to explore it by means of interactive evolution. Even though these systems are exploratory-oriented, they require longer run-times. This thesis investigates inductive rule learning for on-the-fly synthesizer programming. This approach is conceptually different from those found in both synthesizer programming and live coding literature. Rule models offer interpretability and allow working with the parameter values of the synthesis algorithms (even with symbolic data), making preprocessing unnecessary. RuLer, the proposed learning algorithm, receives a dataset containing user labeled combinations of parameter values of a synthesis algorithm. Among those combinations sharing the same label, it analyses the patterns based on dissimilarity. These patterns are described as an IF-THEN rule model. The algorithm parameters provide control to define what is considered a pattern. As patterns are the base for inducting new parameter settings, the algorithm parameters control the degree of consistency of the inducted settings respect to the original input data. An algorithm (named FuzzyRuLer) able to extend IF-THEN rules to hyperrectangles, which in turn are used as the cores of membership functions, is presented. The resulting fuzzy rule model creates a map of the entire input feature space. For such a pursuit, the algorithm generalizes the logical rules solving the contradictions by following a maximum volume heuristics. Across the manuscript it is discussed how, when machine learning algorithms are used as creative tools, glitches, errors or inaccuracies produced by the resulting models are sometimes desirable as they might offer novel, unpredictable results. The evaluation of the algorithms follows two paths. The first focuses on user tests. The second responds to the fact that this work was carried out within the computer science department and is intended to provide a broader, nonspecific domain evaluation of the algorithms performance using extrinsic benchmarks (i.e not belonging to a synthesizer's domain) for cross validation and minority oversampling. In oversampling tasks, using imbalanced datasets, the algorithm yields state-of-the-art results. Moreover, the synthetic points produced are significantly different from those created by the other algorithms and perform (controlled) exploration of more distant regions. Finally, accompanying the research, various performances, concerts and an album were produced with the algorithms and examples of this thesis. The reviews received and collections where the album has been featured show a positive reception within the community. Together, these evaluations suggest that rule learning is both an effective method and a promising path for further research.Aquest manuscrit explora la programació automàtica d’algorismes de síntesi de so dins del context de la pràctica artística performativa coneguda com a live coding. L'escriptura improvisada de codi font per crear música o visuals es va convertir en un instrument en el moment en què els ordinadors van poder realitzar síntesis de so en temps real amb llenguatges que mantenien el seu intèrpret en funcionament. D'aleshores ençà, el live coding comporta la programació en temps real d’algorismes de síntesi de so. Per a aquest propòsit, una possibilitat és tenir un algorisme que creï automàticament variacions a partir d'alguns presets seleccionats. No obstant, la necessitat de retroalimentació en temps real i la petita mida dels conjunts de dades són restriccions que fan que els programadors automàtics de sintetitzadors de so i els algorismes d’aprenentatge no siguin factibles d’utilitzar. A més, el seu disseny no està orientat a crear variacions d'un so, sinó a trobar els paràmetres del sintetitzador que aplicats a l'algorisme de síntesi produeixen un so determinat (target). Altres enfocaments creen representacions de l'espai de sons possibles, per permetre a l'usuari explorar-lo mitjançant l'evolució interactiva, però requereixen temps més llargs. Aquesta tesi investiga l'aprenentatge inductiu de regles per a la programació on-the-fly de sintetitzadors. Aquest enfocament és conceptualment diferent dels que es troben a la literatura. Els models de regles ofereixen interpretabilitat i permeten treballar amb els valors dels paràmetres dels algorismes de síntesi, sense processament previ. RuLer, l'algorisme d'aprenentatge proposat, rep dades amb combinacions etiquetades per l'usuari dels valors dels paràmetres d'un algorisme de síntesi. A continuació, analitza els patrons, basats en la dissimilitud, entre les combinacions de cada etiqueta. Aquests patrons es descriuen com un model de regles IF-THEN. Els paràmetres de l'algorisme proporcionen control per definir el que es considera un patró. Llavors, controlen el grau de consistència dels nous paràmetres de síntesi induïts respecte a les dades d'entrada originals. A continuació, es presenta un algorisme (FuzzyRuLer) capaç d’estendre les regles IF-THEN a hiperrectangles, que al seu torn s’utilitzen com a nuclis de funcions de pertinença. El model de regles difuses resultant crea un mapa complet de l'espai de la funció d'entrada. Per això, l'algorisme generalitza les regles lògiques seguint una heurística de volum màxim. Al llarg del manuscrit es discuteix com, quan s’utilitzen algorismes d’aprenentatge automàtic com a eines creatives, de vegades són desitjables glitches, errors o imprecisions produïdes pels models resultants, ja que poden oferir nous resultats imprevisibles. L'avaluació dels algorismes segueix dos camins. El primer es centra en proves d'usuari. El segon, que respon al fet que aquest treball es va dur a terme dins del departament de ciències de la computació, pretén proporcionar una avaluació més àmplia, no específica d'un domini, del rendiment dels algorismes mitjançant benchmarks extrínsecs utilitzats per cross-validation i minority oversampling. En tasques d'oversampling, mitjançant imbalanced data sets, l'algorisme proporciona resultats equiparables als de l'estat de l'art. A més, els punts sintètics produïts són significativament diferents als creats pels altres algorismes i realitzen exploracions (controlades) de regions més llunyanesEste manuscrito explora la programación automática de algoritmos de síntesis de sonido dentro del contexto de la práctica artística performativa conocida como live coding. La escritura de código fuente de forma improvisada para crear música o imágenes, se convirtió en un instrumento en el momento en que las computadoras asequibles pudieron realizar síntesis de sonido en tiempo real con lenguajes que mantuvieron su interprete en funcionamiento. Desde entonces, el live coding ha implicado la programación en tiempo real de algoritmos de síntesis. Para ese propósito, una posibilidad es tener un algoritmo que cree automáticamente variaciones a partir de unos pocos presets seleccionados. Sin embargo, la necesidad de retroalimentación en tiempo real y el pequeño tamaño de los conjuntos de datos (que incluso pueden recopilarse durante la misma actuación), limitan el uso de los algoritmos existentes, tanto de programación automática de sintetizadores como de aprendizaje de máquina. Además, el diseño de dichos algoritmos no está orientado a crear variaciones de un sonido, sino a encontrar los parámetros del sintetizador que coincidan con un sonido dado. Otros enfoques crean representaciones del espacio de posibles sonidos, para permitir al usuario explorarlo mediante evolución interactiva. Aunque estos sistemas están orientados a la exploración, requieren tiempos más largos. Esta tesis investiga el aprendizaje inductivo de reglas para la programación de sintetizadores on-the-fly. Este enfoque es conceptualmente diferente de los que se encuentran en la literatura, tanto de programación de sintetizadores como de live coding. Los modelos de reglas ofrecen interpretabilidad y permiten trabajar con los valores de los parámetros de los algoritmos de síntesis (incluso con datos simbólicos), haciendo innecesario el preprocesamiento. RuLer, el algoritmo de aprendizaje propuesto, recibe un conjunto de datos que contiene combinaciones, etiquetadas por el usuario, de valores de parámetros de un algoritmo de síntesis. Luego, analiza los patrones, en función de la disimilitud, entre las combinaciones de cada etiqueta. Estos patrones se describen como un modelo de reglas lógicas IF-THEN. Los parámetros del algoritmo proporcionan el control para definir qué se considera un patrón. Como los patrones son la base para inducir nuevas configuraciones de parámetros, los parámetros del algoritmo controlan también el grado de consistencia de las configuraciones inducidas con respecto a los datos de entrada originales. Luego, se presenta un algoritmo (llamado FuzzyRuLer) capaz de extender las reglas lógicas tipo IF-THEN a hiperrectángulos, que a su vez se utilizan como núcleos de funciones de pertenencia. El modelo de reglas difusas resultante crea un mapa completo del espacio de las clases de entrada. Para tal fin, el algoritmo generaliza las reglas lógicas resolviendo las contradicciones utilizando una heurística de máximo volumen. A lo largo del manuscrito se analiza cómo, cuando los algoritmos de aprendizaje automático se utilizan como herramientas creativas, los glitches, errores o inexactitudes producidas por los modelos resultantes son a veces deseables, ya que pueden ofrecer resultados novedosos e impredecibles. La evaluación de los algoritmos sigue dos caminos. El primero se centra en pruebas de usuario. El segundo, responde al hecho de que este trabajo se llevó a cabo dentro del departamento de ciencias de la computación y está destinado a proporcionar una evaluación más amplia, no de dominio específica, del rendimiento de los algoritmos utilizando beanchmarks extrínsecos para cross-validation y oversampling. En estas últimas pruebas, utilizando conjuntos de datos no balanceados, el algoritmo produce resultados equiparables a los del estado del arte. Además, los puntos sintéticos producidos son significativamente diferentes de los creados por los otros algoritmos y realizan una exploración (controlada) de regiones más distantes. Finalmente, acompañando la investigación, realicé diversas presentaciones, conciertos y un ´álbum utilizando los algoritmos y ejemplos de esta tesis. Las críticas recibidas y las listas donde se ha presentado el álbum muestran una recepción positiva de la comunidad. En conjunto, estas evaluaciones sugieren que el aprendizaje de reglas es al mismo tiempo un método eficaz y un camino prometedor para futuras investigaciones.Postprint (published version

Model-Based Environmental Visual Perception for Humanoid Robots

The visual perception of a robot should answer two fundamental questions: What? and Where? In order to properly and efficiently reply to these questions, it is essential to establish a bidirectional coupling between the external stimuli and the internal representations. This coupling links the physical world with the inner abstraction models by sensor transformation, recognition, matching and optimization algorithms. The objective of this PhD is to establish this sensor-model coupling

ROBUST SPEAKER RECOGNITION BASED ON LATENT VARIABLE MODELS

Automatic speaker recognition in uncontrolled environments is a very challenging task due to channel distortions, additive noise and reverberation. To address these issues, this thesis studies probabilistic latent variable models of short-term spectral information that leverage large amounts of data to achieve robustness in challenging conditions. Current speaker recognition systems represent an entire speech utterance as a single point in a high-dimensional space. This representation is known as "supervector". This thesis starts by analyzing the properties of this representation. A novel visualization procedure of supervectors is presented by which qualitative insight about the information being captured is obtained. We then propose the use of an overcomplete dictionary to explicitly decompose a supervector into a speaker-specific component and an undesired variability component. An algorithm to learn the dictionary from a large collection of data is discussed and analyzed. A subset of the entries of the dictionary is learned to represent speaker-specific information and another subset to represent distortions. After encoding the supervector as a linear combination of the dictionary entries, the undesired variability is removed by discarding the contribution of the distortion components. This paradigm is closely related to the previously proposed paradigm of Joint Factor Analysis modeling of supervectors. We establish a connection between the two approaches and show how our proposed method provides improvements in terms of computation and recognition accuracy. An alternative way to handle undesired variability in supervector representations is to first project them into a lower dimensional space and then to model them in the reduced subspace. This low-dimensional projection is known as "i-vector". Unfortunately, i-vectors exhibit non-Gaussian behavior, and direct statistical modeling requires the use of heavy-tailed distributions for optimal performance. These approaches lack closed-form solutions, and therefore are hard to analyze. Moreover, they do not scale well to large datasets. Instead of directly modeling i-vectors, we propose to first apply a non-linear transformation and then use a linear-Gaussian model. We present two alternative transformations and show experimentally that the transformed i-vectors can be optimally modeled by a simple linear-Gaussian model (factor analysis). We evaluate our method on a benchmark dataset with a large amount of channel variability and show that the results compare favorably against the competitors. Also, our approach has closed-form solutions and scales gracefully to large datasets. Finally, a multi-classifier architecture trained on a multicondition fashion is proposed to address the problem of speaker recognition in the presence of additive noise. A large number of experiments are conducted to analyze the proposed architecture and to obtain guidelines for optimal performance in noisy environments. Overall, it is shown that multicondition training of multi-classifier architectures not only produces great robustness in the anticipated conditions, but also generalizes well to unseen conditions

Functional Sensory Representations of Natural Stimuli: the Case of Spatial Hearing

In this thesis I attempt to explain mechanisms of neuronal coding in the auditory system as a form of adaptation to statistics of natural stereo sounds. To this end I analyse recordings of real-world auditory environments and construct novel statistical models of these data. I further compare regularities present in natural stimuli with known, experimentally observed neuronal mechanisms of spatial hearing. In a more general perspective, I use binaural auditory system as a starting point to consider the notion of function implemented by sensory neurons. In particular I argue for two, closely-related tenets: 1. The function of sensory neurons can not be fully elucidated without understanding statistics of natural stimuli they process. 2. Function of sensory representations is determined by redundancies present in the natural sensory environment. I present the evidence in support of the first tenet by describing and analysing marginal statistics of natural binaural sound. I compare observed, empirical distributions with knowledge from reductionist experiments. Such comparison allows to argue that the complexity of the spatial hearing task in the natural environment is much higher than analytic, physics-based predictions. I discuss the possibility that early brain stem circuits such as LSO and MSO do not \"compute sound localization\" as is often being claimed in the experimental literature. I propose that instead they perform a signal transformation, which constitutes the first step of a complex inference process. To support the second tenet I develop a hierarchical statistical model, which learns a joint sparse representation of amplitude and phase information from natural stereo sounds. I demonstrate that learned higher order features reproduce properties of auditory cortical neurons, when probed with spatial sounds. Reproduced aspects were hypothesized to be a manifestation of a fine-tuned computation specific to the sound-localization task. Here it is demonstrated that they rather reflect redundancies present in the natural stimulus. Taken together, results presented in this thesis suggest that efficient coding is a strategy useful for discovering structures (redundancies) in the input data. Their meaning has to be determined by the organism via environmental feedback

Multimodal dynamics : self-supervised learning in perceptual and motor systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (leaves 178-192).This thesis presents a self-supervised framework for perceptual and motor learning based upon correlations in different sensory modalities. The brain and cognitive sciences have gathered an enormous body of neurological and phenomenological evidence in the past half century demonstrating the extraordinary degree of interaction between sensory modalities during the course of ordinary perception. We develop a framework for creating artificial perceptual systems that draws on these findings, where the primary architectural motif is the cross-modal transmission of perceptual information to enhance each sensory channel individually. We present self-supervised algorithms for learning perceptual grounding, intersensory influence, and sensorymotor coordination, which derive training signals from internal cross-modal correlations rather than from external supervision. Our goal is to create systems that develop by interacting with the world around them, inspired by development in animals. We demonstrate this framework with: (1) a system that learns the number and structure of vowels in American English by simultaneously watching and listening to someone speak. The system then cross-modally clusters the correlated auditory and visual data.(cont.) It has no advance linguistic knowledge and receives no information outside of its sensory channels. This work is the first unsupervised acquisition of phonetic structure of which we are aware, outside of that done by human infants. (2) a system that learns to sing like a zebra finch, following the developmental stages of a juvenile zebra finch. It first learns the song of an adult male and then listens to its own initially nascent attempts at mimicry through an articulatory synthesizer. In acquiring the birdsong to which it was initially exposed, this system demonstrates self-supervised sensorimotor learning. It also demonstrates afferent and efferent equivalence - the system learns motor maps with the same computational framework used for learning sensory maps.by Michael Harlan Coen.Ph.D

Machine Learning

Machine Learning can be defined in various ways related to a scientific domain concerned with the design and development of theoretical and implementation tools that allow building systems with some Human Like intelligent behavior. Machine learning addresses more specifically the ability to improve automatically through experience

Discriminant feature pursuit: from statistical learning to informative learning.

Lin Dahua.Thesis (M.Phil.)--Chinese University of Hong Kong, 2006.Includes bibliographical references (leaves 233-250).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.iiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- The Problem We are Facing --- p.1Chapter 1.2 --- Generative vs. Discriminative Models --- p.2Chapter 1.3 --- Statistical Feature Extraction: Success and Challenge --- p.3Chapter 1.4 --- Overview of Our Works --- p.5Chapter 1.4.1 --- New Linear Discriminant Methods: Generalized LDA Formulation and Performance-Driven Sub space Learning --- p.5Chapter 1.4.2 --- Coupled Learning Models: Coupled Space Learning and Inter Modality Recognition --- p.6Chapter 1.4.3 --- Informative Learning Approaches: Conditional Infomax Learning and Information Chan- nel Model --- p.6Chapter 1.5 --- Organization of the Thesis --- p.8Chapter I --- History and Background --- p.10Chapter 2 --- Statistical Pattern Recognition --- p.11Chapter 2.1 --- Patterns and Classifiers --- p.11Chapter 2.2 --- Bayes Theory --- p.12Chapter 2.3 --- Statistical Modeling --- p.14Chapter 2.3.1 --- Maximum Likelihood Estimation --- p.14Chapter 2.3.2 --- Gaussian Model --- p.15Chapter 2.3.3 --- Expectation-Maximization --- p.17Chapter 2.3.4 --- Finite Mixture Model --- p.18Chapter 2.3.5 --- A Nonparametric Technique: Parzen Windows --- p.21Chapter 3 --- Statistical Learning Theory --- p.24Chapter 3.1 --- Formulation of Learning Model --- p.24Chapter 3.1.1 --- Learning: Functional Estimation Model --- p.24Chapter 3.1.2 --- Representative Learning Problems --- p.25Chapter 3.1.3 --- Empirical Risk Minimization --- p.26Chapter 3.2 --- Consistency and Convergence of Learning --- p.27Chapter 3.2.1 --- Concept of Consistency --- p.27Chapter 3.2.2 --- The Key Theorem of Learning Theory --- p.28Chapter 3.2.3 --- VC Entropy --- p.29Chapter 3.2.4 --- Bounds on Convergence --- p.30Chapter 3.2.5 --- VC Dimension --- p.35Chapter 4 --- History of Statistical Feature Extraction --- p.38Chapter 4.1 --- Linear Feature Extraction --- p.38Chapter 4.1.1 --- Principal Component Analysis (PCA) --- p.38Chapter 4.1.2 --- Linear Discriminant Analysis (LDA) --- p.41Chapter 4.1.3 --- Other Linear Feature Extraction Methods --- p.46Chapter 4.1.4 --- Comparison of Different Methods --- p.48Chapter 4.2 --- Enhanced Models --- p.49Chapter 4.2.1 --- Stochastic Discrimination and Random Subspace --- p.49Chapter 4.2.2 --- Hierarchical Feature Extraction --- p.51Chapter 4.2.3 --- Multilinear Analysis and Tensor-based Representation --- p.52Chapter 4.3 --- Nonlinear Feature Extraction --- p.54Chapter 4.3.1 --- Kernelization --- p.54Chapter 4.3.2 --- Dimension reduction by Manifold Embedding --- p.56Chapter 5 --- Related Works in Feature Extraction --- p.59Chapter 5.1 --- Dimension Reduction --- p.59Chapter 5.1.1 --- Feature Selection --- p.60Chapter 5.1.2 --- Feature Extraction --- p.60Chapter 5.2 --- Kernel Learning --- p.61Chapter 5.2.1 --- Basic Concepts of Kernel --- p.61Chapter 5.2.2 --- The Reproducing Kernel Map --- p.62Chapter 5.2.3 --- The Mercer Kernel Map --- p.64Chapter 5.2.4 --- The Empirical Kernel Map --- p.65Chapter 5.2.5 --- Kernel Trick and Kernelized Feature Extraction --- p.66Chapter 5.3 --- Subspace Analysis --- p.68Chapter 5.3.1 --- Basis and Subspace --- p.68Chapter 5.3.2 --- Orthogonal Projection --- p.69Chapter 5.3.3 --- Orthonormal Basis --- p.70Chapter 5.3.4 --- Subspace Decomposition --- p.70Chapter 5.4 --- Principal Component Analysis --- p.73Chapter 5.4.1 --- PCA Formulation --- p.73Chapter 5.4.2 --- Solution to PCA --- p.75Chapter 5.4.3 --- Energy Structure of PCA --- p.76Chapter 5.4.4 --- Probabilistic Principal Component Analysis --- p.78Chapter 5.4.5 --- Kernel Principal Component Analysis --- p.81Chapter 5.5 --- Independent Component Analysis --- p.83Chapter 5.5.1 --- ICA Formulation --- p.83Chapter 5.5.2 --- Measurement of Statistical Independence --- p.84Chapter 5.6 --- Linear Discriminant Analysis --- p.85Chapter 5.6.1 --- Fisher's Linear Discriminant Analysis --- p.85Chapter 5.6.2 --- Improved Algorithms for Small Sample Size Problem . --- p.89Chapter 5.6.3 --- Kernel Discriminant Analysis --- p.92Chapter II --- Improvement in Linear Discriminant Analysis --- p.100Chapter 6 --- Generalized LDA --- p.101Chapter 6.1 --- Regularized LDA --- p.101Chapter 6.1.1 --- Generalized LDA Implementation Procedure --- p.101Chapter 6.1.2 --- Optimal Nonsingular Approximation --- p.103Chapter 6.1.3 --- Regularized LDA algorithm --- p.104Chapter 6.2 --- A Statistical View: When is LDA optimal? --- p.105Chapter 6.2.1 --- Two-class Gaussian Case --- p.106Chapter 6.2.2 --- Multi-class Cases --- p.107Chapter 6.3 --- Generalized LDA Formulation --- p.108Chapter 6.3.1 --- Mathematical Preparation --- p.108Chapter 6.3.2 --- Generalized Formulation --- p.110Chapter 7 --- Dynamic Feedback Generalized LDA --- p.112Chapter 7.1 --- Basic Principle --- p.112Chapter 7.2 --- Dynamic Feedback Framework --- p.113Chapter 7.2.1 --- Initialization: K-Nearest Construction --- p.113Chapter 7.2.2 --- Dynamic Procedure --- p.115Chapter 7.3 --- Experiments --- p.115Chapter 7.3.1 --- Performance in Training Stage --- p.116Chapter 7.3.2 --- Performance on Testing set --- p.118Chapter 8 --- Performance-Driven Subspace Learning --- p.119Chapter 8.1 --- Motivation and Principle --- p.119Chapter 8.2 --- Performance-Based Criteria --- p.121Chapter 8.2.1 --- The Verification Problem and Generalized Average Margin --- p.122Chapter 8.2.2 --- Performance Driven Criteria based on Generalized Average Margin --- p.123Chapter 8.3 --- Optimal Subspace Pursuit --- p.125Chapter 8.3.1 --- Optimal threshold --- p.125Chapter 8.3.2 --- Optimal projection matrix --- p.125Chapter 8.3.3 --- Overall procedure --- p.129Chapter 8.3.4 --- Discussion of the Algorithm --- p.129Chapter 8.4 --- Optimal Classifier Fusion --- p.130Chapter 8.5 --- Experiments --- p.131Chapter 8.5.1 --- Performance Measurement --- p.131Chapter 8.5.2 --- Experiment Setting --- p.131Chapter 8.5.3 --- Experiment Results --- p.133Chapter 8.5.4 --- Discussion --- p.139Chapter III --- Coupled Learning of Feature Transforms --- p.140Chapter 9 --- Coupled Space Learning --- p.141Chapter 9.1 --- Introduction --- p.142Chapter 9.1.1 --- What is Image Style Transform --- p.142Chapter 9.1.2 --- Overview of our Framework --- p.143Chapter 9.2 --- Coupled Space Learning --- p.143Chapter 9.2.1 --- Framework of Coupled Modelling --- p.143Chapter 9.2.2 --- Correlative Component Analysis --- p.145Chapter 9.2.3 --- Coupled Bidirectional Transform --- p.148Chapter 9.2.4 --- Procedure of Coupled Space Learning --- p.151Chapter 9.3 --- Generalization to Mixture Model --- p.152Chapter 9.3.1 --- Coupled Gaussian Mixture Model --- p.152Chapter 9.3.2 --- Optimization by EM Algorithm --- p.152Chapter 9.4 --- Integrated Framework for Image Style Transform --- p.154Chapter 9.5 --- Experiments --- p.156Chapter 9.5.1 --- Face Super-resolution --- p.156Chapter 9.5.2 --- Portrait Style Transforms --- p.157Chapter 10 --- Inter-Modality Recognition --- p.162Chapter 10.1 --- Introduction to the Inter-Modality Recognition Problem . . . --- p.163Chapter 10.1.1 --- What is Inter-Modality Recognition --- p.163Chapter 10.1.2 --- Overview of Our Feature Extraction Framework . . . . --- p.163Chapter 10.2 --- Common Discriminant Feature Extraction --- p.165Chapter 10.2.1 --- Formulation of the Learning Problem --- p.165Chapter 10.2.2 --- Matrix-Form of the Objective --- p.168Chapter 10.2.3 --- Solving the Linear Transforms --- p.169Chapter 10.3 --- Kernelized Common Discriminant Feature Extraction --- p.170Chapter 10.4 --- Multi-Mode Framework --- p.172Chapter 10.4.1 --- Multi-Mode Formulation --- p.172Chapter 10.4.2 --- Optimization Scheme --- p.174Chapter 10.5 --- Experiments --- p.176Chapter 10.5.1 --- Experiment Settings --- p.176Chapter 10.5.2 --- Experiment Results --- p.177Chapter IV --- A New Perspective: Informative Learning --- p.180Chapter 11 --- Toward Information Theory --- p.181Chapter 11.1 --- Entropy and Mutual Information --- p.181Chapter 11.1.1 --- Entropy --- p.182Chapter 11.1.2 --- Relative Entropy (Kullback Leibler Divergence) --- p.184Chapter 11.2 --- Mutual Information --- p.184Chapter 11.2.1 --- Definition of Mutual Information --- p.184Chapter 11.2.2 --- Chain rules --- p.186Chapter 11.2.3 --- Information in Data Processing --- p.188Chapter 11.3 --- Differential Entropy --- p.189Chapter 11.3.1 --- Differential Entropy of Continuous Random Variable . --- p.189Chapter 11.3.2 --- Mutual Information of Continuous Random Variable . --- p.190Chapter 12 --- Conditional Infomax Learning --- p.191Chapter 12.1 --- An Overview --- p.192Chapter 12.2 --- Conditional Informative Feature Extraction --- p.193Chapter 12.2.1 --- Problem Formulation and Features --- p.193Chapter 12.2.2 --- The Information Maximization Principle --- p.194Chapter 12.2.3 --- The Information Decomposition and the Conditional Objective --- p.195Chapter 12.3 --- The Efficient Optimization --- p.197Chapter 12.3.1 --- Discrete Approximation Based on AEP --- p.197Chapter 12.3.2 --- Analysis of Terms and Their Derivatives --- p.198Chapter 12.3.3 --- Local Active Region Method --- p.200Chapter 12.4 --- Bayesian Feature Fusion with Sparse Prior --- p.201Chapter 12.5 --- The Integrated Framework for Feature Learning --- p.202Chapter 12.6 --- Experiments --- p.203Chapter 12.6.1 --- A Toy Problem --- p.203Chapter 12.6.2 --- Face Recognition --- p.204Chapter 13 --- Channel-based Maximum Effective Information --- p.209Chapter 13.1 --- Motivation and Overview --- p.209Chapter 13.2 --- Maximizing Effective Information --- p.211Chapter 13.2.1 --- Relation between Mutual Information and Classification --- p.211Chapter 13.2.2 --- Linear Projection and Metric --- p.212Chapter 13.2.3 --- Channel Model and Effective Information --- p.213Chapter 13.2.4 --- Parzen Window Approximation --- p.216Chapter 13.3 --- Parameter Optimization on Grassmann Manifold --- p.217Chapter 13.3.1 --- Grassmann Manifold --- p.217Chapter 13.3.2 --- Conjugate Gradient Optimization on Grassmann Manifold --- p.219Chapter 13.3.3 --- Computation of Gradient --- p.221Chapter 13.4 --- Experiments --- p.222Chapter 13.4.1 --- A Toy Problem --- p.222Chapter 13.4.2 --- Face Recognition --- p.223Chapter 14 --- Conclusion --- p.23