Graph Regularized Non-negative Matrix Factorization By Maximizing Correntropy

Non-negative matrix factorization (NMF) has proved effective in many clustering and classification tasks. The classic ways to measure the errors between the original and the reconstructed matrix are $l_2$ distance or Kullback-Leibler (KL) divergence. However, nonlinear cases are not properly handled when we use these error measures. As a consequence, alternative measures based on nonlinear kernels, such as correntropy, are proposed. However, the current correntropy-based NMF only targets on the low-level features without considering the intrinsic geometrical distribution of data. In this paper, we propose a new NMF algorithm that preserves local invariance by adding graph regularization into the process of max-correntropy-based matrix factorization. Meanwhile, each feature can learn corresponding kernel from the data. The experiment results of Caltech101 and Caltech256 show the benefits of such combination against other NMF algorithms for the unsupervised image clustering

Sparse feature learning for image analysis in segmentation, classification, and disease diagnosis.

The success of machine learning algorithms generally depends on intermediate data representation, called features that disentangle the hidden factors of variation in data. Moreover, machine learning models are required to be generalized, in order to reduce the specificity or bias toward the training dataset. Unsupervised feature learning is useful in taking advantage of large amount of unlabeled data, which is available to capture these variations. However, learned features are required to capture variational patterns in data space. In this dissertation, unsupervised feature learning with sparsity is investigated for sparse and local feature extraction with application to lung segmentation, interpretable deep models, and Alzheimer\u27s disease classification. Nonnegative Matrix Factorization, Autoencoder and 3D Convolutional Autoencoder are used as architectures or models for unsupervised feature learning. They are investigated along with nonnegativity, sparsity and part-based representation constraints for generalized and transferable feature extraction

Physically inspired methods and development of data-driven predictive systems.

Traditionally building of predictive models is perceived as a combination of both science and art. Although the designer of a predictive system effectively follows a prescribed procedure, his domain knowledge as well as expertise and intuition in the field of machine learning are often irreplaceable. However, in many practical situations it is possible to build well–performing predictive systems by following a rigorous methodology and offsetting not only the lack of domain knowledge but also partial lack of expertise and intuition, by computational power. The generalised predictive model development cycle discussed in this thesis is an example of such methodology, which despite being computationally expensive, has been successfully applied to real–world problems. The proposed predictive system design cycle is a purely data–driven approach. The quality of data used to build the system is thus of crucial importance. In practice however, the data is rarely perfect. Common problems include missing values, high dimensionality or very limited amount of labelled exemplars. In order to address these issues, this work investigated and exploited inspirations coming from physics. The novel use of well–established physical models in the form of potential fields, has resulted in derivation of a comprehensive Electrostatic Field Classification Framework for supervised and semi–supervised learning from incomplete data. Although the computational power constantly becomes cheaper and more accessible, it is not infinite. Therefore efficient techniques able to exploit finite amount of predictive information content of the data and limit the computational requirements of the resource–hungry predictive system design procedure are very desirable. In designing such techniques this work once again investigated and exploited inspirations coming from physics. By using an analogy with a set of interacting particles and the resulting Information Theoretic Learning framework, the Density Preserving Sampling technique has been derived. This technique acts as a computationally efficient alternative for cross–validation, which fits well within the proposed methodology. All methods derived in this thesis have been thoroughly tested on a number of benchmark datasets. The proposed generalised predictive model design cycle has been successfully applied to two real–world environmental problems, in which a comparative study of Density Preserving Sampling and cross–validation has also been performed confirming great potential of the proposed methods

Relevant data representation by a Kernel-based framework

Nowadays, the analysis of a large amount of data has emerged as an issue of great interest taking increasing place in the scientific community, especially in automation, signal processing, pattern recognition, and machine learning. In this sense, the identification, description, classification, visualization, and clustering of events or patterns are important problems for engineering developments and scientific issues, such as biology, medicine, economy, artificial vision, artificial intelligence, and industrial production. Nonetheless, it is difficult to interpret the available information due to its complexity and a large amount of obtained features. In addition, the analysis of the input data requires the development of methodologies that allow to reveal the relevant behaviors of the studied process, particularly, when such signals contain hidden structures varying over a given domain, e.g., space and/or time. When the analyzed signal contains such kind of properties, directly applying signal processing and machine learning procedures without considering a suitable model that deals with both the statistical distribution and the data structure, can lead in unstable performance results. Regarding this, kernel functions appear as an alternative approach to address the aforementioned issues by providing flexible mathematical tools that allow enhancing data representation for supporting signal processing and machine learning systems. Moreover, kernelbased methods are powerful tools for developing better-performing solutions by adapting the kernel to a given problem, instead of learning data relationships from explicit raw vector representations. However, building suitable kernels requires some user prior knowledge about input data, which is not available in most of the practical cases. Furthermore, using the definitions of traditional kernel methods directly, possess a challenging estimation problem that often leads to strong simplifications that restrict the kind of representation that we can use on the data. In this study, we propose a data representation framework based on kernel methods to learn automatically relevant sample relationships in learning systems. Namely, the proposed framework is divided into five kernel-based approaches, which aim to compute relevant data representations by adapting them according to both the imposed sample relationships constraints and the learning scenario (unsupervised or supervised task). First, we develop a kernel-based representation approach that allows revealing the main input sample relations by including relevant data structures using graph-based sparse constraints. Thus, salient data structures are highlighted aiming to favor further unsupervised clustering stages. This approach can be viewed as a graph pruning strategy within a spectral clustering framework which allows enhancing both the local and global data consistencies for a given input similarity matrix. Second, we introduce a kernel-based representation methodology that captures meaningful data relations in terms of their statistical distribution. Thus, an information theoretic learning (ITL) based penalty function is introduced to estimate a kernel-based similarity that maximizes the whole information potential variability. So, we seek for a reproducing kernel Hilbert space (RKHS) that spans the widest information force magnitudes among data points to support further clustering stages. Third, an entropy-like functional on positive definite matrices based on Renyi’s definition is adapted to develop a kernel-based representation approach which considers the statistical distribution and the salient data structures. Thereby, relevant input patterns are highlighted in unsupervised learning tasks. Particularly, the introduced approach is tested as a tool to encode relevant local and global input data relationships in dimensional reduction applications. Fourth, a supervised kernel-based representation is introduced via a metric learning procedure in RKHS that takes advantage of the user-prior knowledge, when available, regarding the studied learning task. Such an approach incorporates the proposed ITL-based kernel functional estimation strategy to adapt automatically the relevant representation using both the supervised information and the input data statistical distribution. As a result, relevant sample dependencies are highlighted by weighting the input features that mostly encode the supervised learning task. Finally, a new generalized kernel-based measure is proposed by taking advantage of different RKHSs. In this way, relevant dependencies are highlighted automatically by considering the input data domain-varying behavior and the user-prior knowledge (supervised information) when available. The proposed measure is an extension of the well-known crosscorrentropy function based on Hilbert space embeddings. Throughout the study, the proposed kernel-based framework is applied to biosignal and image data as an alternative to support aided diagnosis systems and image-based object analysis. Indeed, the introduced kernel-based framework improve, in most of the cases, unsupervised and supervised learning performances, aiding researchers in their quest to process and to favor the understanding of complex dataResumen: Hoy en día, el análisis de datos se ha convertido en un tema de gran interés para la comunidad científica, especialmente en campos como la automatización, el procesamiento de señales, el reconocimiento de patrones y el aprendizaje de máquina. En este sentido, la identificación, descripción, clasificación, visualización, y la agrupación de eventos o patrones son problemas importantes para desarrollos de ingeniería y cuestiones científicas, tales como: la biología, la medicina, la economía, la visión artificial, la inteligencia artificial y la producción industrial. No obstante, es difícil interpretar la información disponible debido a su complejidad y la gran cantidad de características obtenidas. Además, el análisis de los datos de entrada requiere del desarrollo de metodologías que permitan revelar los comportamientos relevantes del proceso estudiado, en particular, cuando tales señales contienen estructuras ocultas que varían sobre un dominio dado, por ejemplo, el espacio y/o el tiempo. Cuando la señal analizada contiene este tipo de propiedades, los rendimientos pueden ser inestables si se aplican directamente técnicas de procesamiento de señales y aprendizaje automático sin tener en cuenta la distribución estadística y la estructura de datos. Al respecto, las funciones núcleo (kernel) aparecen como un enfoque alternativo para abordar las limitantes antes mencionadas, proporcionando herramientas matemáticas flexibles que mejoran la representación de los datos de entrada. Por otra parte, los métodos basados en funciones núcleo son herramientas poderosas para el desarrollo de soluciones de mejor rendimiento mediante la adaptación del núcleo de acuerdo al problema en estudio. Sin embargo, la construcción de funciones núcleo apropiadas requieren del conocimiento previo por parte del usuario sobre los datos de entrada, el cual no está disponible en la mayoría de los casos prácticos. Por otra parte, a menudo la estimación de las funciones núcleo conllevan sesgos el modelo, siendo necesario apelar a simplificaciones matemáticas que no siempre son acordes con la realidad. En este estudio, se propone un marco de representación basado en métodos núcleo para resaltar relaciones relevantes entre los datos de forma automática en sistema de aprendizaje de máquina. A saber, el marco propuesto consta de cinco enfoques núcleo, en aras de adaptar la representación de acuerdo a las relaciones impuestas sobre las muestras y sobre el escenario de aprendizaje (sin/con supervisión). En primer lugar, se desarrolla un enfoque de representación núcleo que permite revelar las principales relaciones entre muestras de entrada mediante la inclusión de estructuras relevantes utilizando restricciones basadas en modelado por grafos. Por lo tanto, las estructuras de datos más sobresalientes se destacan con el objetivo de favorecer etapas posteriores de agrupamiento no supervisado. Este enfoque puede ser visto como una estrategia de depuración de grafos dentro de un marco de agrupamiento espectral que permite mejorar las consistencias locales y globales de los datos En segundo lugar, presentamos una metodología de representación núcleo que captura relaciones significativas entre muestras en términos de su distribución estadística. De este modo, se introduce una función de costo basada en aprendizaje por teoría de la información para estimar una similitud que maximice la variabilidad del potencial de información de los datos de entrada. Así, se busca un espacio de Hilbert generado por el núcleo que contenga altas fuerzas de información entre los puntos para favorecer el agrupamiento entre los mismos. En tercer lugar, se propone un esquema de representación que incluye un funcional de entropía para matrices definidas positivas a partir de la definición de Renyi. En este sentido, se pretenden incluir la distribución estadística de las muestras y sus estructuras relevantes. Por consiguiente, los patrones de entrada pertinentes se destacan en tareas de aprendizaje sin supervisión. En particular, el enfoque introducido se prueba como una herramienta para codificar las relaciones locales y globales de los datos en tareas de reducción de dimensión. En cuarto lugar, se introduce una metodología de representación núcleo supervisada a través de un aprendizaje de métrica en el espacio de Hilbert generado por una función núcleo en aras de aprovechar el conocimiento previo del usuario con respecto a la tarea de aprendizaje. Este enfoque incorpora un funcional por teoría de información que permite adaptar automáticamente la representación utilizando tanto información supervisada y la distribución estadística de los datos de entrada. Como resultado, las dependencias entre las muestras se resaltan mediante la ponderación de las características de entrada que codifican la tarea de aprendizaje supervisado. Por último, se propone una nueva medida núcleo mediante el aprovechamiento de diferentes espacios de representación. De este modo, las dependencias más relevantes entre las muestras se resaltan automáticamente considerando el dominio de interés de los datos de entrada y el conocimiento previo del usuario (información supervisada). La medida propuesta es una extensión de la función de cross-correntropia a partir de inmersiones en espacios de Hilbert. A lo largo del estudio, el esquema propuesto se valida sobre datos relacionados con bioseñales e imágenes como una alternativa para apoyar sistemas de apoyo diagnóstico y análisis objetivo basado en imágenes. De hecho, el marco introducido permite mejorar, en la mayoría de los casos, el rendimiento de sistemas de aprendizaje supervisado y no supervisado, favoreciendo la precisión de la tarea y la interpretabilidad de los datosDoctorad

Bayesian calibration for multiple source regression model

In large variety of practical applications, using information from different sources or different kind of data is a reasonable demand. The problem of studying multiple source data can be represented as a multi-task learning problem, and then the information from one source can help to study the information from the other source by extracting a shared common structure. From the other hand, parameter evaluations obtained from various sources can be confused and conflicting. This paper proposes a Bayesian based approach to calibrate data obtained from different sources and to solve nonlinear regression problem in the presence of heteroscedastisity of the multiple-source model. An efficient algorithm is developed for implementation. Using analytical and simulation studies, it is shown that the proposed Bayesian calibration improves the convergence rate of the algorithm and precision of the model. The theoretical results are supported by a synthetic example, and a real-world problem, namely, modeling unsteady pitching moment coefficient of aircraft, for which a recurrent neural network is constructed

Physically inspired methods and development of data-driven predictive systems

Traditionally building of predictive models is perceived as a combination of both science and art. Although the designer of a predictive system effectively follows a prescribed procedure, his domain knowledge as well as expertise and intuition in the field of machine learning are often irreplaceable. However, in many practical situations it is possible to build well–performing predictive systems by following a rigorous methodology and offsetting not only the lack of domain knowledge but also partial lack of expertise and intuition, by computational power. The generalised predictive model development cycle discussed in this thesis is an example of such methodology, which despite being computationally expensive, has been successfully applied to real–world problems. The proposed predictive system design cycle is a purely data–driven approach. The quality of data used to build the system is thus of crucial importance. In practice however, the data is rarely perfect. Common problems include missing values, high dimensionality or very limited amount of labelled exemplars. In order to address these issues, this work investigated and exploited inspirations coming from physics. The novel use of well–established physical models in the form of potential fields, has resulted in derivation of a comprehensive Electrostatic Field Classification Framework for supervised and semi–supervised learning from incomplete data. Although the computational power constantly becomes cheaper and more accessible, it is not infinite. Therefore efficient techniques able to exploit finite amount of predictive information content of the data and limit the computational requirements of the resource–hungry predictive system design procedure are very desirable. In designing such techniques this work once again investigated and exploited inspirations coming from physics. By using an analogy with a set of interacting particles and the resulting Information Theoretic Learning framework, the Density Preserving Sampling technique has been derived. This technique acts as a computationally efficient alternative for cross–validation, which fits well within the proposed methodology. All methods derived in this thesis have been thoroughly tested on a number of benchmark datasets. The proposed generalised predictive model design cycle has been successfully applied to two real–world environmental problems, in which a comparative study of Density Preserving Sampling and cross–validation has also been performed confirming great potential of the proposed methods.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Multi-Objective Evolutionary Optimisation for Prototype-Based Fuzzy Classifiers

Evolving intelligent systems (EISs), particularly, the zero-order ones have demonstrated strong performance on many real-world problems concerning data stream classification, while offering high model transparency and interpretability thanks to their prototype-based nature. Zero-order EISs typically learn prototypes by clustering streaming data online in a “one pass” manner for greater computation efficiency. However, such identified prototypes often lack optimality, resulting in less precise classification boundaries, thereby hindering the potential classification performance of the systems. To address this issue, a commonly adopted strategy is to minimise the training error of the models on historical training data or alternatively, to iteratively minimise the intra-cluster variance of the clusters obtained via online data partitioning. This recognises the fact that the ultimate classification performance of zero-order EISs is driven by the positions of prototypes in the data space. Yet, simply minimising the training error may potentially lead to overfitting, whilst minimising the intra-cluster variance does not necessarily ensure the optimised prototype-based models to attain improved classification outcomes. To achieve better classification performance whilst avoiding overfitting for zero-order EISs, this paper presents a novel multi-objective optimisation approach, enabling EISs to obtain optimal prototypes via involving these two disparate but complementary strategies simultaneously. Five decision-making schemes are introduced for selecting a suitable solution to deploy from the final non-dominated set of the resulting optimised models. Systematic experimental studies are carried out to demonstrate the effectiveness of the proposed optimisation approach in improving the classification performance of zero-order EISs

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity

Multiobjective Evolutionary Optimization for Prototype-Based Fuzzy Classifiers

Evolving intelligent systems (EISs), particularly, the zero-order ones have demonstrated strong performance on many real-world problems concerning data stream classification, while offering high model transparency and interpretability thanks to their prototype-based nature. Zero-order EISs typically learn prototypes by clustering streaming data online in a “one pass” manner for greater computation efficiency. However, such identified prototypes often lack optimality, resulting in less precise classification boundaries, thereby hindering the potential classification performance of the systems. To address this issue, a commonly adopted strategy is to minimise the training error of the models on historical training data or alternatively, to iteratively minimise the intra-cluster variance of the clusters obtained via online data partitioning. This recognises the fact that the ultimate classification performance of zero-order EISs is driven by the positions of prototypes in the data space. Yet, simply minimising the training error may potentially lead to overfitting, whilst minimising the intra-cluster variance does not necessarily ensure the optimised prototype-based models to attain improved classification outcomes. To achieve better classification performance whilst avoiding overfitting for zero-order EISs, this paper presents a novel multi-objective optimisation approach, enabling EISs to obtain optimal prototypes via involving these two disparate but complementary strategies simultaneously. Five decision-making schemes are introduced for selecting a suitable solution to deploy from the final non-dominated set of the resulting optimised models. Systematic experimental studies are carried out to demonstrate the effectiveness of the proposed optimisation approach in improving the classification performance of zero-order EISs