A Novel Hybrid Dimensionality Reduction Method using Support Vector Machines and Independent Component Analysis

Due to the increasing demand for high dimensional data analysis from various applications such as electrocardiogram signal analysis and gene expression analysis for cancer detection, dimensionality reduction becomes a viable process to extracts essential information from data such that the high-dimensional data can be represented in a more condensed form with much lower dimensionality to both improve classification accuracy and reduce computational complexity. Conventional dimensionality reduction methods can be categorized into stand-alone and hybrid approaches. The stand-alone method utilizes a single criterion from either supervised or unsupervised perspective. On the other hand, the hybrid method integrates both criteria. Compared with a variety of stand-alone dimensionality reduction methods, the hybrid approach is promising as it takes advantage of both the supervised criterion for better classification accuracy and the unsupervised criterion for better data representation, simultaneously. However, several issues always exist that challenge the efficiency of the hybrid approach, including (1) the difficulty in finding a subspace that seamlessly integrates both criteria in a single hybrid framework, (2) the robustness of the performance regarding noisy data, and (3) nonlinear data representation capability. This dissertation presents a new hybrid dimensionality reduction method to seek projection through optimization of both structural risk (supervised criterion) from Support Vector Machine (SVM) and data independence (unsupervised criterion) from Independent Component Analysis (ICA). The projection from SVM directly contributes to classification performance improvement in a supervised perspective whereas maximum independence among features by ICA construct projection indirectly achieving classification accuracy improvement due to better intrinsic data representation in an unsupervised perspective. For linear dimensionality reduction model, I introduce orthogonality to interrelate both projections from SVM and ICA while redundancy removal process eliminates a part of the projection vectors from SVM, leading to more effective dimensionality reduction. The orthogonality-based linear hybrid dimensionality reduction method is extended to uncorrelatedness-based algorithm with nonlinear data representation capability. In the proposed approach, SVM and ICA are integrated into a single framework by the uncorrelated subspace based on kernel implementation. Experimental results show that the proposed approaches give higher classification performance with better robustness in relatively lower dimensions than conventional methods for high-dimensional datasets

Two Criteria for Model Selection in Multiclass Support Vector Machines

Practical applications call for efficient model selection criteria for multiclass support vector machine (SVM) classification. To solve this problem, this paper develops two model selection criteria by combining or redefining the radius–margin bound used in binary SVMs. The combination is justified by linking the test error rate of a multiclass SVM with that of a set of binary SVMs. The redefinition, which is relatively heuristic, is inspired by the conceptual relationship between the radius–margin bound and the class separability measure. Hence, the two criteria are developed from the perspective of model selection rather than a generalization of the radius–margin bound for multiclass SVMs. As demonstrated by extensive experimental study, the minimization of these two criteria achieves good model selection on most data sets. Compared with the k-fold cross validation which is often regarded as a benchmark, these two criteria give rise to comparable performance with much less computational overhead, particularly when a large number of model parameters are to be optimized

Weighted Fisher Discriminant Analysis in the Input and Feature Spaces

Fisher Discriminant Analysis (FDA) is a subspace learning method which minimizes and maximizes the intra- and inter-class scatters of data, respectively. Although, in FDA, all the pairs of classes are treated the same way, some classes are closer than the others. Weighted FDA assigns weights to the pairs of classes to address this shortcoming of FDA. In this paper, we propose a cosine-weighted FDA as well as an automatically weighted FDA in which weights are found automatically. We also propose a weighted FDA in the feature space to establish a weighted kernel FDA for both existing and newly proposed weights. Our experiments on the ORL face recognition dataset show the effectiveness of the proposed weighting schemes.Comment: Accepted (to appear) in International Conference on Image Analysis and Recognition (ICIAR) 2020, Springe

Simple but Not Simplistic: Reducing the Complexity of Machine Learning Methods

Programa Oficial de Doutoramento en Computación . 5009V01[Resumo] A chegada do Big Data e a explosión do Internet das cousas supuxeron un gran reto para os investigadores en Aprendizaxe Automática, facendo que o proceso de aprendizaxe sexa mesmo roáis complexo. No mundo real, os problemas da aprendizaxe automática xeralmente teñen complexidades inherentes, como poden ser as características intrínsecas dos datos, o gran número de mostras, a alta dimensión dos datos de entrada, os cambios na distribución entre o conxunto de adestramento e test, etc. Todos estes aspectos son importantes, e requiren novoS modelos que poi dan facer fronte a estas situacións. Nesta tese, abordáronse todos estes problemas, tratando de simplificar o proceso de aprendizaxe automática no escenario actual. En primeiro lugar, realízase unha análise de complexidade para observar como inflúe esta na tarefa de clasificación, e se é posible que a aplicación dun proceso previo de selección de características reduza esta complexidade. Logo, abórdase o proceso de simplificación da fase de aprendizaxe automática mediante a filosofía divide e vencerás, usando un enfoque distribuído. Seguidamente, aplicamos esa mesma filosofía sobre o proceso de selección de características. Finalmente, optamos por un enfoque diferente seguindo a filosofía do Edge Computing, a cal permite que os datos producidos polos dispositivos do Internet das cousas se procesen máis preto de onde se crearon. Os enfoques propostos demostraron a súa capacidade para reducir a complexidade dos métodos de aprendizaxe automática tradicionais e, polo tanto, espérase que a contribución desta tese abra as portas ao desenvolvemento de novos métodos de aprendizaxe máquina máis simples, máis robustos, e máis eficientes computacionalmente.[Resumen] La llegada del Big Data y la explosión del Internet de las cosas han supuesto un gran reto para los investigadores en Aprendizaje Automático, haciendo que el proceso de aprendizaje sea incluso más complejo. En el mundo real, los problemas de aprendizaje automático generalmente tienen complejidades inherentes) como pueden ser las características intrínsecas de los datos, el gran número de muestras, la alta dimensión de los datos de entrada, los cambios en la distribución entre el conjunto de entrenamiento y test, etc. Todos estos aspectos son importantes, y requieren nuevos modelos que puedan hacer frente a estas situaciones. En esta tesis, se han abordado todos estos problemas, tratando de simplificar el proceso de aprendizaje automático en el escenario actual. En primer lugar, se realiza un análisis de complejidad para observar cómo influye ésta en la tarea de clasificación1 y si es posible que la aplicación de un proceso previo de selección de características reduzca esta complejidad. Luego, se aborda el proceso de simplificación de la fase de aprendizaje automático mediante la filosofía divide y vencerás, usando un enfoque distribuido. A continuación, aplicamos esa misma filosofía sobre el proceso de selección de características. Finalmente, optamos por un enfoque diferente siguiendo la filosofía del Edge Computing, la cual permite que los datos producidos por los dispositivos del Internet de las cosas se procesen más cerca de donde se crearon. Los enfoques propuestos han demostrado su capacidad para reducir la complejidad de los métodos de aprendizaje automático tnidicionales y, por lo tanto, se espera que la contribución de esta tesis abra las puertas al desarrollo de nuevos métodos de aprendizaje máquina más simples, más robustos, y más eficientes computacionalmente.[Abstract] The advent of Big Data and the explosion of the Internet of Things, has brought unprecedented challenges to Machine Learning researchers, making the learning task more complexo Real-world machine learning problems usually have inherent complexities, such as the intrinsic characteristics of the data, large number of instauces, high input dimensionality, dataset shift, etc. AH these aspects matter, and can fOI new models that can confront these situations. Thus, in this thesis, we have addressed aH these issues) simplifying the machine learning process in the current scenario. First, we carry out a complexity analysis to see how it inftuences the classification models, and if it is possible that feature selection might result in a deerease of that eomplexity. Then, we address the proeess of simplifying learning with the divide-and-conquer philosophy of the distributed approaeh. Later, we aim to reduce the complexity of the feature seleetion preprocessing through the same philosophy. FinallYl we opt for a different approaeh following the eurrent philosophy Edge eomputing, whieh allows the data produeed by Internet of Things deviees to be proeessed closer to where they were ereated. The proposed approaehes have demonstrated their eapability to reduce the complexity of traditional maehine learning algorithms, and thus it is expeeted that the eontribution of this thesis will open the doors to the development of new maehine learning methods that are simpler, more robust, and more eomputationally efficient