Kernel Spectral Clustering and applications

In this chapter we review the main literature related to kernel spectral clustering (KSC), an approach to clustering cast within a kernel-based optimization setting. KSC represents a least-squares support vector machine based formulation of spectral clustering described by a weighted kernel PCA objective. Just as in the classifier case, the binary clustering model is expressed by a hyperplane in a high dimensional space induced by a kernel. In addition, the multi-way clustering can be obtained by combining a set of binary decision functions via an Error Correcting Output Codes (ECOC) encoding scheme. Because of its model-based nature, the KSC method encompasses three main steps: training, validation, testing. In the validation stage model selection is performed to obtain tuning parameters, like the number of clusters present in the data. This is a major advantage compared to classical spectral clustering where the determination of the clustering parameters is unclear and relies on heuristics. Once a KSC model is trained on a small subset of the entire data, it is able to generalize well to unseen test points. Beyond the basic formulation, sparse KSC algorithms based on the Incomplete Cholesky Decomposition (ICD) and $L_0$, $L_1, L_0 + L_1$, Group Lasso regularization are reviewed. In that respect, we show how it is possible to handle large scale data. Also, two possible ways to perform hierarchical clustering and a soft clustering method are presented. Finally, real-world applications such as image segmentation, power load time-series clustering, document clustering and big data learning are considered.Comment: chapter contribution to the book "Unsupervised Learning Algorithms

Semi-Supervised Kernel PCA

We present three generalisations of Kernel Principal Components Analysis (KPCA) which incorporate knowledge of the class labels of a subset of the data points. The first, MV-KPCA, penalises within class variances similar to Fisher discriminant analysis. The second, LSKPCA is a hybrid of least squares regression and kernel PCA. The final LR-KPCA is an iteratively reweighted version of the previous which achieves a sigmoid loss function on the labeled points. We provide a theoretical risk bound as well as illustrative experiments on real and toy data sets

Deep learning architectures for Computer Vision

Deep learning has become part of many state-of-the-art systems in multiple disciplines (specially in computer vision and speech processing). In this thesis Convolutional Neural Networks are used to solve the problem of recognizing people in images, both for verification and identification. Two different architectures, AlexNet and VGG19, both winners of the ILSVRC, have been fine-tuned and tested with four datasets: Labeled Faces in the Wild, FaceScrub, YouTubeFaces and Google UPC, a dataset generated at the UPC. Finally, with the features extracted from these fine-tuned networks, some verifications algorithms have been tested including Support Vector Machines, Joint Bayesian and Advanced Joint Bayesian formulation. The results of this work show that an Area Under the Receiver Operating Characteristic curve of 99.6% can be obtained, close to the state-of-the-art performance.El aprendizaje profundo se ha convertido en parte de muchos sistemas en el estado del arte de múltiples ámbitos (especialmente en visión por computador y procesamiento de voz). En esta tesis se utilizan las Redes Neuronales Convolucionales para resolver el problema de reconocer a personas en imágenes, tanto para verificación como para identificación. Dos arquitecturas diferentes, AlexNet y VGG19, ambas ganadores del ILSVRC, han sido afinadas y probadas con cuatro conjuntos de datos: Labeled Faces in the Wild, FaceScrub, YouTubeFaces y Google UPC, un conjunto generado en la UPC. Finalmente con las características extraídas de las redes afinadas, se han probado diferentes algoritmos de verificación, incluyendo Maquinas de Soporte Vectorial, Joint Bayesian y Advanced Joint Bayesian. Los resultados de este trabajo muestran que el Área Bajo la Curva de la Característica Operativa del Receptor puede llegar a ser del 99.6%, cercana al valor del estado del arte.L’aprenentatge profund s’ha convertit en una part importat de molts sistemes a l’estat de l’art de múltiples àmbits (especialment de la visió per computador i el processament de veu). A aquesta tesi s’utilitzen les Xarxes Neuronals Convolucionals per a resoldre el problema de reconèixer persones a imatges, tant per verificació com per identificatió. Dos arquitectures diferents, AlexNet i VGG19, les dues guanyadores del ILSVRC, han sigut afinades i provades amb quatre bases de dades: Labeled Faces in the Wild, FaceScrub, YouTubeFaces i Google UPC, un conjunt generat a la UPC. Finalment, amb les característiques extretes de les xarxes afinades, s’han provat diferents algoritmes de verificació, incloent Màquines de Suport Vectorial, Joint Bayesian i Advanced Joint Bayesian. Els resultats d’aquest treball mostres que un Àrea Baix la Curva de la Característica Operativa del Receptor por arribar a ser del 99.6%, propera al valor de l’estat de l’art