Deep Divergence-Based Approach to Clustering

A promising direction in deep learning research consists in learning representations and simultaneously discovering cluster structure in unlabeled data by optimizing a discriminative loss function. As opposed to supervised deep learning, this line of research is in its infancy, and how to design and optimize suitable loss functions to train deep neural networks for clustering is still an open question. Our contribution to this emerging field is a new deep clustering network that leverages the discriminative power of information-theoretic divergence measures, which have been shown to be effective in traditional clustering. We propose a novel loss function that incorporates geometric regularization constraints, thus avoiding degenerate structures of the resulting clustering partition. Experiments on synthetic benchmarks and real datasets show that the proposed network achieves competitive performance with respect to other state-of-the-art methods, scales well to large datasets, and does not require pre-training steps

Improved neural network generalization using channel-wise NNK graph constructions

State-of-the-art neural network architectures continue to scale in size and deliver impressive results on unseen data points at the expense of poor interpretability. In the deep layers of these models we often encounter very high dimensional feature spaces, where constructing graphs from intermediate data representations can lead to the well-known curse of dimensionality. We propose a channel-wise graph construction method that works on lower dimensional subspaces and provides a new channel-based perspective that leads to better interpretability of the data and relationship between channels. In addition, we introduce a novel generalization estimate based on the proposed graph construction method with which we perform local polytope interpolation. We show its potential to replace the standard generalization estimate based on validation set performance to perform progressive channel-wise early stopping without requiring a validation set.Las arquitecturas de redes neuronales más avanzadas siguen aumentando en tamaño y ofreciendo resultados impresionantes en nuevos datos a costa de una escasa interpretabilidad. En las capas profundas de estos modelos nos encontramos a menudo con espacios de características de muy alta dimensión, en los que la construcción de grafos a partir de representaciones de datos intermedias puede llevar al conocido ''curse of dimensionality''. Proponemos un método de construcción de grafos por canal que trabaja en subespacios de menor dimensión y proporciona una nueva perspectiva basada en canales, que lleva a una mejor interpretabilidad de los datos y de la relación entre canales. Además, introducimos un nuevo estimador de generalización basado en el método de construcción de grafos propuesto con el que realizamos interpolación local en politopos. Mostramos su potencial para sustituir el estimador de generalización estándar basado en el rendimiento en un set de validación independiente para realizar ''early stopping'' progresivo por canales y sin necesidad de un set de validación.Les arquitectures de xarxes neuronals més avançades segueixen augmentant la seva mida i oferint resultats impressionants en noves dades a costa d'una escassa interpretabilitat. A les capes profundes d'aquests models ens trobem sovint amb espais de característiques de molt alta dimensió, en què la construcció de grafs a partir de representacions de dades intermèdies pot portar al conegut ''curse of dimensionality''. Proposem un mètode de construcció de grafs per canal que treballa en subespais de menor dimensió i proporciona una nova perspectiva basada en canals, que porta a una millor interpretabilitat de les dades i de la relació entre canals. A més, introduïm un nou estimador de generalització basat en el mètode de construcció de grafs proposat amb el qual realitzem interpolació local en polítops. Mostrem el seu potencial per substituir l'estimador de generalització estàndard basat en el rendiment en un set de validació independent per a realitzar ''early stopping'' progressiu per canals i sense necessitat d'un set de validació

The Role of Riemannian Manifolds in Computer Vision: From Coding to Deep Metric Learning

A diverse number of tasks in computer vision and machine learning enjoy from representations of data that are compact yet discriminative, informative and robust to critical measurements. Two notable representations are offered by Region Covariance Descriptors (RCovD) and linear subspaces which are naturally analyzed through the manifold of Symmetric Positive Definite (SPD) matrices and the Grassmann manifold, respectively, two widely used types of Riemannian manifolds in computer vision. As our first objective, we examine image and video-based recognition applications where the local descriptors have the aforementioned Riemannian structures, namely the SPD or linear subspace structure. Initially, we provide a solution to compute Riemannian version of the conventional Vector of Locally aggregated Descriptors (VLAD), using geodesic distance of the underlying manifold as the nearness measure. Next, by having a closer look at the resulting codes, we formulate a new concept which we name Local Difference Vectors (LDV). LDVs enable us to elegantly expand our Riemannian coding techniques to any arbitrary metric as well as provide intrinsic solutions to Riemannian sparse coding and its variants when local structured descriptors are considered. We then turn our attention to two special types of covariance descriptors namely infinite-dimensional RCovDs and rank-deficient covariance matrices for which the underlying Riemannian structure, i.e. the manifold of SPD matrices is out of reach to great extent. %Generally speaking, infinite-dimensional RCovDs offer better discriminatory power over their low-dimensional counterparts. To overcome this difficulty, we propose to approximate the infinite-dimensional RCovDs by making use of two feature mappings, namely random Fourier features and the Nystrom method. As for the rank-deficient covariance matrices, unlike most existing approaches that employ inference tools by predefined regularizers, we derive positive definite kernels that can be decomposed into the kernels on the cone of SPD matrices and kernels on the Grassmann manifolds and show their effectiveness for image set classification task. Furthermore, inspired by attractive properties of Riemannian optimization techniques, we extend the recently introduced Keep It Simple and Straightforward MEtric learning (KISSME) method to the scenarios where input data is non-linearly distributed. To this end, we make use of the infinite dimensional covariance matrices and propose techniques towards projecting on the positive cone in a Reproducing Kernel Hilbert Space (RKHS). We also address the sensitivity issue of the KISSME to the input dimensionality. The KISSME algorithm is greatly dependent on Principal Component Analysis (PCA) as a preprocessing step which can lead to difficulties, especially when the dimensionality is not meticulously set. To address this issue, based on the KISSME algorithm, we develop a Riemannian framework to jointly learn a mapping performing dimensionality reduction and a metric in the induced space. Lastly, in line with the recent trend in metric learning, we devise end-to-end learning of a generic deep network for metric learning using our derivation