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The continuing neuroscience advances, catalysed by multidisciplinary collaborations between the biological, computational, physical and chemical areas, have implied in increasingly more complex approaches to understand and model the mammals…

Reformulating computer vision problems over Riemannian manifolds has demonstrated superior performance in various computer vision applications. This is because visual data often forms a special structure lying on a lower dimensional space…

Specific data compression techniques, formalized by the concept of coresets, proved to be powerful for many optimization problems. In fact, while tightly controlling the approximation error, coresets may lead to significant speed up of the…

Unsupervised feature learning often finds low-dimensional embeddings that capture the structure of complex data. For tasks for which prior expert topological knowledge is available, incorporating this into the learned representation may…

In this paper, I outline several conceptual and methodological issues related to modeling individual and group processes embedded in clustered/hierarchical data structures. We position multilevel modeling techniques within a broader set of…

The segmentation, seen as the association of a partition with an image, is a difficult task. It can be decomposed in two steps: at first, a family of contours associated with a series of nested partitions (or hierarchy) is created and…

Graph clustering is a fundamental problem in unsupervised learning, with numerous applications in computer science and in analysing real-world data. In many real-world applications, we find that the clusters have a significant high-level…

Visual analytics have played an increasingly critical role in the Internet of Things, where massive visual signals have to be compressed and fed into machines. But facing such big data and constrained bandwidth capacity, existing…

A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The…

A main challenge in mining network-based data is finding effective ways to represent or encode graph structures so that it can be efficiently exploited by machine learning algorithms. Several methods have focused in network representation…

The new concept of multilevel network is introduced in order to embody some topological properties of complex systems with structures in the mesoscale which are not completely captured by the classical models. This new model, which…

During recent years, the renaissance of neural networks as the major machine learning paradigm and more specifically, the confirmation that deep learning techniques provide state-of-the-art results for most of computer vision tasks has been…

Understanding the response of an output variable to multi-dimensional inputs lies at the heart of many data exploration endeavours. Topology-based methods, in particular Morse theory and persistent homology, provide a useful framework for…

The cluster analysis of very large objects is an important problem, which spans several theoretical as well as applied branches of mathematics and computer science. Here we suggest a novel approach: under assumption of local convergence of…

Image segmentation has come a long way since the early days of computer vision, and still remains a challenging task. Modern variations of the classical (purely bottom-up) approach, involve, e.g., some form of user assistance (interactive…

Current distributed data fabrics lack a rigorous mathematical foundation, often relying on ad-hoc architectures that struggle with consistency, lineage, and scale. We propose a mathematical framework for data fabrics, unifying heterogeneous…

The problem of ensuring constraints satisfaction on the output of machine learning models is critical for many applications, especially in safety-critical domains. Modern approaches rely on penalty-based methods at training time, which do…

Subspace clustering is an unsupervised clustering technique designed to cluster data that is supported on a union of linear subspaces, with each subspace defining a cluster with dimension lower than the ambient space. Many existing…

The integration of structured hierarchical embeddings into transformer-based architectures introduces a refined approach to lexical representation, ensuring that multi-scale semantic relationships are preserved without compromising…

Graphs have become increasingly popular in modeling structures and interactions in a wide variety of problems during the last decade. Graph-based clustering and semi-supervised classification techniques have shown impressive performance.…