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Dynamical systems are found in innumerable forms across the physical and biological sciences, yet all these systems fall naturally into universal equivalence classes: conservative or dissipative, stable or unstable, compressible or…

Object identification is one of the most fundamental and difficult issues in computer vision. It aims to discover object instances in real pictures from a huge number of established categories. In recent years, deep learning-based object…

Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great…

We develop a new framework for estimating joint probability distributions using tensor product reproducing kernel Hilbert spaces (RKHS). Our framework accommodates a low-dimensional, normalized and positive model of a Radon--Nikodym…

This is a tutorial and survey paper on kernels, kernel methods, and related fields. We start with reviewing the history of kernels in functional analysis and machine learning. Then, Mercer kernel, Hilbert and Banach spaces, Reproducing…

Reproducing kernel Hilbert spaces (RKHSs) are Hilbert spaces of functions where pointwise evaluation is continuous. There are known examples of RKHSs that are Banach algebras under pointwise multiplication. These examples are built from…

We study the problem of object detection over scanned images of scientific documents. We consider images that contain objects of varying aspect ratios and sizes and range from coarse elements such as tables and figures to fine elements such…

To avoid the exhaustive search over locations and scales, current state-of-the-art object detection systems usually involve a crucial component generating a batch of candidate object proposals from images. In this paper, we present a simple…

Hierarchical data pervades diverse machine learning applications, including natural language processing, computer vision, and social network analysis. Hyperbolic space, characterized by its negative curvature, has demonstrated strong…

The ever-increasing use of artificial intelligence in autonomous systems has significantly contributed to advance the research on multi-object tracking, adopted in several real-time applications (e.g., autonomous driving, surveillance…

Consider a BV function on a Riemannian manifold. What is its differential? And what about the Hessian of a convex function? These questions have clear answers in terms of (co)vector/matrix valued measures if the manifold is the Euclidean…

In computer vision and medical imaging, the problem of matching structures finds numerous applications from automatic annotation to data reconstruction. The data however, while corresponding to the same anatomy, are often very different in…

Object detection serves as a significant step in improving performance of complex downstream computer vision tasks. It has been extensively studied for many years now and current state-of-the-art 2D object detection techniques proffer…

Shape is an important physical property of natural and manmade 3D objects that characterizes their external appearances. Understanding differences between shapes and modeling the variability within and across shape classes, hereinafter…

We propose a method for the approximation of high- or even infinite-dimensional feature vectors, which play an important role in supervised learning. The goal is to reduce the size of the training data, resulting in lower storage…

Manifold reconstruction has been extensively studied for the last decade or so, especially in two and three dimensions. Recently, significant improvements were made in higher dimensions, leading to new methods to reconstruct large classes…

This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…

We present a novel approach to object classification and detection which requires minimal supervision and which combines visual texture cues and shape information learned from freely available unlabeled web search results. The explosion of…

Most methods for time series classification that attain state-of-the-art accuracy have high computational complexity, requiring significant training time even for smaller datasets, and are intractable for larger datasets. Additionally, many…

Classification of sets of inputs (e.g., images and texts) is an active area of research within both computer vision (CV) and natural language processing (NLP). A common way to represent a set of vectors is to model them as linear subspaces.…