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Low-rank matrix approximations play a fundamental role in numerical linear algebra and signal processing applications. This paper introduces a novel rank-revealing matrix decomposition algorithm termed Compressed Randomized UTV (CoR-UTV)…

The last decade has seen a revolution in the theory and application of machine learning and pattern recognition. Through these advancements, variable ranking has emerged as an active and growing research area and it is now beginning to be…

The focus of this article is to develop computationally efficient mathematical morphology operators on hypergraphs. To this aim we consider lattice structures on hypergraphs on which we build morphological operators. We develop a pair of…

Visual reasoning with compositional natural language instructions, e.g., based on the newly-released Cornell Natural Language Visual Reasoning (NLVR) dataset, is a challenging task, where the model needs to have the ability to create an…

In the realm of tensor optimization, the low-rank Tucker decomposition is crucial for reducing the number of parameters and for saving storage. We explore the geometry of Tucker tensor varieties -- the set of tensors with bounded Tucker…

Despite significant progress of deep learning in recent years, state-of-the-art semantic matching methods still rely on legacy features such as SIFT or HoG. We argue that the strong invariance properties that are key to the success of…

The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…

Learning high-dimensional distributions is often done with explicit likelihood modeling or implicit modeling via minimizing integral probability metrics (IPMs). In this paper, we expand this learning paradigm to stochastic orders, namely,…

Differentiable vector graphics have enabled powerful gradient-based optimization of vector primitives directly from raster images. However, existing frameworks formulate this as a flat optimization problem, forcing hundreds to thousands of…

In this paper, we propose a Newton method for unconstrained set optimization problems to find its weakly minimal solutions with respect to lower set-less ordering. The objective function of the problem under consideration is given by…

In several domains, data objects can be decomposed into sets of simpler objects. It is then natural to represent each object as the set of its components or parts. Many conventional machine learning algorithms are unable to process this…

Quaternion matrices are employed successfully in many color image processing applications. In particular, a pure quaternion matrix can be used to represent red, green and blue channels of color images. A low-rank approximation for a pure…

Convolutional Neural Networks (CNN) have been pivotal to the success of many state-of-the-art classification problems, in a wide variety of domains (for e.g. vision, speech, graphs and medical imaging). A commonality within those domains is…

Image feature matching plays a vital role in many computer vision tasks. Although many image feature detection and matching techniques have been proposed over the past few decades, it is still time-consuming to match feature points in two…

Mathematical morphology contributes many profitable tools to image processing area. Some of these methods considered to be basic but the most important fundamental of data processing in many various applications. In this paper, we modify…

We study electoral campaign management scenarios in which an external party can buy votes, i.e., pay the voters to promote its preferred candidate in their preference rankings. The external party's goal is to make its preferred candidate a…

Physically rearranging objects is an important capability for embodied agents. Visual room rearrangement evaluates an agent's ability to rearrange objects in a room to a desired goal based solely on visual input. We propose a simple yet…

Variable order structures model situations in which the comparison between two points depends on a point-to-cone map. In this paper, an inexact projected gradient method for solving smooth constrained vector optimization problems on…

Good pre-trained visual representations could enable robots to learn visuomotor policy efficiently. Still, existing representations take a one-size-fits-all-tasks approach that comes with two important drawbacks: (1) Being completely…

Deep Neural Networks (DNNs) are generated by sequentially performing linear and non-linear processes. Using a combination of linear and non-linear procedures is critical for generating a sufficiently deep feature space. The majority of…