Related papers: A convex method for classification of groups of ex…
This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints,…
In this work, we present a new efficient method for convex shape representation, which is regardless of the dimension of the concerned objects, using level-set approaches. Convexity prior is very useful for object completion in computer…
Most systems and learning algorithms optimize average performance or average loss -- one reason being computational complexity. However, many objectives of practical interest are more complex than simply average loss. This arises, for…
This study concentrates on clustering problems and aims to find compact clusters that are informative regarding the outcome variable. The main goal is partitioning data points so that observations in each cluster are similar and the outcome…
We present a mathematical and algorithmic scheme for learning the principal geometric elements in an image or 3D object. We build on recent work that convexifies the basic problem of finding a combination of a small number shapes that…
The effectiveness of Symmetric Positive Definite (SPD) manifold features has been proven in various computer vision tasks. However, due to the non-Euclidean geometry of these features, existing Euclidean machineries cannot be directly used.…
We study the large sample behavior of a convex clustering framework, which minimizes the sample within cluster sum of squares under an~$\ell_1$ fusion constraint on the cluster centroids. This recently proposed approach has been gaining in…
With the recent growth in data availability and complexity, and the associated outburst of elaborate modelling approaches, model selection tools have become a lifeline, providing objective criteria to deal with this increasingly challenging…
Computer vision tasks are traditionally defined and evaluated using semantic categories. However, it is known to the field that semantic classes do not necessarily correspond to a unique visual class (e.g. inside and outside of a car).…
Locating the center of convex objects is important in both image processing and unsupervised machine learning/data clustering fields. The automated analysis of biological images uses both of these fields for locating cell nuclei and for…
The standard way of training video models entails sampling at each iteration a single clip from a video and optimizing the clip prediction with respect to the video-level label. We argue that a single clip may not have enough temporal…
The support vector machine (SVM) algorithm is well known to the computer learning community for its very good practical results. The goal of the present paper is to study this algorithm from a statistical perspective, using tools of…
Optimization problems with set-valued objective functions arise in contexts such as multi-stage optimization with vector-valued objectives. The aim is to identify an optimizer -- a feasible point with an optimal objective value -- based on…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
Hyperbolic spaces have increasingly been recognized for their outstanding performance in handling data with inherent hierarchical structures compared to their Euclidean counterparts. However, learning in hyperbolic spaces poses significant…
This paper introduces a general multi-class approach to weakly supervised classification. Inferring the labels and learning the parameters of the model is usually done jointly through a block-coordinate descent algorithm such as…
The method of Hol\'y, Sokol and \v{C}ern\'y (Applied Soft Computing, 2017, Vol. 60, p. 752-762) clusters objects based on their incidence in a large number of given sets. The idea is to minimize the occurrence of multiple objects from the…
Image clustering is a very useful technique that is widely applied to various areas, including remote sensing. Recently, visual representations by self-supervised learning have greatly improved the performance of image clustering. To…
In this paper, we propose a method for image-set classification based on convex cone models, focusing on the effectiveness of convolutional neural network (CNN) features as inputs. CNN features have non-negative values when using the…
Graph-based variational methods have recently shown to be highly competitive for various classification problems of high-dimensional data, but are inherently difficult to handle from an optimization perspective. This paper proposes a convex…