Related papers: The Flag Median and FlagIRLS

This paper addresses the problem of object recognition given a set of images as input (e.g., multiple camera sources and video frames). Convolutional neural network (CNN)-based frameworks do not exploit these sets effectively, processing a…

Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in…

The classification of forged videos has been a challenge for the past few years. Deepfake classifiers can now reliably predict whether or not video frames have been tampered with. However, their performance is tied to both the dataset used…

Subspace clustering is the problem of clustering data that lie close to a union of linear subspaces. In the abstract form of the problem, where no noise or other corruptions are present, the data are assumed to lie in general position…

We consider the problem of clustering data points coming from sub-Gaussian mixtures. Existing methods that provably achieve the optimal mislabeling error, such as the Lloyd algorithm, are usually vulnerable to outliers. In contrast,…

We propose a new clustering algorithm that is robust to the presence of outliers in the dataset. We perform Lloyd-type iterations with robust estimates of the centroids. More precisely, we build on the idea of median-of-means statistics to…

Federated Learning (FL) is currently one of the most popular technologies in the field of Artificial Intelligence (AI) due to its collaborative learning and ability to preserve client privacy. However, it faces challenges such as…

Finding a suitable data representation for a specific task has been shown to be crucial in many applications. The success of subspace clustering depends on the assumption that the data can be separated into different subspaces. However,…

We study the classic $k$-means/median clustering, which are fundamental problems in unsupervised learning, in the setting where data are partitioned across multiple sites, and where we are allowed to discard a small portion of the data by…

Clustering is one of the most fundamental tasks in machine learning, and the k-means clustering algorithm is perhaps one of the most widely used clustering algorithms. However, it suffers from several limitations, such as sensitivity to…

In addition to finding meaningful clusters, centroid-based clustering algorithms such as K-means or mean-shift should ideally find centroids that are valid patterns in the input space, representative of data in their cluster. This is…

Overcomplete representations and dictionary learning algorithms kept attracting a growing interest in the machine learning community. This paper addresses the emerging problem of comparing multivariate overcomplete representations. Despite…

Gaussian Mixture Models are one of the most studied and mature models in unsupervised learning. However, outliers are often present in the data and could influence the cluster estimation. In this paper, we study a new model that assumes…

Federated Learning (FL) provides a privacy-preserving mechanism for distributed training of machine learning models on networked devices (e.g., mobile devices, IoT edge nodes). It enables Artificial Intelligence (AI) at the edge by creating…

This work introduces the Grassmannian Diffusion Maps, a novel nonlinear dimensionality reduction technique that defines the affinity between points through their representation as low-dimensional subspaces corresponding to points on the…

The $k$-median and $k$-means clustering objectives are classic objectives for modeling clustering in a metric space. Given a set of points in a metric space, the goal of the $k$-median (resp. $k$-means) problem is to find $k$ representative…

Many successful learning algorithms have been recently developed to represent graph-structured data. For example, Graph Neural Networks (GNNs) have achieved considerable successes in various tasks such as node classification, graph…

We present an algorithm for computing $\epsilon$-coresets for $(k, \ell)$-median clustering of polygonal curves in $\mathbb{R}^d$ under the Fr\'echet distance. This type of clustering is an adaption of Euclidean $k$-median clustering: we…

Due to advancements in digital cameras, it is easy to gather multiple images (or videos) from an object under different conditions. Therefore, image-set classification has attracted more attention, and different solutions were proposed to…

The problem of clustering noisy and incompletely observed high-dimensional data points into a union of low-dimensional subspaces and a set of outliers is considered. The number of subspaces, their dimensions, and their orientations are…