Related papers: Interpolating between Clustering and Dimensionalit…

We present an efficient method for image segmentation in the presence of strong inhomogeneities. The approach can be interpreted as a two-level clustering procedure: pixels are first grouped into superpixels via a linear least-squares…

Applying dimensionality reduction (DR) to large, high-dimensional data sets can be challenging when distinguishing the underlying high-dimensional data clusters in a 2D projection for exploratory analysis. We address this problem by first…

Flow Matching (FM) generative models offer efficient simulation-free training and deterministic sampling, but their practical deployment is challenged by high-precision parameter requirements. We adapt optimal transport (OT)-based…

Decentralized nonconvex optimization has received increasing attention in recent years in machine learning due to its advantages in system robustness, data privacy, and implementation simplicity. However, three fundamental challenges in…

Dimensionality reduction techniques play an essential role in data analytics, signal processing and machine learning. Dimensionality reduction is usually performed in a preprocessing stage that is separate from subsequent data analysis,…

In this paper, we propose a Dimension-Reduced Second-Order Method (DRSOM) for convex and nonconvex (unconstrained) optimization. Under a trust-region-like framework, our method preserves the convergence of the second-order method while…

Embedding models are central to dense retrieval, semantic search, and recommendation systems, but their size often makes them impractical to deploy in resource-constrained environments such as browsers or edge devices. While smaller…

The Gromov-Wasserstein (GW) problem is an extension of the classical optimal transport problem to settings where the source and target distributions reside in incomparable spaces, and for which a cost function that attributes the price of…

Low-dimensional embeddings and visualizations are an indispensable tool for analysis of high-dimensional data. State-of-the-art methods, such as tSNE and UMAP, excel in unveiling local structures hidden in high-dimensional data and are…

Sharpened dimensionality reduction (SDR), which belongs to the class of multidimensional projection techniques, has recently been introduced to tackle the challenges in the exploratory and visual analysis of high-dimensional data. SDR has…

Regularized optimal transport (OT) is now increasingly used as a loss or as a matching layer in neural networks. Entropy-regularized OT can be computed using the Sinkhorn algorithm but it leads to fully-dense transportation plans, meaning…

In projective clustering we are given a set of n points in $R^d$ and wish to cluster them to a set $S$ of $k$ linear subspaces in $R^d$ according to some given distance function. An $\eps$-coreset for this problem is a weighted (scaled)…

We introduce Deep Set Linearized Optimal Transport, an algorithm designed for the efficient simultaneous embedding of point clouds into an $L^2-$space. This embedding preserves specific low-dimensional structures within the Wasserstein…

Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…

Dimension reduction (DR) is commonly utilized to capture the intrinsic structure and transform high-dimensional data into low-dimensional space while retaining meaningful properties of the original data. It is used in various applications,…

The optimal transport (OT) problem is a classical optimization problem having the form of linear programming. Machine learning applications put forward new computational challenges in its solution. In particular, the OT problem defines a…

With the discovery of Wasserstein GANs, Optimal Transport (OT) has become a powerful tool for large-scale generative modeling tasks. In these tasks, OT cost is typically used as the loss for training GANs. In contrast to this approach, we…

Aligning EM density maps and fitting atomic models are essential steps in single particle cryogenic electron microscopy (cryo-EM), with recent methods leveraging various algorithms and machine learning tools. As aligning maps remains…

Neural network-based clustering has recently gained popularity, and in particular a constrained clustering formulation has been proposed to perform transfer learning and image category discovery using deep learning. The core idea is to…

Optimal transport (OT) has gained popularity due to its various applications in fields such as machine learning, statistics, and signal processing. However, the balanced mass requirement limits its performance in practical problems. To…