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Mining useful clusters from high dimensional data has received significant attention of the computer vision and pattern recognition community in the recent years. Linear and non-linear dimensionality reduction has played an important role…
Spectral Clustering (SC) is a widely used data clustering method which first learns a low-dimensional embedding $U$ of data by computing the eigenvectors of the normalized Laplacian matrix, and then performs k-means on $U^\top$ to get the…
This paper studies the convergence difficulty of cohesive zone models in static analysis. It is shown that an inappropriate starting point of iterations in the Newton-Raphson method is responsible for the convergence difficulty. A simple,…
In 3D human shape and pose estimation from a monocular video, models trained with limited labeled data cannot generalize well to videos with occlusion, which is common in the wild videos. The recent human neural rendering approaches…
Dual averaging and gradient descent with their stochastic variants stand as the two canonical recipe books for first-order optimization: Every modern variant can be viewed as a descendant of one or the other. In the convex regime, these…
Most previous learning-based visual odometry (VO) methods take VO as a pure tracking problem. In contrast, we present a VO framework by incorporating two additional components called Memory and Refining. The Memory component preserves…
This dissertation advances the state of the art for AR/VR tracking systems by increasing the tracking frequency by orders of magnitude and proposes an efficient algorithm for the problem of edge-aware optimization. AR/VR is a natural way of…
We introduce a new multimodal optimization approach called Natural Variational Annealing (NVA) that combines the strengths of three foundational concepts to simultaneously search for multiple global and local modes of black-box nonconvex…
We propose and analyze the convergence of a novel stochastic algorithm for solving monotone inclusions that are the sum of a maximal monotone operator and a monotone, Lipschitzian operator. The propose algorithm requires only unbiased…
This paper presents a novel non-rigid point set registration method that is inspired by unsupervised clustering analysis. Unlike previous approaches that treat the source and target point sets as separate entities, we develop a holistic…
We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap…
Anderson mixing (AM) is an acceleration method for fixed-point iterations. Despite its success and wide usage in scientific computing, the convergence theory of AM remains unclear, and its applications to machine learning problems are not…
This study introduces a novel technique for multi-view clustering known as the "Consensus Graph-Based Multi-View Clustering Method Using Low-Rank Non-Convex Norm" (CGMVC-NC). Multi-view clustering is a challenging task in machine learning…
This paper proposes a new algorithm that solves non-convex optimal control problems with a theoretical guarantee for global convergence to a feasible local solution of the original problem. The proposed algorithm extends the recently…
This paper presents new projection-free algorithms for Online Convex Optimization (OCO) over a convex domain $\mathcal{K} \subset \mathbb{R}^d$. Classical OCO algorithms (such as Online Gradient Descent) typically need to perform Euclidean…
A central challenge to using first-order methods for optimizing nonconvex problems is the presence of saddle points. First-order methods often get stuck at saddle points, greatly deteriorating their performance. Typically, to escape from…
In this paper, we consider a time-varying optimization approach to the problem of tracking a moving target using noisy time-of-arrival (TOA) measurements. Specifically, we formulate the problem as that of sequential TOA-based source…
A novel approach to detect road surface anomalies by visual tracking of a preceding vehicle is proposed. The method is versatile, predicting any kind of road anomalies, such as potholes, bumps, debris, etc., unlike direct observation…
A new method for the simulation of evolving multi-domains problems has been introduced in previous works (RealIMotion), Florez et al. (2020) and further developed in parallel in the context of isotropic Grain Growth (GG) with no…
This paper presents an accelerated composite gradient (ACG) variant, referred to as the AC-ACG method, for solving nonconvex smooth composite minimization problems. As opposed to well-known ACG variants that are either based on a known…