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Pose-graph SLAM is the de facto standard framework for constructing large-scale maps from multi-session experiences of relative observations and motions during visual robot navigation. It has received increasing attention in the context of…

A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on…

Adoption of deep learning in safety-critical systems raise the need for understanding what deep neural networks do not understand after models have been deployed. The behaviour of deep neural networks is undefined for so called…

Outlier or anomaly detection is an important task in data analysis. We discuss the problem from a geometrical perspective and provide a framework that exploits the metric structure of a data set. Our approach rests on the manifold…

Improvements in computational and experimental capabilities are rapidly increasing the amount of scientific data that is routinely generated. In applications that are constrained by memory and computational intensity, excessively large…

Low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection are among the most important problems in machine learning. The existing methods usually consider the case when each instance has a fixed,…

Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric…

This work introduces an online greedy method for constructing quadratic manifolds from streaming data, designed to enable in-situ analysis of numerical simulation data on the Petabyte scale. Unlike traditional batch methods, which require…

Recent advances in robotics are driving real-world autonomy for long-term and large-scale missions, where loop closures via place recognition are vital for mitigating pose estimation drift. However, achieving real-time performance remains…

This paper proposes a framework for simultaneous dimensionality reduction and regression in the presence of outliers in data by applying low-rank and sparse matrix decomposition. For multivariate data corrupted with outliers, it is…

Randomized dimensionality reduction is a widely-used algorithmic technique for speeding up large-scale Euclidean optimization problems. In this paper, we study dimension reduction for a variety of maximization problems, including…

For many machine learning tasks, the input data lie on a low-dimensional manifold embedded in a high dimensional space and, because of this high-dimensional structure, most algorithms are inefficient. The typical solution is to reduce the…

Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have…

Out-of-distribution (OOD) detection is an important topic for real-world machine learning systems, but settings with limited in-distribution samples have been underexplored. Such few-shot OOD settings are challenging, as models have scarce…

We introduce four new real-world distribution shift datasets consisting of changes in image style, image blurriness, geographic location, camera operation, and more. With our new datasets, we take stock of previously proposed methods for…

A population quantity of interest in statistical shape analysis is the location of landmarks, which are points that aid in reconstructing and representing shapes of objects. We provide an automated, model-based approach to inferring…

Deep Metric Learning (DML) aims to find representations suitable for zero-shot transfer to a priori unknown test distributions. However, common evaluation protocols only test a single, fixed data split in which train and test classes are…

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…

We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…

We present a framework for supervised subspace tracking, when there are two time series $x_t$ and $y_t$, one being the high-dimensional predictors and the other being the response variables and the subspace tracking needs to take into…