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Distance metric learning is successful in discovering intrinsic relations in data. However, most algorithms are computationally demanding when the problem size becomes large. In this paper, we propose a discriminative metric learning…
We demonstrate that a graph-based search algorithm-relying on the construction of an approximate neighborhood graph-can directly work with challenging non-metric and/or non-symmetric distances without resorting to metric-space mapping…
Classifying large-scale image data into object categories is an important problem that has received increasing research attention. Given the huge amount of data, non-parametric approaches such as nearest neighbor classifiers have shown…
Deep discriminative approaches, such as decision forests and deep neural networks, have recently found applications in many important real-world scenarios. However, deploying these learning algorithms in safety-critical applications raises…
In the study of high-dimensional data, it is often assumed that the data set possesses an underlying lower-dimensional structure. A practical model for this structure is an embedded compact manifold with boundary. Since the underlying…
This paper extends k-means algorithms from the Euclidean domain to the domain of graphs. To recompute the centroids, we apply subgradient methods for solving the optimization-based formulation of the sample mean of graphs. To accelerate the…
Supervised learning is ubiquitous in medical image analysis. In this paper we consider the problem of meta-learning -- predicting which methods will perform well in an unseen classification problem, given previous experience with other…
We consider machine learning in a comparison-based setting where we are given a set of points in a metric space, but we have no access to the actual distances between the points. Instead, we can only ask an oracle whether the distance…
In this paper, we investigate the learning-augmented $k$-median clustering problem, which aims to improve the performance of traditional clustering algorithms by preprocessing the point set with a predictor of error rate $\alpha \in [0,1)$.…
We consider the popular $k$-means problem in $d$-dimensional Euclidean space. Recently Friggstad, Rezapour, Salavatipour [FOCS'16] and Cohen-Addad, Klein, Mathieu [FOCS'16] showed that the standard local search algorithm yields a…
Many methods have been developed for data clustering, such as k-means, expectation maximization and algorithms based on graph theory. In this latter case, graphs are generally constructed by taking into account the Euclidian distance as a…
To improve our understanding of connected systems, different tools derived from statistics, signal processing, information theory and statistical physics have been developed in the last decade. Here, we will focus on the graph comparison…
Lidar sensors are widely used in various applications, ranging from scientific fields over industrial use to integration in consumer products. With an ever growing number of different driver assistance systems, they have been introduced to…
The efficiency of graph-based semi-supervised algorithms depends on the graph of instances on which they are applied. The instances are often in a vectorial form before a graph linking them is built. The construction of the graph relies on…
Interactive exploration of large, multidimensional datasets plays a very important role in various scientific fields. It makes it possible not only to identify important structural features and forms, such as clusters of vertices and their…
We study the k nearest neighbors problem in the plane for general, convex, pairwise disjoint sites of constant description complexity such as line segments, disks, and quadrilaterals and with respect to a general family of distance…
Graph analytics attract much attention from both research and industry communities. Due to the linear time complexity, the $k$-core decomposition is widely used in many real-world applications such as biology, social networks, community…
Deep learning based LiDAR odometry (LO) estimation attracts increasing research interests in the field of autonomous driving and robotics. Existing works feed consecutive LiDAR frames into neural networks as point clouds and match pairs in…
LiDAR odometry (LO) describes the task of finding an alignment of subsequent LiDAR point clouds. This alignment can be used to estimate the motion of the platform where the LiDAR sensor is mounted on. Currently, on the well-known KITTI…
The orthogonal beltway problem is the problem of recovering the $\mathrm{O}(n)$-orbit of a $\delta$-function supported at a finite number of points in $\r^n$ from its auto-correlation or, equivalently, second moment. It was introduced as a…