Related papers: Euclidean Distance Matrices: Essential Theory, Alg…
Many metric learning tasks, such as triplet learning, nearest neighbor retrieval, and visualization, are treated primarily as embedding tasks where the ultimate metric is some variant of the Euclidean distance (e.g., cosine or Mahalanobis),…
The usual Euclidean distance may be generalized to extended objects such as polymers or membranes. Here, this distance is used for the first time as a cost function to align structures. We examined the alignment of extended strands to…
We develop a new class of distances for objects including lines, hyperplanes, and trajectories, based on the distance to a set of landmarks. These distances easily and interpretably map objects to a Euclidean space, are simple to compute,…
In machine learning, distance-based algorithms, and other approaches, use information that is represented by propositional data. However, this kind of representation can be quite restrictive and, in many cases, it requires more complex…
Distance metric learning can be viewed as one of the fundamental interests in pattern recognition and machine learning, which plays a pivotal role in the performance of many learning methods. One of the effective methods in learning such a…
Embedding complex objects as vectors in low dimensional spaces is a longstanding problem in machine learning. We propose in this work an extension of that approach, which consists in embedding objects as elliptical probability…
The success of intelligent robotic missions relies on integrating various research tasks, each demanding distinct representations. Designing task-specific representations for each task is costly and impractical. Unified representations…
Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line…
The Earth Mover's Distance (EMD) computes the optimal cost of transforming one distribution into another, given a known transport metric between them. In deep learning, the EMD loss allows us to embed information during training about the…
In a recent paper the author proved a theorem to the effect that the matrix of normalized Euclidean distances on the set of specially distributed random points in the $n$-dimensional Euclidean space $\mathbb R^{n}$ with independent…
We investigate the use of Minimax distances to extract in a nonparametric way the features that capture the unknown underlying patterns and structures in the data. We develop a general-purpose and computationally efficient framework to…
Understanding how explicit theoretical features are encoded in opaque neural systems is a central challenge now common to neuroscience and AI. We introduce Metric Learning Encoding Models (MLEMs) to address this challenge most directly as a…
Storing information in DNA molecules is of great interest because of its advantages in longevity, high storage density, and low maintenance cost. A key step in the DNA storage pipeline is to efficiently cluster the retrieved DNA sequences…
Structured Low-Rank Approximation is a problem arising in a wide range of applications in Numerical Analysis and Engineering Sciences. Given an input matrix $M$, the goal is to compute a matrix $M'$ of given rank $r$ in a linear or affine…
We map categorical variables in a function approximation problem into Euclidean spaces, which are the entity embeddings of the categorical variables. The mapping is learned by a neural network during the standard supervised training…
Over the past few years, symmetric positive definite (SPD) matrices have been receiving considerable attention from computer vision community. Though various distance measures have been proposed in the past for comparing SPD matrices, the…
In this paper, we give the first algorithm that outputs a faithful reconstruction of a submanifold of Euclidean space without maintaining or even constructing complicated data structures such as Voronoi diagrams or Delaunay complexes. Our…
We study the problem of estimating the Earth Mover's Distance (EMD) between probability distributions when given access only to samples. We give closeness testers and additive-error estimators over domains in $[0, \Delta]^d$, with sample…
We study the real algebraic variety of real symmetric matrices with eigenvalue multiplicities determined by a partition. We present formulas for the dimension and Euclidean distance degree. We give a parametrization by rational functions.…
FastMap was first introduced in the Data Mining community for generating Euclidean embeddings of complex objects. In this dissertation, we first present FastMap to generate Euclidean embeddings of graphs in near-linear time: The pairwise…