Related papers: Revealing the Basis: Ordinal Embedding Through Geo…
The objective of ordinal embedding is to find a Euclidean representation of a set of abstract items, using only answers to triplet comparisons of the form "Is item $i$ closer to the item $j$ or item $k$?". In recent years, numerous…
Ordinal embedding aims at finding a low dimensional representation of objects from a set of constraints of the form "item $j$ is closer to item $i$ than item $k$". Typically, each object is mapped onto a point vector in a low dimensional…
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…
In the absence of prior knowledge, ordinal embedding methods obtain new representation for items in a low-dimensional Euclidean space via a set of quadruple-wise comparisons. These ordinal comparisons often come from human annotators, and…
Existing ordinal embedding methods usually follow a two-stage routine: outlier detection is first employed to pick out the inconsistent comparisons; then an embedding is learned from the clean data. However, learning in a multi-stage manner…
In recent years it has become popular to study machine learning problems in a setting of ordinal distance information rather than numerical distance measurements. By ordinal distance information we refer to binary answers to distance…
To investigate objects without a describable notion of distance, one can gather ordinal information by asking triplet comparisons of the form "Is object $x$ closer to $y$ or is $x$ closer to $z$?" In order to learn from such data, the…
Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of…
We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…
Metric embeddings traditionally study how to map $n$ items to a target metric space such that distance lengths are not heavily distorted; but what if we only care to preserve the relative order of the distances (and not their length)? In…
In this paper, we aim to learn a low-dimensional Euclidean representation from a set of constraints of the form "item j is closer to item i than item k". Existing approaches for this "ordinal embedding" problem require expensive…
We prove optimal bounds for the convergence rate of ordinal embedding (also known as non-metric multidimensional scaling) in the 1-dimensional case. The examples witnessing optimality of our bounds arise from a result in additive number…
Embeddings mapping high-dimensional discrete input to lower-dimensional continuous vector spaces have been widely adopted in machine learning applications as a way to capture domain semantics. Interviewing 13 embedding users across…
Most problems involving simultaneous localization and mapping can nowadays be solved using one of two fundamentally different approaches. The traditional approach is given by a least-squares objective, which minimizes many local photometric…
Motivated by recent work on ordinal embedding (Kleindessner and von Luxburg, 2014), we derive large sample consistency results and rates of convergence for the problem of embedding points based on triple or quadruple distance comparisons.…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
For natural language understanding and generation, embedding concepts using an order-based representation is an essential task. Unlike traditional point vector based representation, an order-based representation imposes geometric…
We use some of the largest order statistics of the random projections of a reference signal to construct a binary embedding that is adapted to signals correlated with such signal. The embedding is characterized from the analytical…
The goal of image ordinal estimation is to estimate the ordinal label of a given image with a convolutional neural network. Existing methods are mainly based on ordinal regression and particularly focus on modeling the ordinal mapping from…
A class of neural networks that gained particular interest in the last years are neural ordinary differential equations (neural ODEs). We study input-output relations of neural ODEs using dynamical systems theory and prove several results…