Related papers: Comparison Based Nearest Neighbor Search
In the context of post-hoc interpretability, this paper addresses the task of explaining the prediction of a classifier, considering the case where no information is available, neither on the classifier itself, nor on the processed data…
Consider observation data, comprised of n observation vectors with values on a set of attributes. This gives us n points in attribute space. Having data structured as a tree, implied by having our observations embedded in an ultrametric…
Several researchers proposed using non-Euclidean metrics on point sets in Euclidean space for clustering noisy data. Almost always, a distance function is desired that recognizes the closeness of the points in the same cluster, even if the…
Rank-based linkage is a new tool for summarizing a collection $S$ of objects according to their relationships. These objects are not mapped to vectors, and ``similarity'' between objects need be neither numerical nor symmetrical. All an…
Finding similar data in high-dimensional spaces is one of the important tasks in multimedia applications. Approaches introduced to find exact searching techniques often use tree-based index structures which are known to suffer from the…
Approximate K nearest neighbor (AKNN) search is a fundamental and challenging problem. We observe that in high-dimensional space, the time consumption of nearly all AKNN algorithms is dominated by that of the distance comparison operations…
Geometric Near-neighbor Access Tree (GNAT) is a metric space indexing method based on hierarchical hyperplane partitioning of the space. While GNAT is very efficient in proximity searching, it has a bad reputation of being a memory hog. We…
We study metric learning from preference comparisons under the ideal point model, in which a user prefers an item over another if it is closer to their latent ideal item. These items are embedded into $\mathbb{R}^d$ equipped with an unknown…
Twin neural network regression is trained to predict differences between regression targets rather than the targets themselves. A solution to the original regression problem can be obtained by ensembling predicted differences between the…
Motivated by applications in computer vision and databases, we introduce and study the Simultaneous Nearest Neighbor Search (SNN) problem. Given a set of data points, the goal of SNN is to design a data structure that, given a collection of…
Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…
This paper proposes a new probabilistic classification algorithm using a Markov random field approach. The joint distribution of class labels is explicitly modelled using the distances between feature vectors. Intuitively, a class label…
We show that every symmetric normed space admits an efficient nearest neighbor search data structure with doubly-logarithmic approximation. Specifically, for every $n$, $d = n^{o(1)}$, and every $d$-dimensional symmetric norm $\|\cdot\|$,…
Neural networks are not learning optimal decision boundaries. We show that decision boundaries are situated in areas of low training data density. They are impacted by few training samples which can easily lead to overfitting. We provide a…
Building on a specific formalization of analogical relationships of the form "A relates to B as C relates to D", we establish a connection between two important subfields of artificial intelligence, namely analogical reasoning and…
Modern neural network technologies, including large language models, have achieved remarkable success in various applied artificial intelligence applications, however, they face a range of fundamental limitations. Among them are…
Nearest neighbor search has found numerous applications in machine learning, data mining and massive data processing systems. The past few years have witnessed the popularity of the graph-based nearest neighbor search paradigm because of…
Suppose that we wish to estimate a vector $\mathbf{x}$ from a set of binary paired comparisons of the form "$\mathbf{x}$ is closer to $\mathbf{p}$ than to $\mathbf{q}$" for various choices of vectors $\mathbf{p}$ and $\mathbf{q}$. The…
We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…
Distance metric learning is a branch of machine learning that aims to learn distances from the data, which enhances the performance of similarity-based algorithms. This tutorial provides a theoretical background and foundations on this…