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We introduce $k$NN-LMs, which extend a pre-trained neural language model (LM) by linearly interpolating it with a $k$-nearest neighbors ($k$NN) model. The nearest neighbors are computed according to distance in the pre-trained LM embedding…

Similarity search based on a distance function in metric spaces is a fundamental problem for many applications. Queries for similar objects lead to the well-known machine learning task of nearest-neighbours identification. Many data…

In this work we examine recently proposed distance-based classification method designed for near-term quantum processing units with limited resources. We further study possibilities to reduce the quantum resources without any efficiency…

Supervised classification can be effective for prediction but sometimes weak on interpretability or explainability (XAI). Clustering, on the other hand, tends to isolate categories or profiles that can be meaningful but there is no…

The Word Mover's Distance (WMD) proposed by Kusner et al. is a distance between documents that takes advantage of semantic relations among words that are captured by their embeddings. This distance proved to be quite effective, obtaining…

This paper addresses the problem of finding a B-term wavelet representation of a given discrete function $f \in \real^n$ whose distance from f is minimized. The problem is well understood when we seek to minimize the Euclidean distance…

Dimensionality reduction (DR) on the manifold includes effective methods which project the data from an implicit relational space onto a vectorial space. Regardless of the achievements in this area, these algorithms suffer from the lack of…

We consider a classical problem in choice theory -- vote aggregation -- using novel distance measures between permutations that arise in several practical applications. The distance measures are derived through an axiomatic approach, taking…

Recent years have witnessed a tremendous growth using topological summaries, especially the persistence diagrams (encoding the so-called persistent homology) for analyzing complex shapes. Intuitively, persistent homology maps a potentially…

Clustering is widely used in unsupervised learning to find homogeneous groups of observations within a dataset. However, clustering mixed-type data remains a challenge, as few existing approaches are suited for this task. This study…

Pattern recognition constitutes a particularly important task underlying a great deal of scientific and technologica activities. At the same time, pattern recognition involves several challenges, including the choice of features to…

A $k$-nearest neighbor ($k$NN) query determines the $k$ nearest points, using distance metrics, from a specific location. An all $k$-nearest neighbor (A$k$NN) query constitutes a variation of a $k$NN query and retrieves the $k$ nearest…

This work approaches the multidimensional scaling problem from a novel angle. We introduce a scalable method based on the h-plot, which inherently accommodates asymmetric proximity data. Instead of embedding the objects themselves, the…

We describe the Median K-Flats (MKF) algorithm, a simple online method for hybrid linear modeling, i.e., for approximating data by a mixture of flats. This algorithm simultaneously partitions the data into clusters while finding their…

We present an algorithm of clustering of many-dimensional objects, where only the distances between objects are used. Centers of classes are found with the aid of neuron-like procedure with lateral inhibition. The result of clustering does…

Deep learning methods capable of handling relational data have proliferated over the last years. In contrast to traditional relational learning methods that leverage first-order logic for representing such data, these deep learning methods…

This paper addresses the problem of mapping high-dimensional data to a low-dimensional space, in the presence of other known features. This problem is ubiquitous in science and engineering as there are often controllable/measurable features…

Feature selection is an important problem in high-dimensional data analysis and classification. Conventional feature selection approaches focus on detecting the features based on a redundancy criterion using learning and feature searching…

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,…

The Johnson-Lindenstrauss lemma allows dimension reduction on real vectors with low distortion on their pairwise Euclidean distances. This result is often used in algorithms such as $k$-means or $k$ nearest neighbours since they only use…