Related papers: Diversity maximization in doubling metrics
For a given metric measure space $(X,d,\mu)$ we consider finite samples of points, calculate the matrix of distances between them and then reconstruct the points in some finite-dimensional space using the multidimensional scaling (MDS)…
There has been a long-standing interest in computing diverse solutions to optimization problems. Motivated by reallocation of governmental institutions in Sweden, in 1995 J. Krarup posed the problem of finding $k$ edge-disjoint Hamiltonian…
We study safe screening for metric learning. Distance metric learning can optimize a metric over a set of triplets, each one of which is defined by a pair of same class instances and an instance in a different class. However, the number of…
Bayesian inference with nested sampling requires a likelihood-restricted prior sampling method, which draws samples from the prior distribution that exceed a likelihood threshold. For high-dimensional problems, Markov Chain Monte Carlo…
Similarity is a fundamental measure in network analyses and machine learning algorithms, with wide applications ranging from personalized recommendation to socio-economic dynamics. We argue that an effective similarity measurement should…
The most useful data mining primitives are distance measures. With an effective distance measure, it is possible to perform classification, clustering, anomaly detection, segmentation, etc. For single-event time series Euclidean Distance…
Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We overview the theory of classical MDS, along with its…
The performance of many machine learning techniques depends on the choice of an appropriate similarity or distance measure on the input space. Similarity learning (or metric learning) aims at building such a measure from training data so…
Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability…
Dimensionality Reduction (DR) techniques can generate 2D projections and enable visual exploration of cluster structures of high-dimensional datasets. However, different DR techniques would yield various patterns, which significantly affect…
This paper proposes a two-time scale neurodynamic duplex approach to solve distributionally robust geometric joint chance-constrained optimization problems. The probability distributions of the row vectors are not known in advance and…
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…
Finding a \emph{single} best solution is the most common objective in combinatorial optimization problems. However, such a single solution may not be applicable to real-world problems as objective functions and constraints are only…
This work tackles two critical challenges related to the development of metaheuristics for Multi-Objective Optimization Problems (MOOPs): the exponential growth of non-dominated solutions and the tendency of metaheuristics to…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
In general, the clustering problem is NP-hard, and global optimality cannot be established for non-trivial instances. For high-dimensional data, distance-based methods for clustering or classification face an additional difficulty, the…
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…
Collaborative Metric Learning (CML) has recently emerged as a popular method in recommendation systems (RS), closing the gap between metric learning and Collaborative Filtering. Following the convention of RS, existing methods exploit…
We introduce the aggregated clustering problem, where one is given $T$ instances of a center-based clustering task over the same $n$ points, but under different metrics. The goal is to open $k$ centers to minimize an aggregate of the…
We investigate task clustering for deep-learning based multi-task and few-shot learning in a many-task setting. We propose a new method to measure task similarities with cross-task transfer performance matrix for the deep learning scenario.…