Related papers: Diversity maximization in doubling metrics
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…
Skewness plays a relevant role in several multivariate statistical techniques. Sometimes it is used to recover data features, as in cluster analysis. In other circumstances, skewness impairs the performances of statistical methods, as in…
Distance metric learning is an important component for many tasks, such as statistical classification and content-based image retrieval. Existing approaches for learning distance metrics from pairwise constraints typically suffer from two…
Clustering in high-dimensions poses many statistical challenges. While traditional distance-based clustering methods are computationally feasible, they lack probabilistic interpretation and rely on heuristics for estimation of the number of…
Recommendation systems have wide-spread applications in both academia and industry. Traditionally, performance of recommendation systems has been measured by their precision. By introducing novelty and diversity as key qualities in…
The density based clustering method {\em Density-Based Spatial Clustering of Applications with Noise (DBSCAN)} is a popular method for outlier recognition and has received tremendous attention from many different areas. A major issue of the…
We introduce a novel criterion in clustering that seeks clusters with limited range of values associated with each cluster's elements. In clustering or classification the objective is to partition a set of objects into subsets, called…
One of the outstanding challenges of cross-identification is multiplicity: detections in crowded regions of the sky are often linked to more than one candidate associations of similar likelihoods. We map the resulting maximum likelihood…
The design of a metric between probability distributions is a longstanding problem motivated by numerous applications in Machine Learning. Focusing on continuous probability distributions on the Euclidean space $\mathbb{R}^d$, we introduce…
Given a set $X\subseteq\mathbb{R}^2$ of $n$ points and a distance $d>0$, the multiplicity of $d$ is the number of times the distance $d$ appears between points in $X$. Let $a_1(X) \geq a_2(X) \geq \cdots \geq a_m(X)$ denote the…
A novel elastic time distance for sparse multivariate functional data is proposed and used to develop a robust distance-based two-layer partition clustering method. With this proposed distance, the new approach not only can detect correct…
There has been considerable recent interest in computing a diverse collection of solutions to a given optimization problem, both in the AI and theory communities. Given a classical optimization problem $\Pi$ (e.g., spanning tree, minimum…
Crowdsourcing can collect many diverse ideas by prompting ideators individually, but this can generate redundant ideas. Prior methods reduce redundancy by presenting peers' ideas or peer-proposed prompts, but these require much human…
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 study a notion of MDS on infinite metric measure spaces,…
Metric learning has attracted extensive interest for its ability to provide personalized recommendations based on the importance of observed user-item interactions. Current metric learning methods aim to push negative items away from the…
We consider the problem of jointly inferring the M-best diverse labelings for a binary (high-order) submodular energy of a graphical model. Recently, it was shown that this problem can be solved to a global optimum, for many practically…
Evaluating the accuracy of dimensionality reduction (DR) projections in preserving the structure of high-dimensional data is crucial for reliable visual analytics. Diverse evaluation metrics targeting different structural characteristics…
With the rising number of machine learning competitions, the world has witnessed an exciting race for the best algorithms. However, the involved data selection process may fundamentally suffer from evidence ambiguity and concept drift…
The Consensus Clustering problem has been introduced as an effective way to analyze the results of different microarray experiments. The problem consists of looking for a partition that best summarizes a set of input partitions (each…
We continue the investigation of problems concerning correlation clustering or clustering with qualitative information, which is a clustering formulation that has been studied recently. The basic setup here is that we are given as input a…