Related papers: Dimensionality Reduction and (Bucket) Ranking: a M…
Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the…
Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few…
Dislocation networks and their evolution are known to control the mechanical properties of metal samples. However, the lack of computationally efficient and statistically rigorous descriptors for such defect systems has hindered the…
For numerous reasons there raises a need for dimension reduction that preserves certain characteristics of data. In this work we focus on data coming from a mixture of Gaussian distributions and we propose a method that preserves…
Ensemble learning has had many successes in supervised learning, but it has been rare in unsupervised learning and dimensionality reduction. This study explores dimensionality reduction ensembles, using principal component analysis and…
Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…
Given a set of strings over a specified alphabet, identifying a median or consensus string that minimizes the total distance to all input strings is a fundamental data aggregation problem. When the Hamming distance is considered as the…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
A new class of general exponential ranking models is introduced which we label angle-based models for ranking data. A consensus score vector is assumed, which assigns scores to a set of items, where the scores reflect a consensus view of…
Sequential or online dimensional reduction is of interests due to the explosion of streaming data based applications and the requirement of adaptive statistical modeling, in many emerging fields, such as the modeling of energy end-use…
A broad class of systems, including ecological, epidemiological, and sociological ones, are characterized by populations of individuals assigned to specific categories, e.g., a chemical species, an opinion or an epidemic state, that are…
Dimension reduction is a common strategy to study non-linear dynamical systems composed by a large number of variables. The goal is to find a smaller version of the system whose time evolution is easier to predict while preserving some of…
Unsupervised machine learning lacks ground truth by definition. This poses a major difficulty when designing metrics to evaluate the performance of such algorithms. In sharp contrast with supervised learning, for which plenty of quality…
We propose a novel DEA ranking based on a robust optimization viewpoint: the higher ranking for those DMU's that remain efficient even for larger variations of data and vice versa. This ranking can be computed by solving generalized linear…
The article contains a methodology for social statistics assessing. The significance of minorities (groups that differ in their attributes from the majority) has grown substantially in the modern postindustrial economy and society. In the…
Relations between categorical variables can be analyzed conveniently by multiple correspondence analysis (MCA). %It is well suited to discover relations that may exist between categories of different variables. The graphical representation…
We consider models for social choice where voters rank a set of choices (or alternatives) by deliberating in small groups of size at most $k$, and these outcomes are aggregated by a social choice rule to find the winning alternative. We…
Computing with discrete representations of high-dimensional probability distributions is fundamental to uncertainty quantification, Bayesian inference, and stochastic modeling. However, storing and manipulating such distributions suffers…
We show how to incorporate information from labeled examples into nonnegative matrix factorization (NMF), a popular unsupervised learning algorithm for dimensionality reduction. In addition to mapping the data into a space of lower…
Dimensionality reduction is a popular preprocessing and a widely used tool in data mining. Transparency, which is usually achieved by means of explanations, is nowadays a widely accepted and crucial requirement of machine learning based…