Related papers: A Subspace-based Approach for Dimensionality Reduc…

The rapidly evolving field of engineering design of functional surfaces necessitates sophisticated tools to manage the inherent complexity of high-dimensional design spaces. This survey paper offers a scoping review, i.e., a literature…

The "curse of dimensionality" is a well-known problem in pattern recognition. A widely used approach to tackling the problem is a group of subspace methods, where the original features are projected onto a new space. The lower dimensional…

Feature selection is a critical step in the analysis of high-dimensional data, where the number of features often vastly exceeds the number of samples. Effective feature selection not only improves model performance and interpretability but…

In this study, we propose a new statical approach for high-dimensionality reduction of heterogenous data that limits the curse of dimensionality and deals with missing values. To handle these latter, we propose to use the Random Forest…

Dimensionality reduction is a common method for analyzing and visualizing high-dimensional data across domains. Dimensionality-reduction algorithms involve complex optimizations and the reduced dimensions computed by these algorithms…

Dimensionality reduction techniques play important roles in the analysis of big data. Traditional dimensionality reduction approaches, such as principal component analysis (PCA) and linear discriminant analysis (LDA), have been studied…

Solving large-scale optimization on-the-fly is often a difficult task for real-time computer graphics applications. To tackle this challenge, model reduction is a well-adopted technique. Despite its usefulness, model reduction often…

Large high-dimensional datasets are becoming more and more popular in an increasing number of research areas. Processing the high dimensional data incurs a high computational cost and is inherently inefficient since many of the values that…

It is now practically the norm for data to be very high dimensional in areas such as genetics, machine vision, image analysis and many others. When analyzing such data, parametric models are often too inflexible while nonparametric…

The challenge of taking many variables into account in optimization problems may be overcome under the hypothesis of low effective dimensionality. Then, the search of solutions can be reduced to the random embedding of a low dimensional…

We propose a novel and computationally efficient approach for nonparametric conditional density estimation in high-dimensional settings that achieves dimension reduction without imposing restrictive distributional or functional form…

Bayesian optimization (BO) is a leading method for optimizing expensive black-box optimization and has been successfully applied across various scenarios. However, BO suffers from the curse of dimensionality, making it challenging to scale…

In the covariate shift learning scenario, the training and test covariate distributions differ, so that a predictor's average loss over the training and test distributions also differ. In this work, we explore the potential of extreme…

Visualizing high dimensional data by projecting them into two or three dimensional space is one of the most effective ways to intuitively understand the data's underlying characteristics, for example their class neighborhood structure.…

As data sets continue to grow in size and complexity, effective and efficient techniques are needed to target important features in the variable space. Many of the variable selection techniques that are commonly used alongside clustering…

Technological innovations have revolutionized the process of scientific research and knowledge discovery. The availability of massive data and challenges from frontiers of research and development have reshaped statistical thinking, data…

Dimensionality reduction is often used as an initial step in data exploration, either as preprocessing for classification or regression or for visualization. Most dimensionality reduction techniques to date are unsupervised; they do not…

We introduce a dimension reduction method for visualizing the clustering structure obtained from a finite mixture of Gaussian densities. Information on the dimension reduction subspace is obtained from the variation on group means and,…

Data are not only ubiquitous in society, but are increasingly complex both in size and dimensionality. Dimension reduction offers researchers and scholars the ability to make such complex, high dimensional data spaces simpler and more…

One of the central issues of several machine learning applications on real data is the choice of the input features. Ideally, the designer should select only the relevant, non-redundant features to preserve the complete information…