Related papers: Averaging orthogonal projectors
Random projection is widely used as a method of dimension reduction. In recent years, its combination with standard techniques of regression and classification has been explored. Here we examine its use with principal component analysis…
In regression analysis, we employ contour projection (CP) to develop a new dimension reduction theory. Accordingly, we introduce the notions of the central contour subspace and generalized contour subspace. We show that both of their…
In our "big data" age, the size and complexity of data is steadily increasing. Methods for dimension reduction are ever more popular and useful. Two distinct types of dimension reduction are "data-oblivious" methods such as random…
Dimensionality reduction is a fundamental technique in machine learning and data analysis, enabling efficient representation and visualization of high-dimensional data. This paper explores five key methods: Principal Component Analysis…
The development and use of dimension reduction methods is prevalent in modern statistical literature. This paper reviews a class of dimension reduction techniques which aim to simultaneously select relevant predictors and find clusters…
This is a tutorial and survey paper on various methods for Sufficient Dimension Reduction (SDR). We cover these methods with both statistical high-dimensional regression perspective and machine learning approach for dimensionality…
Scalability of statistical estimators is of increasing importance in modern applications and dimension reduction is often used to extract relevant information from data. A variety of popular dimension reduction approaches can be framed as…
We propose a novel approach to sufficient dimension reduction in regression, based on estimating contour directions of small variation in the response. These directions span the orthogonal complement of the minimal space relevant for the…
We introduce a new framework for dimension reduction in the context of high-dimensional regression. Our proposal is to aggregate an ensemble of random projections, which have been carefully chosen based on the empirical regression…
We provide new theoretical results in the field of inverse regression methods for dimension reduction. Our approach is based on the study of some empirical processes that lie close to a certain dimension reduction subspace, called the…
Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC…
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…
A plethora of dimension reduction methods have been developed to visualize high-dimensional data in low dimensions. However, different dimension reduction methods often output different and possibly conflicting visualizations of the same…
In applications involving ordinal predictors, common approaches to reduce dimensionality are either extensions of unsupervised techniques such as principal component analysis, or variable selection procedures that rely on modeling the…
High dimensional data and systems with many degrees of freedom are often characterized by covariance matrices. In this paper, we consider the problem of simultaneously estimating the dimension of the principal (dominant) subspace of these…
An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…
Dimension reduction techniques typically seek an embedding of a high-dimensional point cloud into a low-dimensional Euclidean space which optimally preserves the geometry of the input data. Based on expert knowledge, one may instead wish to…
We propose a new method for dimension reduction in regression using the first two inverse moments. We develop corresponding weighted chi-squared tests for the dimension of the regression. The proposed method considers linear combinations of…
High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of…
Online dimension reduction is a common method for high-dimensional streaming data processing. Online principal component analysis, online sliced inverse regression, online kernel principal component analysis and other methods have been…