Related papers: On dimension folding of matrix- or array-valued st…
Dimensionality reduction (DR) on the manifold includes effective methods which project the data from an implicit relational space onto a vectorial space. Regardless of the achievements in this area, these algorithms suffer from the lack of…
Beginning with a discussion of R. A. Fisher's early written remarks that relate to dimension reduction, this article revisits principal components as a reductive method in regression, develops several model-based extensions and ends with…
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…
The vast majority of Dimensionality Reduction (DR) techniques rely on second-order statistics to define their optimization objective. Even though this provides adequate results in most cases, it comes with several shortcomings. The methods…
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…
Static word embedding is still useful, particularly for context-unavailable tasks, because in the case of no context available, pre-trained language models often perform worse than static word embeddings. Although dimension is a key factor…
Recently, Su and Cook proposed a dimension reduction technique called the inner envelope which can be substantially more efficient than the original envelope or existing dimension reduction techniques for multivariate regression. However,…
With the rapid development of data collection techniques, complex data objects that are not in the Euclidean space are frequently encountered in new statistical applications. Fr\'echet regression model (Peterson & M\"uller 2019) provides a…
As is known, factor analysis is a popular method to reduce dimension for high-dimensional data. For matrix data, the dimension reduction can be more effectively achieved through both row and column directions. In this paper, we introduce a…
We address the problem of sufficient dimension reduction for feature matrices, which arises often in sensor network localization, brain neuroimaging, and electroencephalography analysis. In general, feature matrices have both row- and…
To solve key biomedical problems, experimentalists now routinely measure millions or billions of features (dimensions) per sample, with the hope that data science techniques will be able to build accurate data-driven inferences. Because…
Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low dimensional linear time invariant dynamics underlying high-dimensional data. For systems in which such underlying low-dimensional dynamics is time-varying, a…
The joint optimization of the reconstruction and classification error is a hard non convex problem, especially when a non linear mapping is utilized. In order to overcome this obstacle, a novel optimization strategy is proposed, in which a…
Dimensionality reduction (DR) is often used as a preprocessing step in classification, but usually one first fixes the DR mapping, possibly using label information, and then learns a classifier (a filter approach). Best performance would be…
This paper proposes a tool for dimension reduction where the dimension of the original space is reduced: a Principal Loading Analysis (PLA). PLA is a tool to reduce dimensions by discarding variables. The intuition is that variables are…
It has previously been shown that response transformations can be very effective in improving dimension reduction outcomes for a continuous response. The choice of transformation used can make a big difference in the visualization of the…
The goal of dimension reduction tools is to construct a low-dimensional representation of high-dimensional data. These tools are employed for a variety of reasons such as noise reduction, visualization, and to lower computational costs.…
Dimensionality Reduction plays a pivotal role in improving feature learning accuracy and reducing training time by eliminating redundant features, noise, and irrelevant data. Nonnegative Matrix Factorization (NMF) has emerged as a popular…
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…
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…