Related papers: Linear Dimensionality Reduction
Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…
How to solve high-dimensional linear programs (LPs) efficiently is a fundamental question. Recently, there has been a surge of interest in reducing LP sizes using random projections, which can accelerate solving LPs independently of…
We propose a modification of linear discriminant analysis, referred to as compressive regularized discriminant analysis (CRDA), for analysis of high-dimensional datasets. CRDA is specially designed for feature elimination purpose and can be…
Dimensionality reduction is a classical technique widely used for data analysis. One foundational instantiation is Principal Component Analysis (PCA), which minimizes the average reconstruction error. In this paper, we introduce the…
We present a supervised dimensionality reduction technique called Convex Linear Discriminant Analysis (ConvexLDA). The proposed model optimizes a multi-objective cost function by balancing two complementary terms. The first term pulls the…
Supervised dimensionality reduction has emerged as an important theme in the last decade. Despite the plethora of models and formulations, there is a lack of a simple model which aims to project the set of patterns into a space defined by…
We present a tutorial on reduced-rank signal processing, design methods and algorithms for dimensionality reduction, and cover a number of important applications. A general framework based on linear algebra and linear estimation is employed…
Sentence embeddings produced by Pretrained Language Models (PLMs) have received wide attention from the NLP community due to their superior performance when representing texts in numerous downstream applications. However, the high…
There has been a lot of interest in sufficient dimension reduction (SDR) methodologies as well as nonlinear extensions in the statistics literature. In this note, we use classical results regarding metric spaces and positive definite…
Principal Subspace Analysis (PSA) -- and its sibling, Principal Component Analysis (PCA) -- is one of the most popular approaches for dimensionality reduction in signal processing and machine learning. But centralized PSA/PCA solutions are…
Dimension reduction is an important tool for analyzing high-dimensional data. The predictor envelope is a method of dimension reduction for regression that assumes certain linear combinations of the predictors are immaterial to the…
Dimensionality reduction (DR) is a popular method for preparing and analyzing high-dimensional data. Reduced data representations are less computationally intensive and easier to manage and visualize, while retaining a significant…
High dimensional data reduction techniques are provided by using partial least squares within deep learning. Our framework provides a nonlinear extension of PLS together with a disciplined approach to feature selection and architecture…
The availability of large amounts of data and compelling computation power have made deep learning models much popular for text classification and sentiment analysis. Deep neural networks have achieved competitive performance on the above…
In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…
Methods for supervised principal component analysis (SPCA) aim to incorporate label information into principal component analysis (PCA), so that the extracted features are more useful for a prediction task of interest. Prior work on SPCA…
Representing images and videos with Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, has been shown to yield high discriminative power in many visual recognition tasks.…
Dimensionality reduction methods are an essential tool for multidimensional data analysis, and many interesting processes can be studied as time-dependent multivariate datasets. There are, however, few studies and proposals that leverage on…
In many social, economical, biological and medical studies, one objective is to classify a subject into one of several classes based on a set of variables observed from the subject. Because the probability distribution of the variables is…
This paper addresses the problem of mapping high-dimensional data to a low-dimensional space, in the presence of other known features. This problem is ubiquitous in science and engineering as there are often controllable/measurable features…