Related papers: Dimensionality Reduction with Subspace Structure P…
Dimensionality reduction has become an important research topic as demand for interpreting high-dimensional datasets has been increasing rapidly in recent years. There have been many dimensionality reduction methods with good performance in…
Many machine learning applications deal with high dimensional data. To make computations feasible and learning more efficient, it is often desirable to reduce the dimensionality of the input variables by finding linear combinations of the…
In our work, we propose a novel formulation for supervised dimensionality reduction based on a nonlinear dependency criterion called Statistical Distance Correlation, Szekely et. al. (2007). We propose an objective which is free of…
This paper addresses the construction of a short-vector (128D) image representation for large-scale image and particular object retrieval. In particular, the method of joint dimensionality reduction of multiple vocabularies is considered.…
The unprecedented prowess of measurement techniques provides a detailed, multi-scale look into the depths of living systems. Understanding these avalanches of high-dimensional data -- by distilling underlying principles and mechanisms --…
Many applications, such as optimization, uncertainty quantification and inverse problems, require repeatedly performing simulations of large-dimensional physical systems for different choices of parameters. This can be prohibitively…
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…
We explore two primary classes of approaches to dimensionality reduction (DR): Independent Dimensionality Reduction (IDR) and Simultaneous Dimensionality Reduction (SDR). In IDR methods, of which Principal Components Analysis is a…
We present a novel approach for the construction of ensemble classifiers based on dimensionality reduction. Dimensionality reduction methods represent datasets using a small number of attributes while preserving the information conveyed by…
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…
When performing classification tasks, raw high dimensional features often contain redundant information, and lead to increased computational complexity and overfitting. In this paper, we assume the data samples lie on a single underlying…
Private data analysis suffers a costly curse of dimensionality. However, the data often has an underlying low-dimensional structure. For example, when optimizing via gradient descent, the gradients often lie in or near a low-dimensional…
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…
In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential…
Complex systems are ubiquitous in nature and engineering, but their analysis and control are hampered by their high dimensionality and the influence of various factors on their dynamics. Dimensionality reduction aims to find a…
Dimensionality reduction can distort vector space properties such as orthogonality and linear independence, which are critical for tasks including cross-modal retrieval, clustering, and classification. We propose a Relationship Preserving…
Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…
The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…
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…
We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…