Related papers: Dimension Reduction with Prior Information for Kno…
Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…
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…
Sufficient dimension reduction aims for reduction of dimensionality of a regression without loss of information by replacing the original predictor with its lower-dimensional subspace. Partial (sufficient) dimension reduction arises when…
A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on…
Missing data present challenges in data analysis. Naive analyses such as complete-case and available-case analysis may introduce bias and loss of efficiency, and produce unreliable results. Multiple imputation (MI) is one of the most widely…
We consider the problem of reducing the dimensions of parameters and data in non-Gaussian Bayesian inference problems. Our goal is to identify an "informed" subspace of the parameters and an "informative" subspace of the data so that a…
The concept of matching dependencies (mds) is recently pro- posed for specifying matching rules for object identification. Similar to the functional dependencies (with conditions), mds can also be applied to various data quality…
In order to avoid the curse of dimensionality, frequently encountered in Big Data analysis, there was a vast development in the field of linear and nonlinear dimension reduction techniques in recent years. These techniques (sometimes…
Multidimensional scaling is a statistical process that aims to embed high dimensional data into a lower-dimensional space; this process is often used for the purpose of data visualisation. Common multidimensional scaling algorithms tend to…
A novel method for common and individual feature analysis from exceedingly large-scale data is proposed, in order to ensure the tractability of both the computation and storage and thus mitigate the curse of dimensionality, a major…
Metric embeddings are a widely used method in algorithm design, where generally a ``complex'' metric is embedded into a simpler, lower-dimensional one. Historically, the theoretical computer science community has focused on bi-Lipschitz…
This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…
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…
Manifold learning (ML) aims to seek low-dimensional embedding from high-dimensional data. The problem is challenging on real-world datasets, especially with under-sampling data, and we find that previous methods perform poorly in this case.…
In instance-level detection tasks (e.g., object detection), reducing input resolution is an easy option to improve runtime efficiency. However, this option traditionally hurts the detection performance much. This paper focuses on boosting…
We propose a multifidelity dimension reduction method to identify a low-dimensional structure present in many engineering models. The structure of interest arises when functions vary primarily on a low-dimensional subspace of the…
Progressive dimensionality reduction algorithms allow for visually investigating intermediate results, especially for large data sets. While different algorithms exist that progressively increase the number of data points, we propose an…
We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards…
Large models and enormous data are essential driving forces of the unprecedented successes achieved by modern algorithms, especially in scientific computing and machine learning. Nevertheless, the growing dimensionality and model…
Dimension reduction is a technique used to transform data from a high-dimensional space into a lower-dimensional space, aiming to retain as much of the original information as possible. This approach is crucial in many disciplines like…