Related papers: Dimension Reduction with Prior Information for Kno…
We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…
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…
Even the best scientific equipment can only partially observe reality. Recorded data is often lower-dimensional, e.g., two-dimensional pictures of the three-dimensional world. Combining data from multiple experiments then results in a…
Science mapping (SM), the study of the organization and development of science and technology, is a rapidly developing field within information science. The volume of available data allows this methodology to empirically address such issues…
High-dimensional representations for words, text, images, knowledge graphs and other structured data are commonly used in different paradigms of machine learning and data mining. These representations have different degrees of…
Dimensionality reduction can be applied to hyperspectral images so that the most useful data can be extracted and processed more quickly. This is critical in any situation in which data volume exceeds the capacity of the computational…
Clustering and dimensionality reduction have been crucial topics in machine learning and computer vision. Clustering high-dimensional data has been challenging for a long time due to the curse of dimensionality. For that reason, a more…
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…
Consider a high-dimensional data set, in which for every data-point there is incomplete information. Each object in the data set represents a real entity, which is described by a point in high-dimensional space. We model the lack of…
This paper proposes a supervised dimension reduction methodology for tensor data which has two advantages over most image-based prognostic models. First, the model does not require tensor data to be complete which expands its application to…
These notes are an overview of some classical linear methods in Multivariate Data Analysis. This is a good old domain, well established since the 60's, and refreshed timely as a key step in statistical learning. It can be presented as part…
We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…
Diffusion Map is a spectral dimensionality reduction technique which is able to uncover nonlinear submanifolds in high-dimensional data. And, it is increasingly applied across a wide range of scientific disciplines, such as biology,…
Finding rare information hidden in a huge amount of data from the Internet is a necessary but complex issue. Many researchers have studied this issue and have found effective methods to detect anomaly data in low dimensional space. However,…
While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality reduction methods are not amenable to the analysis of such manifolds. This is mainly…
Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to…
Knowledge distillation (KD) has proven highly effective for compressing large models and enhancing the performance of smaller ones. However, its effectiveness diminishes in cross-modal scenarios, such as vision-to-language distillation,…
In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying…
There exist many high-dimensional data in real-world applications such as biology, computer vision, and social networks. Feature selection approaches are devised to confront with high-dimensional data challenges with the aim of efficient…
Researchers in the biological sciences nowadays often encounter the curse of high-dimensionality, which many previously developed statistical models fail to overcome. To tackle this problem, sufficient dimension reduction aims to estimate…