Beyond the Third Dimension: Visualizing High-Dimensional Data with Projections

Beyond the Third Dimension: Visualizing High-Dimensional Data with Projections

Visualizing Large-scale and High-dimensional Data

We study the problem of visualizing large-scale and highdimensional data in a low-dimensional (typically 2D or 3D) space. Much success has been reported recently by techniques that first compute a similarity structure of the data points and then project them into a low-dimensional space with the structure preserved. These two steps suffer from considerable computational costs, preventing the st...

Manual Controls For High-Dimensional Data Projections

Projections of high-dimensional data onto low-dimensional subspaces provide insightful views for understanding multivariate relationships. In this paper we discuss how to manually control the variable contributions to the projection. The user has control of the way a particular variable contributes to the viewed projection and can interactively adjust the variable's contribution. These manual c...

Dimension reduction for high-dimensional data.

With advancing of modern technologies, high-dimensional data have prevailed in computational biology. The number of variables p is very large, and in many applications, p is larger than the number of observational units n. Such high dimensionality and the unconventional small-n-large-p setting have posed new challenges to statistical analysis methods. Dimension reduction, which aims to reduce t...

High-Dimensional Principal Projections

The Principal Component Analysis (PCA) is a famous technique from multivariate statistics. It is frequently carried out in dimension reduction either for functional data or in a high dimensional framework. To that aim PCA yields the eigenvectors (φ̂i)i of the covariance operator of a sample of interest. Dimension reduction is obtained by projecting on the eigenspaces spanned by the φ̂i’s usually ...