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Principal component analysis is a useful dimension reduction and data visualization method. However, in high dimension, low sample size asymptotic contexts, where the sample size is fixed and the dimension goes to infinity,a paradox has…
We propose a high dimensional mean test framework for shrinking random variables, where the underlying random variables shrink to zero as the sample size increases. By pooling observations across overlapping subsets of dimensions, we…
Synthesizing accurate geometry and photo-realistic appearance of small scenes is an active area of research with compelling use cases in gaming, virtual reality, robotic-manipulation, autonomous driving, convenient product capture, and…
Suppose the data consist of a set $S$ of points $x_j, 1 \leq j \leq J$, distributed in a bounded domain $D \subset R^N$, where $N$ and $J$ are large numbers. In this paper an algorithm is proposed for checking whether there exists a…
The analysis of neural representation has become an integral part of research aiming to better understand the inner workings of neural networks. While there are many different approaches to investigate neural representations, an important…
Multiview depth imagery will play a critical role in free-viewpoint television. This technology requires high quality virtual view synthesis to enable viewers to move freely in a dynamic real world scene. Depth imagery at different…
Dimensionality Reduction (DR) is widely used for visualizing high-dimensional data, often with the goal of revealing expected cluster structure. However, such a structure may not always appear in the projections. Existing DR quality metrics…
Three-dimensional (3D) reconstruction from two-dimensional images is an active research field in computer vision, with applications ranging from navigation and object tracking to segmentation and three-dimensional modeling. Traditionally,…
In this paper, we investigate Dimensionality reduction (DR) maps in an information retrieval setting from a quantitative topology point of view. In particular, we show that no DR maps can achieve perfect precision and perfect recall…
Measuring the similarity of images is a fundamental problem to computer vision for which no universal solution exists. While simple metrics such as the pixel-wise L2-norm have been shown to have significant flaws, they remain popular. One…
Recently, Su and Cook proposed a dimension reduction technique called the inner envelope which can be substantially more efficient than the original envelope or existing dimension reduction techniques for multivariate regression. However,…
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…
Recent work has established clear links between the generalization performance of trained neural networks and the geometry of their loss landscape near the local minima to which they converge. This suggests that qualitative and quantitative…
High dynamic range (HDR) rendering has the ability to faithfully reproduce the wide luminance ranges in natural scenes, but how to accurately assess the rendering quality is relatively underexplored. Existing quality models are mostly…
Dimensionality reduction (DR) methods are commonly used for analyzing and visualizing multidimensional data. However, when data is a live streaming feed, conventional DR methods cannot be directly used because of their computational…
Unsupervised and supervised learning methods conventionally use kernels to capture nonlinearities inherent in data structure. However experts have to ensure their proposed nonlinearity maximizes variability and capture inherent diversity of…
The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing…
Datasets such as images, text, or movies are embedded in high-dimensional spaces. However, in important cases such as images of objects, the statistical structure in the data constrains samples to a manifold of dramatically lower…
The effectiveness of dimensionality reduction with quadratic manifolds hinges on the choice of a reduced basis and the associated quadratic correction terms. Existing approaches typically rely on subspaces spanned by the leading principal…
One of the challenges in analyzing high-dimensional expression data is the detection of important biological signals. A common approach is to apply a dimension reduction method, such as principal component analysis. Typically, after…