Related papers: Dimension Reduction for Data with Heterogeneous Mi…
We present new findings in regard to data analysis in very high dimensional spaces. We use dimensionalities up to around one million. A particular benefit of Correspondence Analysis is its suitability for carrying out an orthonormal…
Dimensionality reduction (DR) is often used as a preprocessing step in classification, but usually one first fixes the DR mapping, possibly using label information, and then learns a classifier (a filter approach). Best performance would be…
Dimensionality reduction and matrix factorization techniques are important and useful machine-learning techniques in many fields. Nonnegative matrix factorization (NMF) is particularly useful for spectral analysis and image processing in…
In many important statistical analyses, the number of covariates $p$ often exceeds the data size $n$, a regime commonly referred to as high-dimensional. While considerable progress has been made in high-dimensional regression under the…
Unsupervised dimension selection is an important problem that seeks to reduce dimensionality of data, while preserving the most useful characteristics. While dimensionality reduction is commonly utilized to construct low-dimensional…
In this note we discuss a common misconception, namely that embeddings are always used to reduce the dimensionality of the item space. We show that when we measure dimensionality in terms of information entropy then the embedding of sparse…
As a typical dimensionality reduction technique, random projection can be simply implemented with linear projection, while maintaining the pairwise distances of high-dimensional data with high probability. Considering this technique is…
Matrix completion constantly receives tremendous attention from many research fields. It is commonly applied for recommender systems such as movie ratings, computer vision such as image reconstruction or completion, multi-task learning such…
We reframe linear dimensionality reduction as a problem of Bayesian inference on matrix manifolds. This natural paradigm extends the Bayesian framework to dimensionality reduction tasks in higher dimensions with simpler models at greater…
The concept of depth has proved very important for multivariate and functional data analysis, as it essentially acts as a surrogate for the notion a ranking of observations which is absent in more than one dimension. Motivated by the rapid…
We investigate the application of the Density Matrix Renormalization Group (DMRG) to the Hubbard model in momentum-space. We treat the one-dimensional models with dispersion relations corresponding to nearest-neighbor hopping and $1/r$…
Parametric dimensionality reduction methods have gained prominence for their ability to generalize to unseen datasets, an advantage that traditional approaches typically lack. Despite their growing popularity, there remains a prevalent…
Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have…
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,…
Modern surveys with large sample sizes and growing mixed-type questionnaires require robust and scalable analysis methods. In this work, we consider recovering a mixed dataframe matrix, obtained by complex survey sampling, with entries…
This paper models categorical data with two or multiple responses, focusing on the interactions between responses. We propose an efficient iterative procedure based on sufficient dimension reduction. We study the theoretical guarantees of…
This article considers a novel and widely applicable approach to modeling high-dimensional dependent data when a large number of explanatory variables are available and the signal-to-noise ratio is low. We postulate that a $p$-dimensional…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
Estimation of a high dimensional precision matrix is a critical problem to many areas of statistics including Gaussian graphical models and inference on high dimensional data. Working under the structural assumption of sparsity, we propose…
Change point testing for high-dimensional data has attracted a lot of attention in statistics and machine learning owing to the emergence of high-dimensional data with structural breaks from many fields. In practice, when the dimension is…