Related papers: Orthogonal projections of hypercubes
Of particular interest is to discover useful representations solely from observations in an unsupervised generative manner. However, the question of whether existing normalizing flows provide effective representations for downstream tasks…
This work uses visual knowledge discovery in parallel coordinates to advance methods of interpretable machine learning. The graphic data representation in parallel coordinates made the concepts of hypercubes and hyperblocks (HBs) simple to…
Distributed algorithms and theories are called for in this era of big data. Under weaker local signal-to-noise ratios, we improve upon the celebrated one-round distributed principal component analysis (PCA) algorithm designed in the spirit…
Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional dataset. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional…
We use Principal Component Analysis (PCA) to study the gas dynamics in numerical simulations of typical MCs. Our simulations account for the non-isothermal nature of the gas and include a simplified treatment of the time-dependent gas…
Dimension reduction and visualization is a staple of data analytics. Methods such as Principal Component Analysis (PCA) and Multidimensional Scaling (MDS) provide low dimensional (LD) projections of high dimensional (HD) data while…
Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data.…
Principal component analysis (PCA) is possibly one of the most widely used statistical tools to recover a low-rank structure of the data. In the high-dimensional settings, the leading eigenvector of the sample covariance can be nearly…
Traditional principal component analysis (PCA) is well known in high-dimensional data analysis, but it requires to express data by a matrix with observations to be continuous. To overcome the limitations, a new method called flexible PCA…
TimeCluster is a visual analytics technique for discovering structure in long multivariate time series by projecting overlapping windows of data into a low-dimensional space. We show that, when Principal Component Analysis (PCA) is chosen…
Generalization of time series prediction remains an important open issue in machine learning, wherein earlier methods have either large generalization error or local minima. We develop an analytically solvable, unsupervised learning scheme…
Classical machine learning algorithms often face scalability bottlenecks when they are applied to large-scale data. Such algorithms were designed to work with small data that is assumed to fit in the memory of one machine. In this report,…
Probabilistic circuits (PCs) are powerful probabilistic models that enable exact and tractable inference, making them highly suitable for probabilistic reasoning and inference tasks. While dominant in neural networks, representation…
Real-time or near real-time hyperspectral detection and identification are extremely useful and needed in many fields. These data sets can be quite large, and the algorithms can require numerous computations that slow the process down. A…
Many machine learning systems are vulnerable to small perturbations made to inputs either at test time or at training time. This has received much recent interest on the empirical front due to applications where reliability and security are…
Understanding the morphology of galaxies is a critical aspect of astrophysics research, providing insight into the formation, evolution, and physical properties of these vast cosmic structures. Various observational and computational…
The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of…
Principal component analysis (PCA) is a dimensionality reduction method in data analysis that involves diagonalizing the covariance matrix of the dataset. Recently, quantum algorithms have been formulated for PCA based on diagonalizing a…
The growing size of modern data sets brings many challenges to the existing statistical estimation approaches, which calls for new distributed methodologies. This paper studies distributed estimation for a fundamental statistical machine…
Principal component analysis (PCA) is a statistical technique commonly used in multivariate data analysis. However, PCA can be difficult to interpret and explain since the principal components (PCs) are linear combinations of the original…