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This paper is concerned with the analysis of correlation between two high-dimensional data sets when there are only few correlated signal components but the number of samples is very small, possibly much smaller than the dimensions of the…
Covariance matrix estimation and principal component analysis (PCA) are two cornerstones of multivariate analysis. Classic textbook solutions perform poorly when the dimension of the data is of a magnitude similar to the sample size, or…
Climate models play a crucial role in understanding the effect of environmental and man-made changes on climate to help mitigate climate risks and inform governmental decisions. Large global climate models such as the Community Earth System…
How does one find dimensions in multivariate data that are reliably expressed across repetitions? For example, in a brain imaging study one may want to identify combinations of neural signals that are reliably expressed across multiple…
The best 3-channel projectile-inelastic [H(1s)+Ps(1s,2s,2p)] close-coupling approximation (CCA) is performed for positronium (Ps) and hydrogen (H) collision considering both the atoms in ground states at the incident channel. The s-wave…
We propose a new technique, Singular Vector Canonical Correlation Analysis (SVCCA), a tool for quickly comparing two representations in a way that is both invariant to affine transform (allowing comparison between different layers and…
We analyze the applicability of our analytical theory of combination harmonics in canonical low-dimensional multi-band Fermi liquids, which was recently criticized by Champel (Phys. Rev. B 65, 153403 (2002)). It is shown that his claim that…
We propose computationally efficient methods for estimating stationary multivariate spatial and spatial-temporal spectra from incomplete gridded data. The methods are iterative and rely on successive imputation of data and updating of model…
Canonical correlation analysis (CCA) is a multivariate statistical method which describes the associations between two sets of variables. The objective is to find linear combinations of the variables in each data set having maximal…
Spectra of exoplanet atmospheres provide us the opportunity to improve our understanding of these objects just as remote sensing in our own solar system has increased our understanding of the solar system bodies. The challenge is to…
Sparse Canonical Correlation Analysis (CCA) has received considerable attention in high-dimensional data analysis to study the relationship between two sets of random variables. However, there has been remarkably little theoretical…
Nowadays, tens of satellites carry hyperspectral spectrometers. Such instruments allow decomposing the light that exits the atmosphere from its top into hundreds to thousands of contiguous spectral channels. By analysis of the light…
Compressive Sensing (CS) theory states that real-world signals can often be recovered from much fewer measurements than those suggested by the Shannon sampling theorem. Nevertheless, recoverability does not only depend on the signal, but…
We study the problem of estimating the frequencies of several complex sinusoids with constant amplitude (CA) (also called constant modulus) from multichannel signals of their superposition. To exploit the CA property for frequency…
Spectral PCA (sPCA), in contrast to classical PCA, offers the advantage of identifying organized spatio-temporal patterns within specific frequency bands and extracting dynamical modes. However, the unavoidable tradeoff between frequency…
The recently established RPCA method provides us a convenient way to restore low-rank matrices from grossly corrupted observations. While elegant in theory and powerful in reality, RPCA may be not an ultimate solution to the low-rank matrix…
Critical decisions frequently rely on high-dimensional output from complex computer simulation models that show intricate cross-variable, spatial and temporal dependence structures, with weather and climate predictions being key examples.…
Canonical Correlation Analysis, CCA, is a widely used multivariate method in omics research for integrating high dimensional datasets. CCA identifies hidden links by deriving linear projections of features maximally correlating datasets.…
Residual wavefront errors in optical elements limit the performance of coronagraphs. To improve their efficiency, different types of devices have been proposed to correct or calibrate these errors. In this paper, we study one of these…
We analyze recent results for a harmonic oscillator in an environment with a pointlike defect. We show that the allowed oscillator frequencies predicted by the authors stem from a misinterpretation of the exact solutions of a conditionally…