Related papers: Principal component proxy tracer analysis
We develop a numerical method to reconstruct systems of ordinary differential equations (ODEs) from time series data without {\it a priori} knowledge of the underlying ODEs using sparse basis learning and sparse function reconstruction. We…
The luminosity changes of most types of variable stars are correlated in the different wavelengths, and these correlations may be exploited for several purposes: for variability detection, for distinction of microvariability from noise, for…
Principal component analysis (PCA) represents a standard approach to identify collective variables $\{x_i\}\!=\!\boldsymbol{x}$, which can be used to construct the free energy landscape $\Delta G(\boldsymbol{x})$ of a molecular system.…
In the next decades, the astrobiological community will debate whether the first observations of oxygen in an exoplanet$'$s atmosphere signifies life, so it is critical to establish procedures now for collection and interpretation of such…
In this paper, we study the nonlinear inverse problem of estimating the spectrum of a system matrix, that drives a finite-dimensional affine dynamical system, from partial observations of a single trajectory data. In the noiseless case, we…
This work studies the recursive robust principal components analysis (PCA) problem. If the outlier is the signal-of-interest, this problem can be interpreted as one of recursively recovering a time sequence of sparse vectors, $S_t$, in the…
The Lunar CRater Observation and Sensing Satellite (LCROSS) observed the distant Earth on three occasions in 2009. These data span a range of phase angles, including a rare crescent phase view. For each epoch, the satellite acquired…
In this paper we present closed-form solutions for efficiently updating the principal components of a set of $n$ points, when $m$ points are added or deleted from the point set. For both operations performed on a discrete point set in…
Many have suggested a bootstrap procedure for estimating the sampling variability of principal component analysis (PCA) results. However, when the number of measurements per subject ($p$) is much larger than the number of subjects ($n$),…
Phase retrieval is a nonlinear inverse problem that arises in a wide range of imaging modalities, from electron microscopy to Fourier ptychography. In particular, the reconstruction is facilitated when the sensing matrix is i.i.d. random,…
In a longitudinal metabolomics study, multiple metabolites are measured from several observations at many time points. Interest lies in reducing the dimensionality of such data and in highlighting influential metabolites which change over…
We demonstrate a novel approach to the reconstruction of scanning probe x-ray diffraction tomography data with anisotropic poly crystalline samples. The method involves reconstructing a voxel map containing an orientation distribution…
This paper presents the standardization of Proton Induced X-rays Emission (PIXE) technique for the trace element analysis of thick standard samples. Three standard reference materials (SRMs) viz-\`a-vis titanium, copper and iron base alloys…
Previous versions of sparse principal component analysis (PCA) have presumed that the eigen-basis (a $p \times k$ matrix) is approximately sparse. We propose a method that presumes the $p \times k$ matrix becomes approximately sparse after…
A new look on the principal component analysis has been presented. Firstly, a geometric interpretation of determination coefficient was shown. In turn, the ability to represent the analyzed data and their interdependencies in the form of…
We propose the world first longitudinal gOSNR estimation by using correlation template method at Rx, without any monitoring devices located in the middle of the link. The proposed method is experimentally demonstrated in a 12-span link with…
Techniques have been developed to measure the isotopic composition of trace elements from matrices predominantly consisting of interfering isotopes. These techniques have been applied to measuring mass-independent fractionation of…
Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…
PSR B1508+55 is known to have a single component profile above 300 MHz. However, when we study it at frequencies below 100 MHz using the first station of the Long Wavelength Array, it shows multiple components. These include the main pulse,…
We study the problem of high-dimensional Principal Component Analysis (PCA) with missing observations. In simple, homogeneous missingness settings with a noise level of constant order, we show that an existing inverse-probability weighted…