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Principal component analysis is a powerful statistical system to investigate the structure and dynamics of the molecular interstellar medium, with particular emphasis on the study of turbulence, as revealed by spectroscopic imaging of…

We present a method for automated classification of galaxies with low signal-to-noise (S/N) spectra typical of redshift surveys. We develop spectral simulations based on the parameters for the 2dF Galaxy Redshift Survey, and with these…

We investigate the integrated spectra of a sample of 24 normal galaxies. A principal component analysis suggests that most of the variance present in the spectra is due to the differences in morphology of the galaxies in the sample. We show…

We present a new technique called contrastive principal component analysis (cPCA) that is designed to discover low-dimensional structure that is unique to a dataset, or enriched in one dataset relative to other data. The technique is a…

Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a…

Principal component analysis (PCA) is a popular dimension reduction technique often used to visualize high-dimensional data structures. In genomics, this can involve millions of variables, but only tens to hundreds of observations.…

Dimensionality reduction represents a critical preprocessing step in order to increase the efficiency and the performance of many hyperspectral imaging algorithms. However, dimensionality reduction algorithms, such as the Principal…

Principal Component Analysis (PCA) and other multi-variate models are often used in the analysis of "omics" data. These models contain much information which is currently neither easily accessible nor interpretable. Here we present an…

Principal component analysis (PCA) is a well-established tool in machine learning and data processing. The principal axes in PCA were shown to be equivalent to the maximum marginal likelihood estimator of the factor loading matrix in a…

We describe a simple technique for the acceleration of spectro-polarimetric inversions based on principal component analysis (PCA) of Stokes profiles. This technique involves the indexing of the database models based on the sign of the…

Methods for analysis of principal components in discrete data have existed for some time under various names such as grade of membership modelling, probabilistic latent semantic analysis, and genotype inference with admixture. In this paper…

Principal Component Analysis (PCA) finds the best linear representation of data, and is an indispensable tool in many learning and inference tasks. Classically, principal components of a dataset are interpreted as the directions that…

We analyse 400 ks of XMM-Newton data on the active galactic nucleus NGC 1365 using principal component analysis (PCA) to identify model independent spectral components. We find two significant components and demonstrate that they are…

Principal component analysis (PCA) is a widely employed statistical tool used primarily for dimensionality reduction. However, it is known to be adversely affected by the presence of outlying observations in the sample, which is quite…

In this paper, we consider the problem of forming machine cell in cellular manufacturing (CM). The major problem in the design of a CM system is to identify the part families and machine groups and consequently to form manufacturing cells.…

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.…

In many scientific disciplines, the features of interest cannot be observed directly, so must instead be inferred from observed behaviour. Latent variable analyses are increasingly employed to systematise these inferences, and Principal…

Principal Component Analysis (PCA) and its nonlinear extension Kernel PCA (KPCA) are widely used across science and industry for data analysis and dimensionality reduction. Modern deep learning tools have achieved great empirical success,…

Spectral clustering is a popular algorithm that clusters points using the eigenvalues and eigenvectors of Laplacian matrices derived from the data. For years, spectral clustering has been working mysteriously. This paper explains spectral…

Principal component analysis (PCA) has been a prominent tool for high-dimensional data analysis. Online algorithms that estimate the principal component by processing streaming data are of tremendous practical and theoretical interests.…