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Cosmological parameter inference from galaxy clustering relies critically on accurate estimates of the covariance and precision matrices. These are often obtained from a limited number of mock catalogs, introducing noise and bias in the…

Sparse Principal Component Analysis (PCA) is a dimensionality reduction technique wherein one seeks a low-rank representation of a data matrix with additional sparsity constraints on the obtained representation. We consider two…

We consider the problem of maximizing the variance explained from a data matrix using orthogonal sparse principal components that have a support of fixed cardinality. While most existing methods focus on building principal components (PCs)…

Let $X_1, \ldots, X_n$ be i.i.d. sample in $\mathbb{R}^p$ with zero mean and the covariance matrix $\mathbf{\Sigma^*}$. The classical PCA approach recovers the projector $\mathbf{P^*_{\mathcal{J}}}$ onto the principal eigenspace of…

We present a new algorithm, ChunkedPCA, to remove common background fluctuations from datasets acquired with a radio camera. ChunkedPCA is an improvement on using PCA to achieve fewer artifacts and better RMS on the cleaned dataset. The…

Cryo-Electron Microscopy (Cryo-EM) is a Nobel prize-winning technology for determining the 3D structure of particles at near-atomic resolution. A fundamental step in the recovering of the 3D single-particle structure is to align its 2D…

Principal Component Analysis (PCA) finds a linear mapping and maximizes the variance of the data which makes PCA sensitive to outliers and may cause wrong eigendirection. In this paper, we propose techniques to solve this problem; we use…

An efficient computational approach for optimal reconstructing parameters of binary-type physical properties for models in biomedical applications is developed and validated. The methodology includes gradient-based multiscale optimization…

The Phase Estimation Algorithm (PEA) is an important quantum algorithm used independently or as a key subroutine in other quantum algorithms. Currently most implementations of the PEA are based on qubits, where the computational units in…

This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to…

Positron emission tomography (PET) is an important functional medical imaging technique often used in the evaluation of certain brain disorders, whose reconstruction problem is ill-posed. The vast majority of reconstruction methods in PET…

In this paper we propose a modified cross correlation method to align images from the same class in single-particle electron microscopy of highly non-spherical structures. In this new method, First we coarsely align projection images, and…

Single particle diffraction imaging experiments at free-electron lasers (FEL) have a great potential for structure determination of reproducible biological specimens that can not be crystallized. One of the challenges in processing the data…

We consider the problem of decomposing a large covariance matrix into the sum of a low-rank matrix and a diagonally dominant matrix, and we call this problem the "Diagonally-Dominant Principal Component Analysis (DD-PCA)". DD-PCA is an…

Suppose we observe data of the form $Y_i = D_i (S_i + \varepsilon_i) \in \mathbb{R}^p$ or $Y_i = D_i S_i + \varepsilon_i \in \mathbb{R}^p$, $i=1,\ldots,n$, where $D_i \in \mathbb{R}^{p\times p}$ are known diagonal matrices, $\varepsilon_i$…

The high dynamic range between contaminating foreground emission and the fluctuating 21cm brightness temperature field is one of the most problematic characteristics of 21cm intensity mapping data. While these components would ordinarily…

In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…

Sparse Principal Component Analysis (sparse PCA) is a fundamental dimension-reduction tool that enhances interpretability in various high-dimensional settings. An important variant of sparse PCA studies the scenario when samples are…

In recent years, studies on image generation models of spiking neural networks (SNNs) have gained the attention of many researchers. Variational autoencoders (VAEs), as one of the most popular image generation models, have attracted a lot…

Principal component analysis (PCA) is one of the most popular dimension reduction techniques in statistics and is especially powerful when a multivariate distribution is concentrated near a lower-dimensional subspace. Multivariate extreme…