Related papers: Optimal whitening and decorrelation
In this paper we promote a method for the evaluation of a surface topography which we call the correlogram correlation method. Employing a theoretical analysis as well as numerical simulations the method is proven to be the most accurate…
Optical approaches for wavefront shaping traditionally rely on phase modulation through holographic techniques. Shaping the phase determines a wave's diffraction and hence its intensity distribution in space. We instead show that shaping…
A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance…
We introduce a cluster-based technique to automate pixel-wise reconstruction of $\beta$ orientations from parent $\alpha$ orientations over large, indexed regions. This approach provides a valuable tool for analyzing problems that require…
This work presents a novel framework for spherical mesh parameterization. An efficient angle-preserving spherical parameterization algorithm is introduced, which is based on dynamic Yamabe flow and the conformal welding method with solid…
We consider the scenario where one observes an outcome variable and sets of features from multiple assays, all measured on the same set of samples. One approach that has been proposed for dealing with this type of data is ``sparse multiple…
Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical…
The best-understood crystal ordering transition is that of two-dimensional freezing, which proceeds by the rapid eradication of lattice defects as the temperature is lowered below a critical threshold. But crystals that assemble on closed…
Learning invariant representations from images is one of the hardest challenges facing computer vision. Spatial pooling is widely used to create invariance to spatial shifting, but it is restricted to convolutional models. In this paper, we…
We present a rotation-equivariant unsupervised learning framework for the sparse deconvolution of non-negative scalar fields defined on the unit sphere. Spherical signals with multiple peaks naturally arise in Diffusion MRI (dMRI), where…
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…
Herein the topics of (natural) gradient descent, data decorrelation, and approximate methods for backpropagation are brought into a common discussion. Natural gradient descent illuminates how gradient vectors, pointing at directions of…
Principal Component Analysis (PCA) is a well-known multivariate technique used to decorrelate a set of vectors. PCA has been extensively applied in the past to the classification of stellar and galaxy spectra. Here we apply PCA to 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…
Deep cosmic microwave background polarization experiments allow a very precise internal reconstruction of the gravitational lensing signal in pricinple. For this aim, likelihood-based or Bayesian methods are typically necessary, where very…
In this paper, we propose a scalable Bayesian method for sparse covariance matrix estimation by incorporating a continuous shrinkage prior with a screening procedure. In the first step of the procedure, the off-diagonal elements with small…
Spectral clustering has found extensive use in many areas. Most traditional spectral clustering algorithms work in three separate steps: similarity graph construction; continuous labels learning; discretizing the learned labels by k-means…
Principal component analysis (PCA), a ubiquitous dimensionality reduction technique in signal processing, searches for a projection matrix that minimizes the mean squared error between the reduced dataset and the original one. Since…
Principal component analysis (PCA) is a widely used unsupervised dimensionality reduction technique in machine learning, applied across various fields such as bioinformatics, computer vision and finance. However, when the response variables…
Magnetic resonance imaging (MRI) is a non-invasive medical imaging technique offering high-resolution 3D images and valuable insights into human tissue conditions. Even at present, the refinement of denoising methods for MRI remains a…