Related papers: A Spectral Graph Approach to Discovering Genetic A…
Spectral clustering is one of the most popular, yet still incompletely understood, methods for community detection on graphs. This article studies spectral clustering based on the Bethe-Hessian matrix $H_r = (r^2-1)I_n + D-rA$ for sparse…
Principal component analysis (PCA) is a longstanding and well-studied approach for dimension reduction. It rests upon the assumption that the underlying signal in the data has low rank, and thus can be well-summarized using a small number…
We present a spectral theory of hypergraphs that closely parallels Spectral Graph Theory. A number of recent developments building upon classical work has led to a rich understanding of "hyperdeterminants" of hypermatrices, a.k.a.…
Spectral clustering is popular among practitioners and theoreticians alike. While performance guarantees for spectral clustering are well understood, recent studies have focused on enforcing ``fairness'' in clusters, requiring them to be…
Predicting genetic perturbations enables the identification of potentially crucial genes prior to wet-lab experiments, significantly improving overall experimental efficiency. Since genes are the foundation of cellular life, building gene…
Many estimation problems in astrophysics are highly complex, with high-dimensional, non-standard data objects (e.g., images, spectra, entire distributions, etc.) that are not amenable to formal statistical analysis. To utilize such data and…
Motivation: Although principal component analysis (PCA) is widely used for the dimensional reduction of biomedical data, interpretation of PCA results remains daunting. Most existing methods attempt to explain each principal component (PC)…
Motivation: Genome-wide association studies (GWASs), which assay more than a million single nucleotide polymorphisms (SNPs) in thousands of individuals, have been widely used to identify genetic risk variants for complex diseases. However,…
Spectral kernel methods are techniques for transforming data into a coordinate system that efficiently reveals the geometric structure - in particular, the "connectivity" - of the data. These methods depend on certain tuning parameters. We…
Many methods have been developed for finding the commonalities between different organisms to study their phylogeny. The structure of metabolic networks also reveal valuable insights into metabolic capacity of species as well as into the…
It is of great interest to quantify the contributions of genetic variation to brain structure and function, which are usually measured by high-dimensional imaging data (e.g., magnetic resonance imaging). In addition to the variance, the…
Spectral dimensionality reduction methods enable linear separations of complex data with high-dimensional features in a reduced space. However, these methods do not always give the desired results due to irregularities or uncertainties of…
Spectral algorithms are graph partitioning algorithms that partition a node set of a graph into groups by using a spectral embedding map. Clustering techniques based on the algorithms are referred to as spectral clustering and are widely…
Gene conversion is a mechanism by which a double-strand break in a DNA molecule is repaired using a homologous DNA molecule as a template. As a result, one gene is 'copied and pasted' onto the other gene. It was recently reported that the…
We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…
Graph neural networks (GNNs) have attracted considerable attention from the research community. It is well established that GNNs are usually roughly divided into spatial and spectral methods. Despite that spectral GNNs play an important…
Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…
An empirical method of modeling the stellar spectrum of galaxies is proposed, based on two successive applications of Principal Component Analysis (PCA). PCA is first applied to the newly available stellar library STELIB, supplemented by…
We sketch the history of spectral ranking, a general umbrella name for techniques that apply the theory of linear maps (in particular, eigenvalues and eigenvectors) to matrices that do not represent geometric transformations, but rather…
The increased availability of time series genetic variation data from experimental evolution studies and ancient DNA samples has created new opportunities to identify genomic regions under selective pressure and to estimate their associated…